Highly sensitive tube-topology magnetoelectric magnetic ...1427/... · Highly Sensitive...
138
Highly Sensitive Tube-Topology Magnetoelectric Magnetic Sensors A Dissertation Presented by Scott Matthew Gillette to The Department of Electrical and Computer Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the field of Electrical Engineering Northeastern University Boston, Massachusetts November, 2013
Transcript of Highly sensitive tube-topology magnetoelectric magnetic ...1427/... · Highly Sensitive...
Highly Sensitive Tube-Topology Magnetoelectric Magnetic Sensors
A Dissertation Presented
by
Scott Matthew Gillette
to
The Department of Electrical and Computer Engineering
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
in the field of
Electrical Engineering
Northeastern University Boston, Massachusetts
November, 2013
i
Abstract
Magnetoelectric (ME) composites have drawn increasing interest in recent years due to
advancements in the technology resulting in enhanced ME coupling coefficients, stable room-
temperature operation, sub-nanoTesla noise floor, low- and zero-biased operation, and
fabrication of compact, miniaturized devices. Now, more than ever, practical use of ME devices
in commercial magnetometry applications is feasible, while continued development of numerous
other applications, such as voltage-tunable magnetic field generators, voltage-tunable inductors,
and magnetically-tunable capacitors, bolster the overall usefulness of ME composites as a
valuable technology. This dissertation focuses on development and characterization of tube-
topology ME composites as magnetic field sensors. The novel topology is most notable for
demonstrating high zero-external-bias sensitivity, low noise floor, low-frequency bandwidth, and
self-powered, stable room temperature operation. Numerous characterization studies are
included in this work where several devices are analyzed as a function of test-field, DC-bias
field, geometry, material choice, and more. The overall conclusions drawn upon these results
indicate strongly that the tube-topology ME magnetic field sensor holds promise to compete with
existing hall-effect and flux-gate magnetometers. ME composites are at the tipping point of
commercialization for use in magnetometry applications and are emerging as a valuable
technology for use in numerous creative ways.
ii
Acknowledgements
I thank my advisor, Professor Vincent Harris, for giving me the opportunity to work at
Northeastern University’s Center for Microwave Magnetic Materials and Integrated Circuits for
the past four years. He has generously shared his time and knowledge to guide me through a
challenging, invaluably rewarding PhD program. Thank you!
I thank Prof. Yajie Chen for his extensive help, creative wisdom, and strong perspectives
during this time.
I thank Dr. Anton Geiler, who has acted as my mentor, for sharing his brilliant expertise
on numerous research efforts.
While the work performed during these past four years was enjoyable, it was the people
with whom I’ve worked with that have made it a true pleasure, and for that I extend a great
thanks to all of my colleagues at CM3IC.
Finally, I thank my friends and family, my parents, my sister, and my beloved wife
Stephanie who kept me alive during this time, for all of your support and encouragement. I love
you all and am incredibly grateful. Thank you!
iii
Table of Contents
Abstract ............................................................................................................................................ i
Acknowledgements ......................................................................................................................... ii
Table of Contents ........................................................................................................................... iii
Table of Figures .............................................................................................................................. v
Table of Tables .............................................................................................................................. xi
Chapter 1. Introduction ................................................................................................................... 1
1.1. Introduction to Dissertation .......................................................................................................... 1
1.2. Background and Phenomena of the Magnetoelectric Effect ......................................................... 2
1.3. Piezoelectric and Magnetostrictive Materials ............................................................................. 10
1.4. Strain Coupled Magnetoelectric Composites .............................................................................. 16
1.5. ME Composites as Magnetic Field Sensors ................................................................................ 25
1.5.1. D31 Sensor Type ....................................................................................................................... 26
1.5.2. D33 Sensor Type ....................................................................................................................... 27
1.5.3. Tube-Topology Sensor Type .................................................................................................... 28
1.5.4. Operational Modes .................................................................................................................... 30
Chapter 2. Tube-Topology ME Composites as Magnetic Field Sensors ...................................... 34
2.1. Introduction and Motivation ............................................................................................................ 34
2.2. Composite Construction ................................................................................................................... 36
2.2.1. Fabrication Instructions............................................................................................................. 37
2.3. Experimental Setup .......................................................................................................................... 41
2.3.1. Experimental Setup Version 1 .................................................................................................. 42
2.3.2. Experimental Setup Version 2 .................................................................................................. 50
2.4. Effects of Intrinsic Magnetostriction on Tube-Topology Magnetoelectric Composites. ................. 57
2.5. ME Composite Length Study ........................................................................................................... 69
iv
2.5.1. Demagnetization Effects ........................................................................................................... 70
2.5.2. Active-Region Effects ............................................................................................................... 77
2.5.3. Galfenol Length Study .............................................................................................................. 78
2.5.4. Iron-Nickel Length Data ........................................................................................................... 85
2.6. Test Field Amplitude and Frequency Study ..................................................................................... 87
2.6.1. Amplitude Study ....................................................................................................................... 87
2.6.1. Frequency Study ....................................................................................................................... 90
2.7. Array Study ...................................................................................................................................... 95
2.8. 8cm FN ME Composite Highlights ................................................................................................. 97
2.9. D15 Operational Mode Device ...................................................................................................... 102
2.10. Experimental Setup Considerations ............................................................................................. 107
Chapter 3. Conclusion ................................................................................................................. 115
3.1. Research Summary ........................................................................................................................ 115
3.2. Improvements for Future Development ......................................................................................... 118
Appendix ..................................................................................................................................... 119
A.1. Experimental Setup 1 – Equipment List ....................................................................................... 119
A.2. Experimental Setup 2 – Equipment List ....................................................................................... 119
A.3. LabView Program ......................................................................................................................... 120
A.4. MATLAB Demagnetization Factor Calculator ............................................................................. 122
References ................................................................................................................................... 123
v
Table of Figures
Figure 1: Direct interactions between stress (σ) and strain (ϵ), electric field (E) and polarization (P), and magnetic field (H) and magnetization (M), are illustrated with the red, yellow, and blue arrows, respectively. In a single phase multiferroic magnetoelectric material (green arrows), electric field is directly coupled to magnetic field. In many multiferroic magnetoelectric devices, strain-coupling (black arrows) between magnetostrictive and piezoelectric phases provides the magnetoelectric effect.[4] ...... 3
Figure 2: Illustration demonstrating ME effect in single-phase multiferroic Cr2O3. Motion of the Cr3+ ions is observed between states of zero electric field (left), and applied electric field (right), disturbing the ferromagnetic Cr sub-lattice, which demonstrates magnetoelectric coupling.[13]........................................................................................ 5
Figure 3: Three different structural types of ME composite topologies are shown where the green may either represent a piezoelectric or magnetostrictive material and the void volume represents the counterpart. (a) Embedded spheres inside of a volume. (b) Heterostructural stacking is the most common. (c) Pillar arrangement. ........................ 7
Figure 4: The direct magnetoelectric effect refers to a magnetoelectric system that produces an output voltage response caused by an applied magnetic field. ...................................... 8
Figure 5: The converse magnetoelectric effect refers to a system that produces a magnetization within the magnetostrictive component, resulting in a change to the fringe field, caused by an applied electric field (voltage). ................................................................. 9
Figure 6: Piezoelectric strain response as a function of applied electric field for two different aspect ratios of thin film Lead Zirconate Titanate (PZT) substrates. ε33 indicates that both applied electric field and measured strain were in the Z-axis of the substrate.[36] ...................................................................................................................................... 11
Figure 7: Piezoelectric materials exhibit coupling between strain and polarization such that strain is generated due to an applied electric field, and similarly, that a voltage will be generated in response to an applied strain.................................................................... 12
vi
Figure 8: Magnetization and strain for TERFENOL-D as a function of applied magnetic field. The derivative of magnetostriction is plotted with the dashed line.[32] ...................... 13
Figure 9: Magnetostrictive materials exhibit coupling between magnetization and strain such that strain is generated in response to an applied magnetic field, and similarly, magnetization of the sample occurs under applied strain. ........................................... 14
Figure 10: a) A commercial piezoelectric microphone guitar pickup fabricated by Artec.[40] b) A commercial piezoelectric precision actuator capable of micron resolution manufactured by Physik Instruments.[41] ................................................................... 15
Figure 11: a) A magnetostrictive audio transducer that allows a surface, such as a table, wall, or window, to act as a speaker. This commercially available device uses the magnetostrictive material TERFENOL-D and is fabricated by FeONIC.[42] b) A commercial magnetostrictive linear position sensor, with micron resolution, produced by MTS Sensors.[43] ................................................................................................... 16
Figure 12: a) A PZT/Metglas® multiferroic magnetostrictive composite, mounted to a Mylar slab, fabricated by Bolin Hu at Northeastern University's CM3IC. This image shows the leads attached for measuring the magnetoelectric effect. b) Cross-sectional view of the PZT/Metglas® composite fabricated through pulse laser deposition of a PZT target onto a polished Metglas® sheet. Not drawn to scale. ........................................ 17
Figure 13: a-d) SEM surface images of PZT grown under different oxygen pressures. e) SEM cross-section image of 300mTorr growth sample. f) Zoomed view of (e) showing distinct layers and boundaries of PZT, platinum, and Metglas®. ................................ 18
Figure 14: a) A Metglas®/PZT/Metglas® multiferroic magnetostrictive laminate provided by Carmine Carosella, mounted to a Teflon slab. The dime is provided for size reference. b) Cross-sectional view of the Metglas®/PZT/Metglas® heterostructure. The Metglas® strains under an applied magnetic field causing a strain-induced electric field transverse to the PZT. Not drawn to scale. ......................................................... 19
Figure 15: Magnetoelectric multilayer fabricated through epitaxial growth of NiFe2O4 (NFO) on BaTiO3 (BTO) on a SrTiO3 (STO) substrate. The interfaces are emphasized using horizontal lines.[46] ..................................................................................................... 20
Figure 16: ME coupling coefficient of a heterostructural Metglas®/polyvinylidene-flouride magnetoelectric laminate composite magnetic field sensor. ........................................ 24
Figure 17: Metglas®/PZT/Metglas® laminated heterostructural composite, provided by Carmine Carosella, held by tweezers to enable resonance bending modes during testing. Length, height, and thickness dimensions are indicated. ............................................. 27
Figure 18: Metglas®/Poled-PZT/Metglas® laminated heterostructural composite with interdigitated electrodes, provided by Dwight Viehland. Length, height, and thickness (at two locations along the length) dimensions are indicated. ..................................... 28
vii
Figure 19: Metglas®/Poled-PZT/Metglas® laminated heterostructural composite with interdigitated electrodes, provided by Dwight Viehland. Length, height, and thickness (at two locations along the length) dimensions are indicated. ..................................... 30
Figure 20: D31 and D33 mode operation of piezoelectric PZT. For the D31 mode, a longitudinally applied strain results in a transversely generated voltage response. For the D33 mode, a longitudinally applied strain results in a longitudinally generated voltage response. Directions 3 and 1 are denoted on the vertical and horizontal axis, respectively. ................................................................................................................. 31
Figure 21: Example of an interdigitated electrode geometry. Interdigitated electrodes are typically used in ME laminates where the piezoelectric phase is to be operated in a D33 mode, as exemplified by D33 Sensor. .................................................................. 32
Figure 22: Diagram of tube-topology device operational nomenclature. Mechanical action is always applied in the x (1) direct. Devices investigated in this research operate in either a d31 or d51 mode. ............................................................................................... 33
Figure 23: a) Carbolite STF 15/180 tube furnace. b) Fisher Scientific Isotemp 11-600-49HV hot plate. c) Stanford Research Systems PS310 high voltage dc power supply. d) Weller WES51 soldering iron station. e) Omega HH501DK thermometer with Type-K thermocouple. ............................................................................................................... 37
Figure 24: Fabrication diagram of the ME tube-topology composite. The fixed end is where devices are clamped during testing. ............................................................................. 41
Figure 25: a) Dual-Helmholtz coil design with D31 Sensor centered inside. b) Dual-Helmholtz coil inside of the double-layer Gauss chamber. Tube-topology ME composite is positioned inside of Helmholtz coil for characterization. ............................................ 43
Figure 26: DUT mounting apparatus consisting of plastic tweezers held by a table-top vice-grip. All components are non-magnetic. a) Top-down view. b) Rotated side-view. ............ 43
Figure 27: Schematic of single Helmholtz coil design made from PVC tube (not drawn to scale). Radius, R, and distance, D, are made to be equal in order to satisfy Helmholtz design. Dual-Helmholtz design requires use of two PVC tubes that can be nested. ................ 44
Figure 28: Simulated field distribution pattern from dual-nesting Helmholtz coil design. ......... 45
Figure 29: Modeled field uniformity of the fabricated dual-nesting Helmholtz coil. ................. 45
Figure 30: Block diagram of experimental setup 1. ..................................................................... 47
Figure 31: DC calibration curve characterizing relationship between SR830 auxiliary voltage output and the magnetic field generated by the Sorensen DC power supply. .............. 48
Figure 32: Solenoid fabricated for use in experimental setup version 2. ..................................... 51
Figure 33: Schematic of solenoid coil design made from PVC tube (not drawn to scale). ......... 52
viii
Figure 34: Simulated field distribution pattern for solenoid coil design. .................................... 52
Figure 35: Modeled field uniformity of the fabricated solenoid coil. .......................................... 53
Figure 36: Block diagram of experimental setup version 2. ........................................................ 54
Figure 37: DC magnetic bias field calibration curve for solenoid coil. ....................................... 55
Figure 38: Diagram of DUT placement within solenoid. Solenoid is surrounded by a triple-layer Gauss chamber. Drawing is not to scale. ..................................................................... 56
Figure 39: a) Vishay P3 strain meter. b) Omega strain gauge attached to magnetostrictive wire. ...................................................................................................................................... 59
Figure 40: Magnetostriction as a function of applied magnetic field for three types of wire. ..... 60
Figure 41: Derivative of magnetostriction as a function applied field, dλ/dH. ........................... 60
Figure 42: a) VSM data comparing M vs. H for FG (WB21), FC, and FN wire samples. b) Zoomed plot showing low-H magnetization response. ................................................ 61
Figure 43: Sensitivity is plotted as a function of swept bipolar applied magnetic bias field. Sensor FN exhibits highest sensitivity under low- (<20 Oe) and zero-biased conditions while sensor FG exhibits higher sensitivity at bias fields > 20 Oe. ............................. 64
Figure 44: The peak sensitivity curve is captured while sweeping from max applied magnetic field to zero. Magnetic field is applied starting at -50 Oe and swept towards zero. This curve displays peak device performance...................................................................... 65
Figure 45: Magnetic spectral density plots for optimally biased (a, on left) and zero-biased (b, on right) conditions are displayed. All devices exhibit noise floor in the nanoTesla range at low frequency. A 25 Hz, 1 mOe (100 nT), magnetic test field was applied during measurement. ............................................................................................................... 67
Figure 46: Coordinate system used for calculating demagnetization factors. A cylinder, positioned axially along the z axis, is shown, however dimensions a, b, and c may be applied to most shapes. ................................................................................................ 71
Figure 47: Demagnetization factors calculated for the magnetostrictive wire shape. Insert shows zoomed in region where Nx, Ny, and Nz, are equal at a length of 0.1 cm. ................... 73
Figure 48: Normalized effects of Nz demagnetization factor in the wire as a function of length. Insert shows absolute demagnetization factor for Nz. .................................................. 74
Figure 49: a) Magnetostriction as a function of magnetic field applied from 0 Oe, to +500 Oe, to -500 Oe, and then to +500 Oe. Hysteresis effects are observed. b) Notional magnetostrictive data generated by averaging data points at equal bias, per wire. ..... 75
Figure 50: dλ/dH as a function of applied magnetic field for different lengths of iron-nickel wire. .............................................................................................................................. 76
ix
Figure 51: Drift in the magnetostrictive measurement as a function of time. Drift is presented as a percentage-change, relative to the full scale range of collected data. ....................... 76
Figure 52: ME coupling coefficient as a function of applied magnetic bias for Metglas®/PZT/Metglas® heterostructural laminates for different N, where N denotes the number of Metglas® layers. ................................................................................... 78
Figure 53: Sensitivity vs. applied magnetic bias field for various lengths of tube-topology ME composites made using Galfenol wire batch WB21. ................................................... 80
Figure 54: Sensitivity vs. length for varying DC magnetic bias applied to composites fabricated using the Galfenol wire batch WB21. .......................................................................... 81
Figure 55: Sensitivity vs. applied magnetic bias field for various lengths of tube-topology ME composites made using Galfenol wire batch WB14. ................................................... 82
Figure 56: Sensitivity vs. length for varying magnetic DC bias applied to ME composites made using Galfenol wire batch WB14. The cracked 5cm sensor is excluded. .................... 83
Figure 57: Vibrating-sample magnetometer (VSM) data comparing Galfenol wire batches WB14, (a) left, and WB21, (b) right. ........................................................................... 84
Figure 58: (a) VSM comparison at low applied field for WB14 and WB21 Galfenol wire samples. WB14 is shown to be magnetically softer than WB21. The effect of this is shown in (b) which demonstrates sensitivity vs. applied magnetic field for 5cm long devices. ......................................................................................................................... 84
Figure 59: Sensitivity as a function of magnetic bias field for 8 cm and 5 cm lengths of ME composites fabricated using magnetostrictive iron-nickel wire. .................................. 86
Figure 60: (a) Sensitivity as a function of magnetic bias for different amplitudes of test field. (b) Sensitivity vs. test field amplitude under zero external magnetic bias. ....................... 89
Figure 61: Sensitivity vs. test field amplitude for 5 and 7.5 cm WB21 devices. The test field was fixed at 25 Hz. A fixed 20 Oe DC magnetic bias was applied during testing. ............ 90
Figure 62: Sensitivity as a function of frequency for 7.5 cm and 5 cm WB21 device. A 20 Oe bias field was applied constantly. The test field was maintained at 0.25 Oe RMS. .... 92
Figure 63: Sensitivity as a function of frequency for the 8 cm FN device. Test field amplitudes of 0.1 and 1 Oe RMS were measured at zero bias and 1 Oe DC bias conditions. ........... 93
Figure 64: Sensitivity vs. frequency for the 5 cm FN device. Test field amplitudes of 0.1 and 1 Oe RMS were measured at zero bias and 10 Oe DC bias conditions. ......................... 94
Figure 65: Diagram showing three identically-manufactured 5 cm FN tube sensors connected in series. ............................................................................................................................ 95
Figure 66: Sensitivity measurements for individual and series configurations for three 5cm FN devices measured at 100 Hz, 0.25 Oe RMS under a 7.5 Oe magnetic bias field. ........ 96
x
Figure 67: Sensitivity vs. magnetic bias field for the 8cm FN device. A 25 Hz, 10 mOe test field served as reference. ...................................................................................................... 99
Figure 68: Single-polarity plot of sensitivity vs. magnetic bias field to emphasize effect of hysteresis on low-bias sensitivity. ................................................................................ 99
Figure 69: Magnetic spectral density plot from 1 Hz thru 30 Hz demonstrating low-frequency pseudo-noise floor response of the 8cm FN wire with applied bias of 7.5 Oe. ......... 100
Figure 70: Zero-bias frequency response from 0.001 Hz thru 5 KHz of the 8cm FN sensor. The test field was set at 1 Oe RMS and frequency was swept. Log-plot (inset) is shown to emphasize low-frequency response. .......................................................................... 101
Figure 71: Nomenclature for describing directions in a PZT crystal for a 3D system on the left and the XY plane on the right. The shear-y axis (direction 5) is shown by the polarization vector in the XY plane. .......................................................................... 103
Figure 72: D15 mode device fabricated using iron-nickel magnetostrictive wire and PZT tube. a) Diagram showing the double helical electrode structure that was fabricated, (b), using 20 um gold wires tightly wrapped around the tube exterior. ..................................... 104
Figure 73: Sensitivity vs. magnetic bias field for the D15 sensor. A 1.8 Oe RMS test field alternating at 400 Hz was used for reference. ............................................................ 105
Figure 74: Magnetic spectral density plot for the D15 sensor. A 400 Hz, 0.01 Oe RMS magnetic field is applied for reference. ..................................................................................... 106
Figure 75: Sensitivity vs. elapsed time for 5 days. Periodic background environmental noise is apparent during day. 10mV/Oe variations observed during daytime, 4 mV/Oe at night. .................................................................................................................................... 108
Figure 76: Modeled and measured noise for the shorted-input case. Contributing factors for modeled noise are shown along with total noise (sum). ............................................ 110
Figure 77: Modeled open-input state noise contributing factors and total, consisting of sum. Measured data is overlaid. ......................................................................................... 111
Figure 78: 8 cm FN wire voltage output noise floor is shown to be limited by the electronics noise floor, with exception to a few spurious environmental noise peaks. ................ 112
Figure 79: Schematic of charge amplifier circuit (left) used to fabricate battery powered charge amplifier used in noise floor measurements (right). .................................................. 114
Figure 80: Low frequency noise floor measurements for zero-biased and 7.5 Oe biased 8cm FN sensor with and without charge amplifier. ................................................................. 114
xi
Table of Tables
Table 1: Piezoelectric Material Properties. ................................................................................... 22
Table 2: Magnetostrictive Material Properties. ............................................................................ 23
Table 3: Overview and Comparison of Device Performance ..................................................... 116
1
Chapter 1. Introduction
1.1. Introduction to Dissertation
The research presented in this dissertation focuses on the development of novel tube-like
topological magnetoelectric (ME) composites and strongly focuses on examining variations in
the design towards the realization of ME magnetic field sensing devices. The recently developed
tube-topology, sometimes referred to as “quasi-one-dimensional”, but herein referred to as “tube-
topology”, is unique from any previously existing magnetoelectric composite device topology.
Tube-topology ME composites, configured for use as magnetic field sensors, exhibit high
sensitivity at zero-external-bias field, low noise floor, and high signal-to-noise ratio (SNR).
These devices are self-powered and require no conditioning circuitry. They are also miniature,
lightweight, easily fabricated, and exhibit highly directional axial sensitivity which enables better
spatial resolution than heterostructural-laminate topology counterparts. The experiments, results,
discussions, and insights pertaining to the novel tube-topology ME composite developed at
Northeastern University’s Center for Microwave Magnetic Materials and Integrated Circuits
(CM3IC) are reported within.
2
This dissertation consists of three chapters that contain the following information. In
Chapter 1, background to the magnetoelectric effect and similar operational phenomena is
presented. In addition, discussion on piezoelectric and magnetostrictive materials is provided.
Magnetoelectric composites are introduced and examples of devices exhibiting different
operational modes are overviewed. Finally, the magnetoelectric tube-topology device is
introduced. It is assumed the reader is well acquainted with ferromagnetic and ferroelectric
phenomena in materials. In Chapter 2, aspects of the tube-topology ME composite are
investigated in a series of studies that examine effects of externally applied magnetic bias, device
length, magnetostrictive wire type, frequency and amplitude response, noise analysis, and more.
Chapter 3 concludes the dissertation with a general overview of findings, details for future
improvements, and closing thoughts.
1.2. Background and Phenomena of the Magnetoelectric Effect
The magnetoelectric (ME) effect is the underlying phenomena investigated in this
research. The effect was first realized by Pierre Curie in 1894 and later, mathematically theorized
by Landau and Dzyaloshinskii between late 1950’s and early 1960’s.[1-3] The ME effect is
defined as the ability to induce magnetization through an applied electric field and/or to induce
polarization through an applied magnetic field.[4-6] This effect can be enabled due to direct
coupling of electric field with magnetization, magnetic field with polarization, and polarization
with magnetization, or indirectly via strain. Each relationship is illustrated in Figure 1.
3
Figure 1: Direct interactions between stress (σ) and strain (ϵ), electric field (E) and polarization (P), and
magnetic field (H) and magnetization (M), are illustrated with the red, yellow, and blue arrows,
respectively. In a single phase multiferroic magnetoelectric material (green arrows), electric field is
directly coupled to magnetic field. In many multiferroic magnetoelectric devices, strain-coupling (black
arrows) between magnetostrictive and piezoelectric phases provides the magnetoelectric effect.[4]
The term “magnetoelectric effect” may be used to describe the phenomena; however, it is
now conventional and more accurate to describe the flow of energy in ME devices with the
terminology “direct magnetoelectric effect” or “converse magnetoelectric effect”.[5, 7] The
direct magnetoelectric effect (DME) describes magnetic-field-induced polarization, and similarly
magnetic-field-induced voltage, as shown in equation (1.1).
(1.1)
The converse magnetoelectric effect (CME) describes electric field induced
magnetization as shown in equation (1.2).
4
(1.2)
The magnetoelectric coupling coefficient, α, defined in units of ∗ , is the
physical term which serves as the conventional figure of merit for quantifying the ability of a
device to transduce energy between magnetic and electric domains. The magnetoelectric voltage
coefficient, defined in units of , is used to describe the sensitivity of engineered devices
and is more practical for comparing the performance between different types of ME devices and
for evaluating ME devices for specific applications.[5, 8]
The ME effect manifests in two distinct types of structures; single-phase multiferroics,
and composites of magnetostrictive and piezoelectric materials. The effect occurs in single-phase
multiferroic materials that exhibit direct coupling between electrical polarization and magnetic
polarization, where the term “multiferroic” denotes such a material that exhibits two or more
combinations of ferroic orders, such as ferroelectric and ferromagnetic ordering. The first
single-phase multiferroic ME material was discovered over half a century ago, Cr2O3, is shown
in Figure 2. Numerous other single-phase materials have been discovered since then. Despite
discovery of several single-phase multiferroic magnetoelectric materials, efforts towards
realizing them for practical use have been largely unsuccessful.[5, 6, 8-10] The problem with
single-phase multiferroics is that the ME coupling magnitude is relatively weak at room
temperature. At lower temperatures ME coupling coefficients increase but not significantly
enough to justify maintaining a low temperature environment for applications. Research efforts
continue in the field of single-phase multiferroics and recently significantly a higher ME
coupling coefficient for a Z-type hexaferrite compound, Sr3Co2Fe24O41, has been reported thus
maintaining the relevancy of single-phase ME materials.[11, 12]
5
Figure 2: Illustration demonstrating ME effect in single-phase multiferroic Cr2O3. Motion of the Cr3+ ions
is observed between states of zero electric field (left), and applied electric field (right), disturbing the
ferromagnetic Cr sub-lattice, which demonstrates magnetoelectric coupling.[13]
The ME effect may also be enabled by fabricating bulk, micro, and more recently, nano-
scale combinations of piezoelectric and magnetostrictive materials together in a mechanically
elastic manner where electric and magnetic energy transfer is mediated through strain, as
illustrated by the black arrows in Figure 1.[4-8, 14-25] ME composites are unique from single-
phase multiferroics in the sense that composite materials may be chosen based on bulk material
properties, which, depending on scale, remain relatively unchanged when formed into
composites.
6
ME composites have been the most significantly researched method for generating the
ME effect due to ability to predict behavior based on constituent performance prior to composite
fabrication. Strain-coupled composites consisting of a bulk single-phase magnetostrictive
material with a bulk single-phase piezoelectric material have demonstrated direct
magnetoelectric coupling coefficients on the order of 100 ∗⁄ , which is several orders of
magnitude higher than reported coefficients of single phase multiferroic magnetoelectrics.[5] ME
composites are also relatively easy to fabricate and numerous geometries have already been
studied such as those shown in Figure 3. For this reason, strain-coupled ME composites,
exhibiting large ME coupling coefficients at room temperature hold great potential for the
development of applications.
7
Figure 3: Three different structural types of ME composite topologies are shown where the green may
either represent a piezoelectric or magnetostrictive material and the void volume represents the
counterpart. (a) Embedded spheres inside of a volume. (b) Heterostructural stacking is the most common.
(c) Pillar arrangement.
In composites of magnetostrictive and piezoelectric materials, the direct magnetoelectric
effect is the result of the product of the respective magneto-mechanical and inverse
8
electromechanical strain interaction as described in equation (1.3) and the interaction is
illustrated in Figure 4.
(1.3)
Figure 4: The direct magnetoelectric effect refers to a magnetoelectric system that produces an
output voltage response caused by an applied magnetic field.
The converse magnetoelectric effect is the product of the electromechanical and inverse
magneto-mechanical strain interaction as described in equation (1.4) and the interaction is
illustrated in Figure 5.[5]
9
1.4
Figure 5: The converse magnetoelectric effect refers to a system that produces a magnetization
within the magnetostrictive component, resulting in a change to the fringe field, caused by an applied
electric field (voltage).
Equations (1.3) and (1.4) indicate that strain transfer is responsible for transducing
magnetic energy to electric energy for the DME effect and vice versa for the CME effect. For
instance, if a magnetoelectric composite operating in a DME mode is exposed to a magnetic
field, represented by the numerator in the first term of (1.3), the magnetostrictive phase will
10
elastically deform due in response to the magnetic field, represented by the denominator of the
first term in (1.3). The magnetostrictively induced strain will transfer to the piezoelectric phase
causing a mechanical deformation, represented by the numerator of the second term in (1.3), and
generate a separation of charge resulting in polarization, as represented by the denominator of
the second term in (1.3). The reverse flow of energy happens for the CME effect as shown in
equation (1.4).
The research presented in this dissertation pertains to a unique topology of composites
that obtain the magnetoelectric effect through strain coupling between mechanically bonded bulk
magnetostrictive and piezoelectric materials. For related information on single phase
multiferroic magnetoelectric materials that exhibit direct coupling, the reader is encouraged to
review the literature as no additional discussion on this subject is provided in this
dissertation.[26-29]
1.3. Piezoelectric and Magnetostrictive Materials
Ferroelectrics and ferromagnetics are distinct classes of materials under which the
manipulation of polarization and magnetization occurs through the application of electric and
magnetic fields, respectively. Certain types of ferroelectric and ferromagnetic materials exhibit
physical deformation under the influence of applied electric and magnetic fields, respectively.
This property is known as “piezoelectricity” in ferroelectric materials and “magnetostriction” in
ferromagnetic materials. The atomic lattice spacing of piezoelectric and magnetostrictive
materials is strongly coupled to the materials’ state of polarization and magnetization,
11
respectively, allowing for motion to occur via applied fields.[30-35] Although this effect is
minute on the atomic level, strain generation in bulk samples is greatly useful for engineered
structures. These fundamental material properties are ultimately responsible for generation of the
magnetoelectric effect in composites. Atomic lattice coupling with polarization and
magnetization also exists in the forms of electrostriction and piezomagnetism; however, these
similar phenomena are not discussed in this dissertation.
Piezoelectricity is defined as the ability of a material to exhibit coupling between
polarization and strain, therefore enabling a coupling between strain and applied electric field. A
piezoelectric material will undergo bulk dimensional deformation correlating to an applied
electric field as demonstrated by the butterfly-shaped piezoelectric response curve of thin film
lead zircon titanate (PZT) in Figure 6 and as illustrated by the electro-mechanical interaction in
Figure 7.[36]
Figure 6: Piezoelectric strain response as a function of applied electric field for two different aspect ratios
of thin film Lead Zirconate Titanate (PZT) substrates. ε33 indicates that both applied electric field and
measured strain were in the Z-axis of the substrate.[36]
12
Figure 7: Piezoelectric materials exhibit coupling between strain and polarization such that strain
is generated due to an applied electric field, and similarly, that a voltage will be generated in response to
an applied strain.
The general constitutive equations for a piezoelectric material, (1.5) and (1.6),
mathematically describe strain and electric displacement, respectively.
(1.5)
(1.6)
The strain, , is defined as the axial change in length divided by original length ∆ ⁄ .
The magnetic flux density is denoted by D and E is the applied electric field. Variables, and
represent the material’s remnant strain and polarization, respectively. The elastic compliance
tensor , the piezoelectric tensor , and the dielectric permittivity tensor are defined by
the material’s properties.[37, 38]
13
Magnetostriction describes ferromagnetic materials with the ability to exhibit coupling
between magnetization and strain, thus providing a coupling of strain to applied magnetic field.
A magnetostrictive material will strain in response to an applied magnetic field, as demonstrated
by the magnetostriction curve in Figure 8 and as illustrated by the magneto-mechanical
interaction in Figure 9.
Figure 8: Magnetization and strain for TERFENOL-D as a function of applied magnetic field. The
derivative of magnetostriction is plotted with the dashed line.[32]
14
Figure 9: Magnetostrictive materials exhibit coupling between magnetization and strain such that strain is
generated in response to an applied magnetic field, and similarly, magnetization of the sample occurs
under applied strain.
The general constitutive equations for a magnetostrictive material, (1.7) and (1.8),
mathematically describe strain and magnetization, respectively.[39]
(1.7)
(1.8)
Here, strain equals the axial change in length divided by length ∆ ⁄ . The compliance
tensor is denoted by . The applied stress T is in units of force per unit area. The
15
magnetostrictive strain constant is d. The permeability tensor is denoted by . H is the applied
magnetic field and B is the magnetic flux density.
The strain coupling in both piezoelectric and magnetostrictive materials operates in a
reverse manner such that an applied strain will generate net polarization or magnetization,
respectively. The ability to manipulate the dimensions of a piezoelectric material by an applied
electric field and a magnetostrictive material by an applied magnetic field, or to generate
respective electric and magnetic fields by applying strain, has proven useful in numerous
applications. Piezoelectric materials are currently used in commercial devices such as
instrument microphone pickups or precision electrostatic actuators as shown in Figure 10.
Magnetostrictive materials may be found in commercial devices such as audio transducers and
linear position sensors as shown in Figure 11.
Figure 10: a) A commercial piezoelectric microphone guitar pickup fabricated by Artec.[40] b) A
commercial piezoelectric precision actuator capable of micron resolution manufactured by Physik
Instruments.[41]
a b
16
Figure 11: a) A magnetostrictive audio transducer that allows a surface, such as a table, wall, or window,
to act as a speaker. This commercially available device uses the magnetostrictive material TERFENOL-D
and is fabricated by FeONIC.[42] b) A commercial magnetostrictive linear position sensor, with micron
resolution, produced by MTS Sensors.[43]
1.4. Strain Coupled Magnetoelectric Composites
Optimal strain coupling requires intimate contact between the magnetostrictive and
piezoelectric materials that is typically achieved through direct deposition, gluing (also known as
lamination or epoxying), or epitaxial growth fabrication techniques as shown by the examples in
Figure 12, Figure 14, and Figure 15, respectively.
a b
17
Figure 12: a) A PZT/Metglas® multiferroic magnetostrictive composite, mounted to a Mylar slab,
fabricated by Bolin Hu at Northeastern University's CM3IC. This image shows the leads attached for
measuring the magnetoelectric effect. b) Cross-sectional view of the PZT/Metglas® composite fabricated
through pulse laser deposition of a PZT target onto a polished Metglas® sheet. Not drawn to scale.
Direct deposition magnetoelectric composite devices exhibit an atomically distinct yet
direct mechanically bonded interface between piezoelectric and magnetostrictive phases that
enables excellent strain coupling. These composites are typically made using chemical vapor
deposition or pulsed laser deposition of a magnetostrictive phase onto a piezoelectric phase (or
vice-versa) and exhibit a thin-film-on-substrate topology. In some composite combinations,
buffer layers are used to improve growth conditions while maintaining excellent strain transfer.
Buffer layers of gold and platinum were investigated in a recent study at CM3IC determining
that use of platinum, shown in Figure 13, acted best as a seed layer for PZT growth and as a
diffusion barrier. [44, 45]
18
Figure 13: a-d) SEM surface images of PZT grown under different oxygen pressures. e) SEM cross-
section image of 300mTorr growth sample. f) Zoomed view of (e) showing distinct layers and boundaries
of PZT, platinum, and Metglas®.
19
Figure 14: a) A Metglas®/PZT/Metglas® multiferroic magnetostrictive laminate provided by Carmine
Carosella, mounted to a Teflon slab. The dime is provided for size reference. b) Cross-sectional view of
the Metglas®/PZT/Metglas® heterostructure. The Metglas® strains under an applied magnetic field
causing a strain-induced electric field transverse to the PZT. Not drawn to scale.
Epoxied ME composites consist of two or more magnetostrictive and piezoelectric phases
bonded together using an adhesive that enables strain coupling. The adhesive plays an important
role in transferring strain between bulk materials and its mechanical properties must be
considered. In addition, certain glued topologies such as the one in Figure 14, require that the
adhesive is conductive, allowing the Metglas® to serve also as electrodes for collecting charge
generated across the PZT. Magnetoelectric laminate composites are abundant in literature due to
readily accessible, inexpensive, and large variety of materials to choose from. Additionally, such
composites require minimal materials processing and are therefore easily fabricated. The tube-
topology ME composites are categorized as this type due to use of a sintered epoxy that serves as
binding agent.
20
Figure 15: Magnetoelectric multilayer fabricated through epitaxial growth of NiFe2O4 (NFO) on BaTiO3
(BTO) on a SrTiO3 (STO) substrate. The interfaces are emphasized using horizontal lines.[46]
A ME composite fabricated using epitaxial growth techniques exhibits atomic lattice
matching of magnetostrictive and piezoelectric phases. This intimate crystallographic interface
between phases results in favorable, and typically the most efficient, strain coupling.
Epitaxially-grown magnetoelectrics are not as common as laminates due to the complex
fabrication process which requires that each phase exhibits similarly sized crystal lattices. This
requirement also limits the combinations of compatible magnetostrictive and piezoelectric
materials.
21
Strain coupled ME composites can be described using the following constituent
equations, (1.9), (1.10), and (1.11), that relate ME and piezoelectric phases through elastic
interaction.[5]
(1.9)
(1.10)
(1.11)
For equations (1.9), (1.10), and (1.11), σ, D, and B represent stress, electric displacement,
and magnetic induction, respectively. S, E, and H are the strain, electric field, and magnetic field,
respectively. Tensors c, e, q, ε, α, and μ, are the stiffness, piezoelectric coefficient,
piezomagnetic coefficient, dielectric constant, magnetoelectric coefficient, and permeability,
respectively, are determined by the choice of materials used in the composite. The superscript T
denotes the transpose of the tensor.[5]
Properties of several common piezoelectric and magnetostrictive materials used in
magnetoelectric composites are shown in Table 1, and Table 2, respectively.[8]
The piezoelectric material PZT has been widely investigated for use in ME composites of
various topologies. PZT exhibits a relatively high piezoelectric constant, resulting in higher
polarization per input strain than BTO and PVDF. In addition, PZT is abundant, inexpensive,
and available in several unique geometries. Magnetostrictive materials such as iron-nickel alloys,
22
Galfenol, and iron-cobalt-vanadium alloys exhibit relatively low-to-mid saturation
magnetostriction values compared to materials like Terfenol-D. However, unlike Terfenol-D,
which has a saturation magnetostriction of 1400 parts per million at bias fields on the order of
2500 Oe, these alloys exhibit useful magnetostriction under significantly smaller applied bias
magnetic field magnitudes. An important step towards implementing ME composites in
commercial applications is to minimize or eliminate magnetic bias field requirements. By
developing ME composites that require little-to-no magnetic bias, enormous cost, volume, and
weight savings may be realized. In this dissertation, PZT is chosen as the piezoelectric materials
while several magnetostrictive materials that operate under low-bias field are examined.
Table 1: Piezoelectric Material Properties.
BaTiO3 PZT-5 PZT-4 PZNPT PMNPT PVDF
d31(pC/N) -90 -175 -109 N/A 700 16.5
d33(pC/N) 191 400 300 N/A 2000 -33
ε 1700 1750 1350 7200 5000 10
Tc(ºC) 152 360 320 163 80 129
ρ(g/cm3) 6 7.7 7.6 8.2 7.8 1.78
Qm N/A 80 500 N/A N/A 4
k33 0.63 0.72 0.68 0.94 0.9-0.94 0.19
23
For Table 1, d31 and d33 represent piezoelectric constants, ε is the permittivity, Tc is the
Curie temperature, ρ is density, Qm is the mechanical quality factor, and k33 is the
electromechanical coupling factor.
Table 2: Magnetostrictive Material Properties.
NiFe2O4 Terfenol-D Fe-Ga Metglas®
2605
λ(ppm) 27 -1400 200 40
μ 20 6-10 20 >40000
k33 N/A 0.44 N/A 0.37
Qm N/A N/A N/A 1000
ρ(g/cm3) 5.37 7.8 7.7 7.18
R(Ω-m) 1e6 5.8e-7 6e-7 1.3e-6
Tc(ºC) 535 N/A N/A 395
For Table 2, λ is the saturation magnetostriction, μ is the permeability, k33 is the
electromechanical coupling factor, Qm is the mechanical quality factor, ρ is density, R is
resistivity, and Tc is the Curie temperature.[8]
Of the three methods for fabricating strain-coupled ME devices, laminate composites
exhibit the largest sensitivity. Recently, Dr. Dwight Viehland, from the Department of Material
Science and Engineering at Virginia Polytechnic Institute, has demonstrated one of the highest
24
magnetoelectric coupling coefficient in a device fabricated by laminating together thin layers of
Metglas® (25 microns) to polyvinylidene-flouride (28 microns).[47] This device exhibits an off-
resonance ME sensitivity coefficient of approximately 7 V/cm-Oe corresponding to a 1 KHz AC
input magnetic field and an 8 Oe magnetic bias field as shown in Figure 16 (a), left. In Figure 16
b), right, an on-resonance ME sensitivity coefficient of 310 V/cm-Oe, corresponding to an
electro-magneto-mechanical mode stimulation frequency of approximately 50 KHz, is shown for
an applied static magnetic field of 8 Oe.
Figure 16: ME coupling coefficient of a heterostructural Metglas®/polyvinylidene-flouride
magnetoelectric laminate composite magnetic field sensor.
Although no commercial applications utilizing the magnetoelectric effect yet exist,
several proposed applications utilizing the relatively large magnetoelectric effect associated with
ME laminate composites are currently in research and development phases. These applications
25
include the development of tunable microwave devices, voltage-controlled inductors, voltage-
controlled magnetic field generators, magnetically-tunable capacitors, voltage-tunable
transformers, and foremost, magnetic field sensors.[5] Presented in this dissertation is an
investigation of the use of magnetoelectric composites as magnetic field sensors.
1.5. ME Composites as Magnetic Field Sensors
Strain-coupled ME composites that exhibit large coupling coefficients have emerged as
promising candidates for the development of highly-sensitive magnetic field sensors in recent
years.[8] Key advantages of this technology include operation at room temperature, low cost,
and simple fabrication requirements. In addition, steadily increasing magnetoelectric coefficient
values potentially enable these devices to target highly-sensitive magnetometer markets that
include optically pumped cesium vapor magnetometers, spin-exchange relaxation-free (SERF)
atomic magnetometers, and superconducting quantum interference devices (SQUID).[48] As
previously described, ME composite magnetic field sensors rely on a stress-mediated coupling
between magnetostrictive and piezoelectric phases in order to produce an output voltage in
response to an applied magnetic field. Magnetostrictive phases that have been utilized in the
construction of ME sensors include Terfenol-D, Metglas®, and Galfenol intermetallic alloys, as
referenced in Table 2, whereas the piezoelectric phase is typically lead zirconate titanate (PZT)
or lead magnesium niobate - lead titanate (PMN-PT), as referenced in Table 1. The
magnetoelectric effect is obtained through bonding the aforementioned materials together such
that under the influence of an applied magnetic field, the magnetic phase becomes longitudinally
or transversely magnetized, inducing strain on the piezoelectric phase causing longitudinal or
26
transverse poling. Depending on material geometry, the terms longitudinally and transversely are
described using axially or radially, as is the case with cylindrically-shaped devices, to describe
direction of applied fields or induced strain.
1.5.1. D31 Sensor Type
Three types of ME composite magnetic field sensors are overviewed in the following to
demonstrate the most common operational modes in comparison to the novel topology invented
at NU. The first ME composite type, shown in Figure 17, is a laminated composite tri-layer
heterostructure consisting of a piezoelectric PZT film bonded between two magnetostrictive
Metglas® ribbons in a Metglas®/PZT/Metglas® configuration, provided by Carmine Carosella.
The Metglas®/PZT/Metglas® topology allows for the Metglas® to act as both magnetostrictive
phase and electrodes where charge can accumulate as the PZT phase undergoes strain. Leads
were attached to each Metglas® ribbon allowing for voltage measurements. The dimensions of
this magnetoelectric laminate were measured to be 28.3 mm long by 2.0 mm wide by 0.2 mm
thick accounting for a total volume of 11.32 mm3. Metglas® ribbons are manufactured to be 1
mil thick, equal to 0.0254 millimeters. Therefore the PZT film including the thickness of the
lamination adhesive is calculated to be approximately 0.1492 mm thick (149.2 microns). This
device is categorized as a longitudinally magnetized, transversely poled magnetoelectric
magnetic field sensor and is designed to exhibit peak performance for sensing magnetic fields
that interact parallel to its length. This device will be referenced in the following work and
referred to herein as the “D31 Sensor”.
27
Figure 17: Metglas®/PZT/Metglas® laminated heterostructural composite, provided by Carmine
Carosella, held by tweezers to enable resonance bending modes during testing. Length, height, and
thickness dimensions are indicated.
1.5.2. D33 Sensor Type
The second ME composite type, shown in Figure 18, is a laminated tri-layer
heterostructure which consists of a poled PZT film that is bonded between two magnetostrictive
Metglas® ribbons in a Metglas®/Poled-PZT/Metglas® topology. Instead of utilizing the
Metglas® phase as an electrode, this sensor exhibits internal patterned interdigitated electrodes
in contact with the poled-PZT film separated by a distance of approximately 1mm. This ME
magnetic field sensor is categorized as a longitudinally magnetized, longitudinally poled device
and is designed to exhibit peak performance for sensing magnetic fields that interact parallel to
its length. The dimensions of this magnetoelectric laminate were measured to be 80.4 mm long
by 10.4 mm wide and exhibited a thickness of 0.4mm where PZT was sandwiched between
Metglas®, and a thickness of 0.2 mm in the absence of a PZT layer at either end. The total
volume of this device, accounting for the capton-tape edges, is approximately 410 mm3. This
indicates that four layers of Metglas® (two layers laminated together per side of PZT) were used
28
in total. The approximate thickness of PZT, including lamination adhesive, is calculated to be
0.2 mm. The Metglas® layers were purposefully constructed to exhibit a length longer than that
of the PZT phase in order to reduce clamping which ultimately maximizes the ME coefficient by
straining the PZT in a more uniform manner. Extensive optimization regarding number of
Metglas® layers, Metglas® length, and additional factors have been investigated.[49] This
device was generously provided by Dwight Viehland’s Materials Science group at Virginia
Polytechnic Institute. This device will be referenced in the following work and referred to herein
as the “D33 Sensor”.
Figure 18: Metglas®/Poled-PZT/Metglas® laminated heterostructural composite with interdigitated
electrodes, provided by Dwight Viehland. Length, height, and thickness (at two locations along the
length) dimensions are indicated.
1.5.3. Tube-Topology Sensor Type
The third ME composite type, shown in Figure 19, is an epoxy-bound cylindrical
structure consisting of a poled PZT tube surrounding a metallic magnetostrictive wire. It is this
29
tube-topology design that serves as the main research topic in this work. The metallic
magnetostrictive wire also serves as the inner conductor, collecting charge generated at the inner
diameter of the PZT tube, to which it is bonded with using a silver conductive epoxy. Silver
paint applied to the outer surface of the PZT tube acts as the outer conductor. The PZT tube is
1mm in outer diameter and exhibits a ~0.8 mm inner diameter and tube lengths from 1.5 cm thru
8 cm have been manufactured and tested. The magnetostrictive wire exhibits an outer diameter
of 0.6mm and is typically cut to a length ~2 cm longer than the PZT tube. During fabrication the
tube is centered on the wire such that a small extension of wire protrudes on either side of the
PZT tube. Presumably this prevents mechanical clamping at the ends and provides greater strain
transfer, resulting in higher ME coefficient, in a similar fashion as the Virginia Tech device.
This ME magnetic field sensor is categorized as an axially-magnetized, radially-poled device and
is designed exhibit peak performance for sensing magnetic fields vectors that interact parallel to
the length of the cylinder. The dimensions of the tube-topology composites tested in this work
are of varying length but all exhibit a fixed outer diameter of 1mm at the tube, and 0.6mm at the
wire. Lengths have been fabricated from 1.5cm up to 8cm accounting for total device volumes
between 47 mm3 thru 274 mm3. Reference to this sensor type in the following work will include
specifics on sensor length and magnetostrictive wire type.
30
Figure 19: Metglas®/Poled-PZT/Metglas® laminated heterostructural composite with interdigitated
electrodes, provided by Dwight Viehland. Length, height, and thickness (at two locations along the
length) dimensions are indicated.
1.5.4. Operational Modes
The first two types of ME sensors, shown in Figure 17 and Figure 18 as D31 Sensor and
D33 Sensor respectively, are constructed of similar materials in the same layered laminate
topology; however, each sensor operates in a fundamentally different manner due to the
directionally dependent method of harvesting the piezoelectrically generated voltage response of
strained PZT. It is observed in Table 1 that the D33 piezoelectric coefficient is much greater
than the D31 coefficient for PZT of similar types. A diagram demonstrating the difference
between utilizing PZT in a D31 mode and a D33 mode is shown in Figure 20.[50]
31
Figure 20: D31 and D33 mode operation of piezoelectric PZT. For the D31 mode, a longitudinally
applied strain results in a transversely generated voltage response. For the D33 mode, a longitudinally
applied strain results in a longitudinally generated voltage response. Directions 3 and 1 are denoted on the
vertical and horizontal axis, respectively.
D31 Sensor was fabricated to utilize the PZT in a D31 mode where a longitudinally
applied strain, coupled from magnetostrictively induced strain in the Metglas®, results in a
transversely generated voltage response. Conveniently, use of a D31 mode enables D31 Sensor
to utilize the Metglas® as electrodes on either side of the PZT film. Although the piezoelectric
coefficient is lower for ME sensors utilizing the D31 mode, the complexity of sensor
construction is greatly reduced.
D33 Sensor was fabricated to utilize the PZT in a D33 mode where a longitudinally
applied strain, coupled from magnetostrictively induced strain in the Metglas®, results in a
32
longitudinally generated voltage response. In order to detect this voltage response an
interdigitated pair of electrodes, demonstrated by the geometry shown in Figure 21, was placed
longitudinally on the PZT, underneath the Metglas®. Leads were then attached to exposed
portions of the interdigitated pair of electrodes for voltage measurements. By designing a ME
magnetic field senor to utilize the D33 sensing mode, the device benefits from a higher
piezoelectric coefficient but increases the complexity of sensor construction.
Figure 21: Example of an interdigitated electrode geometry. Interdigitated electrodes are typically used
in ME laminates where the piezoelectric phase is to be operated in a D33 mode, as exemplified by D33
Sensor.
The following chapter details the figures of merit of various builds of the tube-topology
ME sensor in a magnetic field sensing application. The majority of tube topology devices
fabricated operate in a d31 mode as illustrated by the diagram in Figure 22, however discussion of
a novel device designed to operate in a d51 mode is also presented.[51] In Chapter 2, several
sensors are characterized using the conventional method of biasing magnetoelectric magnetic
field sensors with an applied static (DC) magnetic field. Numerous characterizations are
presented including; sensitivity vs. DC magnetic bias field, magnetostriction vs. magnetic bias,
Vout
+
-
33
magnetization vs. applied magnetic field, sensitivity vs. length, sensitivity vs. test field
amplitude, frequency response, and noise floor.
Figure 22: Diagram of tube-topology device operational nomenclature. Mechanical action is always
applied in the x (1) direct. Devices investigated in this research operate in either a d31 or d51 mode.
34
Chapter 2. Tube-Topology ME Composites as Magnetic
Field Sensors
2.1. Introduction and Motivation
Magnetoelectric composites have great potential for numerous applications such as
magnetic storage, automotive sensors, navigation systems, non-destructive material testing,
security systems, structural stability, medical sensors, military instruments, and most commonly,
magnetic field sensors.[52, 53] The superconducting quantum interference device (SQUID) is
reputed to be the most sensitive magnetic field sensors, achieving a magnetic field resolution on
the order of several femtoTesla. The sensor itself has a power consumption of several watts and
its operation is based on flux quantization and the Josephson effect, both of which are observable
only in the presence of superconductivity. As such, it operates below the superconducting
transitions temperature at cryogenic temperatures, requiring a significant amount of power, and
suffers from acute sensitivity to electromagnetic interference. Older, more traditional types of
magnetic field sensors are based on the Hall and magnetoresistive effect, which also require
external power supply. As such, a self-powered magnetic field sensor that transduces magnetic
energy to electrical signals would be of great value and utility. Such sensors can be realized
35
through the magnetoelectric (ME) effect, which is observed in single-phase multiferroics (MF),
and piezoelectric-magnetostrictive composites.[14, 54] As previously mentioned, in material
composites, electric polarization occurs in response to an applied magnetic field and similarly,
magnetization occurs in response to an applied voltage. As a result, a transducer capable of large
magnetoelectric coupling coefficients, α=dE/dH, may provide a potential device route towards
development of highly sensitive magnetic field sensors, tunable microwave filters, tunable
transformers, voltage-controlled inductors, magnetically-tunable capacitors, and voltage-driven
magnetic field generators.[55-59]
Magnetic field sensors are needed for the detection of low frequency (10-2 thru 103 Hz)
minute magnetic field variations (~10-12 T) in applications ranging from non-invasive
neurological interfaces for quadriplegics to magneto-encephalography and magnetic anomaly
detectors.[22] Furthermore, in order to be deployable, emerging field sensor technologies need to
operate at room temperature, be electronically passive, and small in volume. No known sensor
meets all of these stringent requirements. However, composite heterostructures consisting of
bonded piezoelectric and magnetostrictive components offer large ME effects at room
temperature allowing for high performance of field sensors.[5, 60] Since magnetostrictive
materials typically operate optimally under DC magnetic bias field conditions, ME field sensors
typically require a DC bias field to maximize sensitivity. Disadvantageously, generation of
magnetic bias fields increases power consumption, volume, and costs. Therefore, reducing, or
even eliminating the need for bias fields, has become of great interest for its potential to provide
new pathways to miniature, lightweight, low power, room-temperature, highly-sensitive
magnetic field sensing technologies. In this chapter, the development of ME tube-topology
composites for use as magnetic field sensors is detailed.
36
2.2. Composite Construction
Fabrication of the tube-topology ME composite took place at Northeastern University’s
CM3IC facility. The composite consists of five basic materials; PZT tubes, magnetostrictive
wire, conductive epoxy, silver paint, and copper magnet wire. The PZT tubes were sourced from
Smart Materials Corporation in geometries of 15 cm long, 1 mm outer diameter, and 0.8mm
inner diameter.[61] The magnetostrictive wires were sourced from the Baotou Research Institute
of Rare Earths in Baotou, Inner Mongolia, China. Three different types of magnetostrictive wires
were experimented with; Galfenol (two separate batches), iron-cobalt-vanadium alloy, and iron-
nickel alloy. The conductive epoxy or “conductive composition” was sourced from ESL
EUROPE and is part number 9910-C. The silver paint, called PELCO Conductive Silver Paint,
was sourced from Ted Pella and has part number 16045. Copper magnet wire, with gauge of 32
AWG, was sourced from the lab and used as leads for connecting to devices.
Fabrication of these devices requires use of the following equipment at NU’s CM3IC
laboratory: furnace capable of 535 ºC and an argon atmosphere, high-voltage DC power supply
capable of applying 200VDC, soldering iron, hot plate capable of 100 ºC, and a thermocouple
with temperature gauge. The specific instruments used are as follows. A Carbolite STF 15/180
tube furnace was used for the sintering process. A Fisher Scientific Isotemp 11-600-49HV hot
plate was used to apply heat during the poling process. A Stanford Research Systems PS310
high voltage dc power supply was used to apply DC voltage during the poling process. An
Omega HH501DK Type-K thermometer with thermocouple was used to monitor temperature
during the poling process. A Weller WES51 soldering iron station was used for attaching copper
37
leads. A Fluke 87V digital multimeter was used to test conductivity. Pictures of each of these
instruments are shown below in Figure 23.
Figure 23: a) Carbolite STF 15/180 tube furnace. b) Fisher Scientific Isotemp 11-600-49HV hot
plate. c) Stanford Research Systems PS310 high voltage dc power supply. d) Weller WES51 soldering
iron station. e) Omega HH501DK thermometer with Type-K thermocouple.
2.2.1. Fabrication Instructions
The following procedure outlines the precise method for fabricating these devices and is
written as a step-by-step instruction set with considerations included.
38
1) Cut PZT tube to length. Due to PZT being a ceramic material, it is not recommended
to simply snap the tube as it will break unevenly and unpredictably. Use of either a
diamond saw or diamond scribe is recommended.
2) Cut magnetostrictive wire to length. The wire is cut longer than the PZT tube to
reduce strain clamping at ends of the tube and to provide access to inner electrode.
3) Using sand paper, or similar abrasive, lightly sand the exterior of the magnetostrictive
wire. This step is designed to remove any oxide coating in order to provide better
adhesion to the epoxy and ultimately better strain transfer. Do not over-sand as
decreasing the diameter of the wire will reduce strain generation.
4) Ensure the wire fits inside the PZT tube. Some of the PZT tubes were noticed to
exhibit non-uniform inner diameters which prevented insertion of the wire.
5) Coat the magnetostrictive wire with silver conductive epoxy compound and insert
into PZT tube. It is recommended that this step is repeated numerous times until the
inner surface of the tube is entirely coated with the epoxy. The tube is slightly
translucent and visually changes once coated. This step is critical because strain is
transferred between active materials via the epoxy.
6) Clean the edges of the tube such that no conductive epoxy overlaps onto the outer
diameter of the tube. If not properly cleaned, the outer diameter surface may become
electrically shorted to the inner diameter surface (wire) once the silver paint is
applied.
7) Sinter the device at 535 degrees Celsius for 35 minutes in an atmosphere of argon. A
ramp rate of + 7 ºC/min was used to ramp from room temp to 535 ºC. The sample
39
was allowed to cool back to RT naturally. Argon atmosphere is used to prevent
oxidation.
8) Apply silver paint to the outer diameter of PZT tube. Be sure the silver paint does not
create an electrical short between the outer diameter of the tube and the
magnetostrictive wire. This layer will cause strain clamping and reduce output
response. Therefore a thin, uniform layer is preferred. Allow at least 20 minutes to
dry.
9) Solder a copper lead onto the magnetostrictive wire. Attach a second copper lead onto
the silver paint. A combination of soldering and silver paint may be used to ensure
good conductivity between copper lead and silver painted surface. Use lowest
temperature soldering as possible as the PZT tube may crack due to thermal shock.
10) Test conductivity between lead attached to magnetostrictive wire and lead attached to
silver paint to ensure proper connection.
11) Test conductivity between leads to ensure they are not shorted. The DC resistance
measurement between inner and outer electrodes (wire and silver paint on tube,
respectively) should be greater than 10 megaohms. If this is not the case, check for
areas where silver paint or conductive epoxy may be in close proximity to one
another. Otherwise check the PZT tube for cracks. A small hairline crack in the tube
may act as a conductive path. Conduction between electrodes will reduce the output
voltage response of the device and therefore should be minimized.
12) Connect the lead attached to the wire to the positive (+) pole of the high voltage DC
power supply and the lead attached to the silver paint on the tube to the negative (-)
pole.
40
13) Place the device on the hot plate and heat the device to 100 ºC. Monitor the
temperature. Optional use of a heat blanket is recommended to maintain uniform
temperature across device.
14) Once heated to 100 ºC, apply DC voltage starting at 0 V up to 200 V in increments of
10 V while waiting at least 5 seconds between each increment. This step polarizes the
PZT tube which enhances the ME coupling coefficient. The increment-and-wait
method was adopted after initial samples fractured under the shock of applying
200VDC directly from zero, without ramping up the field.
15) Allow the device to polarize at 100 ºC, 200 VDC for 30 minutes.
16) After 30 minutes, turn off the hot plate while maintaining the 200 VDC.
17) Once the hot plate reaches room temperature, which can be measured with the
theromocouple, reduce the applied field from 200 VDC to 0 VDC in increments of 10
V while again waiting at least 5 seconds between each increment.
18) Composite fabrication is now complete. The leaded magnetoelectric device is ready
for use. No further processing is necessary.
Several varieties of ME composites were fabricated into the structure shown in Figure 24,
each according to the same fabrication method. Clearly, numerous studies can be done on the
fabrication technique in order to optimize factors such as polarization temperature, poling
voltage, sintering procedure, epoxy type, outer electrode type, and more. However, none of these
are included in this dissertation because they are believed to offer minimal improvements in
performance as opposed to characterizing effects of different magnetostrictive wires and device
41
length. Such manufacturing improvements may be investigated once optimal materials and
configuration are identified.
Figure 24: Fabrication diagram of the ME tube-topology composite. The fixed end is where devices are
clamped during testing.
2.3. Experimental Setup
In simplest form, the sensitivity of a ME composite magnetic field sensor may be
characterized by the ratio of the magnitude of an applied magnetic field to the generated output
voltage of the device and such a measurement is relatively simple. However, like most devices,
these composites are non-linear, frequency-sensitive, directionally-dependent, and sensitive to
environmental conditions. Therefore, significant consideration has gone into the experimental
setup to obtain the most accurate results within the capability of the CM3IC laboratory. The most
42
common method, as demonstrated in the literature, for characterizing ME magnetic field sensors
is to apply a magnetic test field of known frequency and amplitude and measure the voltage
output response as a function of swept amplitude of a superimposed DC magnetic field. The data
collected in this type of measurement reveals the nature of ME composite sensitivity as a
function of applied DC magnetic bias field for a fixed input test magnetic field. The reason this
data type is most common is that it is an efficient way of collecting two important characteristics
of a ME composite sensor simultaneously; absolute sensitivity, and sensitivity vs. bias H-field.
Absolute sensitivity measurements are most useful for comparing device-to-device performance
while sensitivity vs. bias H-field measurements are useful for understanding how to optimize an
individual sensor’s performance. As such, an experimental setup which can collect the output
voltage response both spectrally and at specific frequency as a function of applied magnetic field
was developed. Two versions of the setup were developed throughout the timeframe of these
experiments. Both versions are described in the following.
2.3.1. Experimental Setup Version 1
Experimental setup version 1 consists of a dual-Helmholtz coil design, capable of
generating uniform magnetic fields with only 10% variation over a length of 6 cm. The dual-
Helmholtz coil was positioned inside of a dual-layered Gauss chamber in order to isolate the
device under test (DUT) from external and environmental noise sources as shown in Figure 25.
43
Figure 25: a) Dual-Helmholtz coil design with D31 Sensor centered inside. b) Dual-Helmholtz coil inside
of the double-layer Gauss chamber. Tube-topology ME composite is positioned inside of Helmholtz coil
for characterization.
Figure 26: DUT mounting apparatus consisting of plastic tweezers held by a table-top vice-grip. All
components are non-magnetic. a) Top-down view. b) Rotated side-view.
44
The coil covered in black tape, shown in (a) of Figure 25, was made using 200 turns of 26
AWG wire on each winding side of the Helmholtz coil. The coil with exposed amber colored
wire was made using 400 turns of 32 AWG wire on each winding side. These coils were made
using PVC tubing, a milling machine, and copper magnet wire according to the cross-section
schematic in Figure 27, and were designed to nest inside one another. A model of the dual-
nesting Helmholtz coil’s magnetic field distribution was designed using FEMM and is shown in
Figure 28 and the field distribution along its central axis is plotted in Figure 29. The design
demonstrates approximately 10% error in uniformity over a length of 6 cm, and quickly drops off
to just over 30% error in uniformity over a length of 8 cm, which is sufficient for testing devices
up to 8 cm long.
Figure 27: Schematic of single Helmholtz coil design made from PVC tube (not drawn to scale).
Radius, R, and distance, D, are made to be equal in order to satisfy Helmholtz design. Dual-Helmholtz
design requires use of two PVC tubes that can be nested.
45
Figure 28: Simulated field distribution pattern from dual-nesting Helmholtz coil design.
Figure 29: Modeled field uniformity of the fabricated dual-nesting Helmholtz coil.
46
The Helmholtz coil design was chosen as the magnetic field generation platform due to
its ability to generate relatively uniform fields as opposed to use of permanent magnets. A dual-
Helmholtz coil was pursued in experimental setup 1 in order to generate an overall applied
magnetic field consisting of an alternating magnetic test field superimposed on a static magnetic
bias field. The Helmholtz equation (2.1) calculates magnetic flux density along the central axis
through each coil as a function of permeability , number of turns , current , and coil radius .
⁄ (2.1)
Clearly, magnetic field magnitude is controlled in these experiments by current (I) as the
number of turns and radius of each coil is fixed, and the medium for the field, air, is also fixed.
In these experiments the innermost Helmholtz coil was used to generate the static, or DC, bias
field and the outermost coil used to generate the alternating, or AC, magnetic test field.
The dual-Helmholtz coil was positioned inside a double-layer Gauss chamber which was
used to shield the test volume from external magnetic noise sourced. In addition the Gauss
chamber was electrically grounded, enabling it to act as a partial Faraday cage to reduce effects
of electronic noise in the environment. This testing platform was the foundation of experimental
setup 1. A full list of equipment used in this may be found in the Appendix. A block diagram of
the setup is shown in Figure 30.
47
Figure 30: Block diagram of experimental setup 1.
The bias field coil was driven using a Sorensen DCR 80-12B DC power supply which
was controlled digitally by the auxiliary voltage output from a Stanford Research Systems
SR380 lock-in amplifier. This allowed for precise, repeatable control of the DC output current
enabling DC magnetic field control that was significantly more accurate than by use of the
Sorensen’s analog knobs. Configuration of this setup was achieved using the following steps.
1) Configure the Sorensen DCR 80-12B strapping for signal programming voltage mode:
a. Remove all strapping from current configuration.
b. Connect nodes 7 to 8.
c. Connect node 1 to + Output.
d. Connect node 2 to – Output.
48
e. On Front Panel, connect + Output to Ground.
f. Set Current knobs fully clockwise.
2) Configure SR830 Aux Out 1 to provide voltage programming of the DCR 80-12B:
a. Press Aux Out and set to 0.000 VDC.
b. Connect Aux Out 1 + Voltage signal to node 3 on Sorensen DCR.
c. Connect Aux Out 1 Ground to node 1 on Sorensen DCR.
3) Connect the Sorensen DCR 80-12B DC output to desired load.
A calibration curve, shown in Figure 31, was created to relate the auxiliary voltage out of
the SR830 to magnetic field magnitude. The test field coil was driven by the source output on a
Stanford Research Systems SR770 and experiment-dependent calibration curves were generated
as necessary.
Figure 31: DC calibration curve characterizing relationship between SR830 auxiliary voltage output and
the magnetic field generated by the Sorensen DC power supply.
49
Prior to testing, each ME sensor was mounted into plastic tweezers as shown in Figure
26, and suspended by a table top vice grip fabricated from aluminum and plastic. Supporting
each sensor on the end using a clamp is theorized to promote the generation of bending modes,
resulting in higher sensitivity, and to reduce mechanical damping effects associated with
platform-mounted methods. However, no study was performed to analyze the different sensor
mounting methods due to the scope of this work. For consistency, all sensors were mounted in
an identical manner during testing and positioned in the center, along the axis, of the Helmholtz
coils.
Copper leads from the ME sensor under test were connected directly miniature clip leads
terminated on a BNC cable attached the input channel A of the SR770 spectrum analyzer. The
SR770 was configured to collect data using the following parameters:
1) Setup the SR770 using the following steps:
a. Power on.
b. Set desired frequency scale.
c. Set Window to BMH.
d. Set Measure to PSD.
e. Set Display to Log Mag.
f. Set Units to Volts RMS.
g. Set Input to A.
h. Set Grounding to Ground.
i. Set Coupling to AC.
j. Set Trigger to Continuous.
k. Set Source to Sine.
50
l. Configure source to generate desired magnetic test field.
m. Press Auto Scale.
n. Set Auto-Ranging On.
o. Set Averaging On.
p. Set Number Averages to 1000.
q. Set Average Type to RMS.
r. Set Average Mode to Linear.
2) Connect the SR770 source out to load.
The SR770 configuration was saved to a floppy disk for backup and this configuration
was used for all subsequent measurements in the experimental setup version 1. This experimental
setup was capable of generating static magnetic field magnitudes from 0 to +/-50 Oe and
alternating magnetic field amplitudes, at frequencies between 1 to 400 Hz, of 0.001 to 0.5 Oe
RMS.
2.3.2. Experimental Setup Version 2
Experimental setup version 2 consists of a solenoid coil design, capable of generating
uniform magnetic fields over a length of 12 cm; nearly double that of the Helmholtz design. The
solenoid coil, shown in Figure 32a, was positioned inside of a tri-layered Gauss chamber in this
setup as shown in Figure 32b.
51
Figure 32: Solenoid fabricated for use in experimental setup version 2.
The solenoid consists of 480 turns of 24 AWG wire. This coil was manufactured onto a
PVC tube, however no machining was necessary. Instead, double-sided foam tape was used to
create the raised barriers which contain the coil windings. A small notch was cut into the center
of the tube to fit a transverse hall probe for characterization as shown in the fabrication
schematic in Figure 33. Prior to fabrication, a model of the solenoid coil’s magnetic field
distribution was simulated in FEMM and is shown in Figure 34. The field distribution along its
central axis is plotted in Figure 35. The design demonstrates approximately 10% error in
uniformity over a length of 10 cm, 20% error in uniformity over a length of 12.5 cm, and then
quickly drops off to just over 30% error in uniformity over a length of 14.5 cm, which is more
uniform than the previous Helmholtz design in experimental setup 1.
52
Figure 33: Schematic of solenoid coil design made from PVC tube (not drawn to scale).
Figure 34: Simulated field distribution pattern for solenoid coil design.
53
Figure 35: Modeled field uniformity of the fabricated solenoid coil.
The solenoid coil design was chosen for the second setup in order to achieve higher
uniformity over a longer distance. This design consisted of only a single winding which and, in
order to simultaneously pass alternating and direct currents through the single-solenoid coil, a
simple solution consisting of a DC block capacitor, was employed. In a sufficiently long
solenoid, the induction at the center may be expressed by the solenoid equation (2.2) which
calculates magnetic flux density along the central axis through each coil as a function of
permeability , number of turns , current , and length .
(2.1).
Similarly to experimental setup 1, magnetic field magnitude was controlled by current.
The solenoid was positioned inside a high-permeability Gauss chamber, consisting of three
54
concentric chambers, which were electrically grounded. This testing platform was the foundation
of experimental setup 2. A full list of equipment is listed in the Appendix. A block diagram of
the setup is shown in Figure 36.
Figure 36: Block diagram of experimental setup version 2.
The SR770 source output was connected to the solenoid to provide ac test field. The
output was DC-blocked by using a large, 2500μF electrolytic capacitor rated for 50V. A digitally
programmable AMREL PS30-1.2D DC power supply was directly connected to the solenoid to
generate the static bias field. Testing of the superimposed field revealed that this experimental
setup successfully generates alternating and static magnetic fields superimposed on one another.
A Labview program, shown in the Appendix, was written to enable precise control of the direct
current output of the AMREL power supply and to capture data collected by the SR770. This
55
setup enabled testing of numerous ME composites to be completed in a very quick, easy, and
reproducible manner. A calibration curve, shown in Figure 37, was created to characterize
AMREL output current vs. magnetic bias field. Similarly to experimental setup 1, the alternating
magnetic test field was driven by the source output on the SR770 and experiment-dependent
calibration curves were generated as necessary, which are not included. The ME composite DUT
was positioned in the center of the solenoid, along its central axis, during testing as illustrated in
Figure 38.
Figure 37: DC magnetic bias field calibration curve for solenoid coil.
56
Figure 38: Diagram of DUT placement within solenoid. Solenoid is surrounded by a triple-layer
Gauss chamber. Drawing is not to scale.
DUT mounting, electrical connection to SR770, and configuration of the SR770 was
done in the identical way as experimental setup 1, which is detailed in the previous section. This
experimental setup was capable of generating static magnetic field magnitudes from 0 to +/-50
Oe and alternating magnetic field amplitudes, at frequencies between 1 to 400 Hz, of 0.001 to 1
Oe RMS. This concludes description of the experimental testing setups.
57
2.4. Effects of Intrinsic Magnetostriction on Tube-Topology Magnetoelectric Composites.
Numerous types of topologies, bonding approaches, amplification methods, and sensing
techniques have been investigated using ME composites. However, the most important aspects
of these devices are the magnetostrictive and piezoelectric materials used in composite
fabrication.[22, 48, 62] Typically, piezoelectric materials, exhibiting high piezoelectric
constants, such as PZT and PMN-PT, are desirable for generating large strain-induced charge
separation. However, in a magnetostrictive material, a large value of saturation magnetostriction
does not always make it an optimal material choice. A few factors such as magnetization
process, magnetic hysteresis, and magnetic anisotropy should also be considered. Additionally,
the slope of the magnetostriction curve (dλ/dH) has a significant influence on ME coupling. The
sensitivity of ME magnetic field sensors can be increased by applying an optimal DC magnetic
bias field, which is the motivation for creating a testing platform capable of applying
superimposed static and alternating magnetic fields. Peak ME sensitivity typically occurs when
the magnitude of the external magnetic bias field corresponds with the peak of the derivative of
the magnetostriction curve, a maximum in dλ/dH, which can be offset due to factors such as
magnetic hysteresis, shape anisotropy, and demagnetization. Depending on the magnetostrictive
material, optimal external magnetic bias field magnitude can range from 1’s to 10’s to 1000’s of
Oe. For materials requiring high magnetic bias, use of bulky permanent magnets or power-
hungry electromagnets are then required, making the device unattractive for use in practical
applications. As such, there is increased interest in developing miniature, lightweight, highly-
58
sensitive, low-noise ME magnetic field sensors that require little to no magnetic bias for
deployment in various magnetometry applications such as UAV-mounted gradiometric arrays.
In this study, the magnetostriction curves of three different magnetostrictive wire types
were measured, and then, the wires were fabricated into identical geometries of the quazi-one-
dimensional tube sensor topology. Low-frequency sensitivity and noise floor measurements were
collected and are presented.
Prior to composite fabrication, magnetostriction data was collected using a Vishay P3
Strain Meter as shown in Figure 39. Samples of wire, approximately 3 cm long, were each
bonded to an Omega strain gauge, part number KFG-5-120-C1-11L1M2R, using Loctite super
glue ultra-gel control type. The strain gauge was connected to the Vishay P3 strain meter and the
wire was centered inside of the electromagnet of a LakeShore vibrating sample magnetometer
such that magnetic field was applied axially. Magnetization of the wire samples was achieved by
using the electromagnet on a LakeShore VSM which can apply precise magnetic fields ranging
from 0 to +/- 10 KOe. Strain as a function of applied magnetic field was captured for each wire
type. Due to the strain gauge being larger in size than the diameter of the wires, a correction
factor was applied to the data as shown in equation (2.2).
∗ (2.2).
Where W is the width of the strain gauge pattern and D is the wire diameter.
59
Figure 39: a) Vishay P3 strain meter. b) Omega strain gauge attached to magnetostrictive wire.
The corrected strain, as a function of applied magnetic field, is shown in Figure 40 for
each wire. Magnetostrictive wires Galfenol, iron-cobalt-vanadium, and iron-nickel, are labeled in
Figure 40 as FG, FC, and FN, respectively. The first derivative of strain (slope of the
magnetostriction curve) is shown in Figure 41 revealing important features of each wire.
Vibrating-sample magnetometry (VSM) data, demonstrating magnetization density as a function
of applied magnetic field, is shown in Figure 42, for each wire type. The zoomed in plot in
Figure 42b shows that the wires arranged from magnetically softest to hardest are FN, FC, then
WB21, which is consistent with the magnetostriction data in the previous plots. The terms
magnetically soft or magnetically hard describe the slope of the magnetization vs. H curve. A
magnetically soft material has a steeper slope, indicating that it is more easily magnetized under
lower applied fields whereas a magnetically hard material has a shallow M vs. H slope, and thus
requires larger magnitude applied field to magnetize.
60
Figure 40: Magnetostriction as a function of applied magnetic field for three types of wire.
Figure 41: Derivative of magnetostriction as a function applied field, dλ/dH.
61
Figure 42: a) VSM data comparing M vs. H for FG (WB21), FC, and FN wire samples. b) Zoomed plot
showing low-H magnetization response.
The FG wire exhibits highest value of saturation magnetostriction, ~57 ppm, under a 500
Oe applied magnetic field. The FC and FN wires exhibit saturation magnetostriction (Ms) values
of 11 ppm and 27 ppm, respectively at 500 Oe. Much insight towards optimal wire choice can
be gained by analyzing the magnetostriction (λ), and corresponding derivative, curves. For
instance, although FG exhibits highest Ms, both FG and FC wires exhibit higher magnetostriction
under lower applied bias field. Since it is desirable to reduce and preferably eliminate bias field,
wire materials FC and FN would be better choices than FG. Additionally, it is observed in Figure
41 that wire FN exhibits the greatest change in the slope of the magnetostriction curve at near-
zero bias and that FC behaves similarly to a lesser extent. It is also observed that wire FG a peak
in the dλ/dH curve at approximately 200 Oe, which is out of the range of both experimental
setups. The magnetostriction and dλ/dH results suggest that the FN wire is the best material for
62
use in a composite and would achieve peak ME sensitivity performance under zero- and low-
magnetic bias field. The FC wire material, when built into and ME composite, should exhibit a
sensitivity profile similar to the FN composite, but with reduced sensitivity. The FG composite
can be predicted to exhibit highest sensitivity at higher bias fields.
The three wire types (Galfenol, iron- cobalt-vanadium, and iron-nickel) were then
fabricated into three equal lengths of ME composite magnetic field sensors. Each
magnetostrictive wire had a diameter of 0.5 mm and was coupled into a 5 cm long PZT tube,
exhibiting an inner diameter of 0.8 mm and outer diameter of 1 mm. Wire lengths of 7 cm were
used to reduce strain clamping at opposite ends of the active interface and to provide a contact
point for inner electrode. The PZT tube was centered on each wire such that 1 cm of bare wire
was exposed at either end of the sensor. Devices were fabricated according to the previously
described methodology. In this manner, strain-induced charge separation was detected radially,
in a d31 mode, between the outer and inner diameter of the PZT tube.
The experimental setup version 2 was used for characterizing the ME composites.
An external DC magnetic bias field was superimposed on the test field and was swept through
the values of 0, 1, 2, 3, 5, 7.5, 10, 15, 20, 30, and 50 Oe, throughout the following sequence: 0
Oe, +50 Oe, -50 Oe, and +50 Oe. This sweep pattern was used to collect hysteresis behavior of
the sensors and to eliminate any measurement error associated with only capturing virgin curve
data. Due to relatively low coercivity of each magnetostrictive wire, the sweep pattern
effectively erased any effects of magnetic fields applied prior.
Copper leads of each sensor were directly connected to the input of a Stanford
Research Systems SR770 FFT Analyzer where voltage spectral density (VSD) sweep
63
measurements, in units of Vrms/√Hz, were captured from 1 thru 50 Hz. The measurement
procedure consisted of capturing sensor response as a function of magnetic bias field using an
AMREL PD30-1.2D DC programmable power supply to generate magnetic bias field and then
using the SR770 to capture 1000 linearly-averaged VSD measurements at each step. Sensitivity
(in V/Oe) and magnetic spectral density (in T/√Hz) were calculated from the raw data and are
presented in the following.
Sensitivity behavior of the ME tube sensors containing three different
magnetostrictive wires are shown in Figure 43. For the first time, hysteretic effects exhibiting
butterfly-shaped sensitivity curves were observed in the quasi-one-dimensional tube topology
sensors. For sensors FC and FN, sensitivity was observed to initially increase, peak at 20 and 10
Oe respectively, then decrease as magnetic bias field increased from 0 to +50 Oe during virgin
curve. For sensor FG, sensitivity was observed to continually increase along with bias field from
0 to +50 Oe. All three sensors exhibited similar behavior as bias field reduced from +50 to 0 Oe
in that sensitivity mirrored the shape of the virgin curve but at a higher value, exhibiting
hysteresis.
64
Figure 43: Sensitivity is plotted as a function of swept bipolar applied magnetic bias field.
Sensor FN exhibits highest sensitivity under low- (<20 Oe) and zero-biased conditions while sensor FG
exhibits higher sensitivity at bias fields > 20 Oe.
Interestingly, as bias field polarity reversed and swept from 0 to -50 Oe, sensitivity
minimized for each sensor at -2 Oe, indicating that each magnetostrictive wire has a coercivity of
~2 Oe in this geometrical configuration. More importantly, this indicates that sensors can exhibit
an enhanced zero-external-bias sensitivity when a magnetic field is temporarily applied and then
removed, enabling the wire to exhibit enhanced magnetostriction under the influence of its own
65
internal remnant magnetization. Minimum sensitivity values for FG, FC, and FN sensors were
measured at -2 Oe to be 105, 841, and 672 μV/Oe, respectively. As bias field swept from -2 to -
50 Oe, sensitivity was shown to increase with field, which is consistent with the magnetic
hysteresis loop. Finally, as bias field swept from -50 to +50 Oe, the same trend was exhibited, in
reverse. When optimally biased at 50, 15, and 10 Oe, sensors FG, FC, and FN exhibited
sensitivity values of 6.88, 2.12, and 5.36 mV/Oe, respectively. At zero external-bias, sensors FG,
FC, and FN exhibited sensitivity values of 0.843, 1.12, and 3.15 mV/Oe, respectively
Figure 44: The peak sensitivity curve is captured while sweeping from max applied magnetic
field to zero. Magnetic field is applied starting at -50 Oe and swept towards zero. This curve displays
peak device performance.
66
Peak slope of magnetostriction occurs under very low (<20 Oe) applied magnetic fields
for samples FC and FN whereas it occurs at 200 Oe for sample FG. Magnetostriction data is in
good agreement with the single-ended sensitivity curves shown in Figure 44, indicating that a
maximum in dλ/dH corresponds with peak sensitivity for sensors FC and FN at 15 and 10 Oe,
respectively. It also validates the behavior of FG in that sensitivity increases along with applied
field, up to 50 Oe, due to the wire undergoing steady increase in dλ/dH from 0 to 50 Oe. The
peak sensitivity curves also validate predictions in wire performance based off of
magnetostriction data. FC sensor is shown to exhibit a very similar sensitivity profile as the
sensor made with FN wire, but with overall reduced ME sensitivity. FG sensor exhibits peak
performance under higher bias fields while FN sensor exhibits better performance under low and
zero bias. Figure 44 shows peak sensitivity curves of each sensor as a function of external bias
field and was captured as magnetic bias magnitude decreased from -50 Oe to 0 Oe. In this way,
enhancement to sensitivity was observed relating to hysteresis effects. This effect relates to
hysteresis through net alignment of magnetic dipoles in the wire. In a demagnetized state,
randomly aligned magnetic dipoles cause a lesser net strain due destructive interference of
magnetostriction, resulting in lower strain on the PZT tube, and ultimately a lower voltage
response. As the dipole moments become aligned under influence of an externally applied
magnetic field, magnetostrictively-induced strain interferes constructively and ultimately results
in higher voltage response. Magnetic hysteresis influences not only the degree to which an
applied magnetic field further aligns or misaligns dipoles in the wire, but also the field
dependence of magnetostriction. This effect is shown in the butterfly shaped curves of Figure
43. Figure 44 emphasizes the peak sensitivity curve, which is captured after magnetic dipole
alignment has been established. Most importantly, combination of hysteretic effects and the
67
derivative of magnetostriction jointly determine the sensitivity curve of a ME magnetic field
sensor. It is postulated that the remnant magnetization of the magnetostrictive wire can be
engineered to coincide with the external bias field at which the maximum of the derivative of the
magnetostriction curve occurs, to enable optimal sensitivity under zero external magnetic bias.
Figure 45: Magnetic spectral density plots for optimally biased (a, on left) and zero-biased (b, on
right) conditions are displayed. All devices exhibit noise floor in the nanoTesla range at low frequency.
A 25 Hz, 1 mOe (100 nT), magnetic test field was applied during measurement.
Magnetic spectral density response demonstrating the noise floor of each sensor is
presented in Figure 45. Magnetic spectral density (MSD) measurements were calculated from
measured voltage spectral density (VSD) response. To calculate MSD from VSD the following
steps equation was used. MSD = VSD/(Sensitivity*10000). VSD is in units of V/√Hz.
Sensitivity is in units of V/Oe, and the factor of 10000 converts from Oe to Tesla. Frequency
68
sweeps from 1 thru 50 Hz were averaged and captured while applying a 25 Hz, 1 mOe test field
for reference. Both optimally biased (FG @ 50 Oe, FC @ 15 Oe, and FN @ 10 Oe), and zero-
bias configurations indicate low frequency noise floor in the nanoTesla range for all sensors.
Sensor FN exhibits the lowest 1-Hz noise floor of all three devices at 2.3 nT/√Hz (1.13 nT
accounting for bandwidth) when biased with a 10 Oe H-field. Spurious noise peaks are detected
by each sensor and considered to be background electromagnetic noise caused by various
external sources such as electronics, fans, building systems, traffic, etc. Sensor FC has a unique,
repeatable noise signature at 34 Hz, which does not occur with FN and FG sensors and is
considered to be intrinsic to the device, with exact cause still under investigation. In a zero-
biased state, FN exhibited a noise floor <10 nT/√Hz from 1 thru 50 Hz, which is lowest of the
three devices.
The sensitivity and noise floor of a quasi-one-dimensional ME tube sensor is shown to be
affected by properties of the magnetostrictive wire. Iron-nickel wire type demonstrated the
highest sensitivity, 3.15 mV/Oe (315 mV/cm-Oe), under no external bias field and also
demonstrated the lowest noise floor, <10 nT/√Hz, of all sensors for both bias conditions. Iron-
cobalt-vanadium wire type exhibits sensitivity of 1.12 mV/Oe and Galfenol of 0.843 mV/Oe
under no external bias fields. Due to low sensitivity performance of the FC device, no additional
analysis is performed on devices made with iron-cobalt-vanadium magnetostrictive wire. Iron-
nickel and Galfenol wire type ME devices exhibit high sensitivity at both low- and high-bias
fields, respectively, suggesting that either variety is suitable for use in opposing environments.
High sensitivity in the FN wire type device originates from large changes in magnetostriction
under application of low magnetic bias field. These results indicate that use of magnetostrictive
wire with large saturation magnetostriction and steep magnetostrictive slope at very low bias
69
fields, both attributes of the FN ME composite, may be used to improve zero-bias sensitivity and
decrease noise floor.
2.5. ME Composite Length Study
The length of the magnetoelectric tube-topology composite was investigated to better
understand how geometry affects sensitivity, and seeing as it is the easiest parameter to control,
it was examined first. ME composites were fabricated into ME magnetic field sensors of varying
length using two different magnetostrictive wire types. Two different batches of Galfenol
magnetostrictive wire were available, WB14 and WB21, and both batches were used in this
length study along with the iron-nickel (FN) wire type. The length of the ME composite is
expected to play a strong role in shaping sensitivity profiles of these devices for three main
reasons. First, magnetostriction is dependent on material factors such as magnetization and pre-
strain. Pre-strain is a strain inflicted on the wire by external sources such as strain caused by the
silver conductive epoxy or by the PZT tube after sintering and typically is uncontrollable. Pre-
strain will change the way the magnetostrictive material responds to magnetization, and may
cause changes or shifts in peak dλ/dH, Mz, and influence the way the material responds to a
magnetic bias field. Unfortunately no pre-strain study was completed, but it is acknowledged that
this effect may be reflected in ME sensitivity measurements. A second factor, magnetization of
the wire, is shape dependent. Effective magnetization is influenced by the internal
demagnetization field that is dependent upon the geometrical aspect ratio of cross-sectional area
to length. As length increases, the demagnetization factor decreases, and as length decreases,
70
demagnetization becomes more influential on the effective magnetization of the magnetostrictive
wire. The third factor is active region. The length of an ME composite determines the active
region, which is defined as the interface area between magnetostrictive and piezoelectric
materials. By increasing the active region of the device it is expected that an increase change in
charge generation would occur under identical stimulus. The goal of the length study is to
understand the influence of length on ME sensitivity and to find a preferential geometrical
design.
2.5.1. Demagnetization Effects
The following analysis illustrates the effect of demagnetization as a function of length by
relating the demagnetization field contribution to free energy.[63] Gauss’s law states that the
divergence of magnetic field is zero as shown in equation (2.3).[64]
∙ B 0 (2.3).
The following terms are defined as:
B 4 M (2.4).
is the demagnetizing field. (2.5).
4 M is the magnetization vector in CGS units. (2.6).
71
Assuming uniform magnetization, which is not precisely accurate but provides a good
approximation, the demagnetizing field vector, , may be represented in three dimensions
by the following equation.
(2.7).
Where , , and , are the directionally-dependent demagnetization factors such that,
4 in CGS units. (2.8).
For a cylinder placed in the coordinate system, as shown in Figure 46, geometrical
dimension a along x-axis, b along y-axis, and c along z-axis, may be used in equations (2.9),
(2.10), (2.11), and (2.12) to calculate directionally-dependent demagnetization factors. The sum
of demagnetization factors must equal 4π, which serves as way to verify calculations.
Figure 46: Coordinate system used for calculating demagnetization factors. A cylinder,
positioned axially along the z axis, is shown, however dimensions a, b, and c may be applied to most
shapes.
72
Directionally-dependent demagnetization factors may be calculated using the following
equations:
∙ (2.9).
4 ∙/
(2.10).
4 ∙/
(2.11).
4 ∙ (2.12).
The demagnetization factors were calculated for a cylinder, representing the
magnetostrictive wire, using the MATLAB calculator shown in Appendix A.4 and are shown in
Figure 47. Nx and Ny are expectedly equal due both terms representing the radius and exhibit
identical behavior such that as length decreases, at lengths < 0.1 cm, the demagnetization factor
approaches zero. For lengths >> 0.1 cm, the demagnetization factor approaches 2π. Nz,
representing the demagnetization factor along the axis of the wire, which is the same direction
magnetic field is applied in during characterization, is shown to be near-zero at lengths greater
73
than 4 cm. For completeness, the absolute demagnetization factor value is shown in Figure 48
for lengths of wire used in ME composite fabrication.
Figure 47: Demagnetization factors calculated for the magnetostrictive wire shape. Insert shows zoomed
in region where Nx, Ny, and Nz, are equal at a length of 0.1 cm.
74
Figure 48: Normalized effects of Nz demagnetization factor in the wire as a function of length. Insert
shows absolute demagnetization factor for Nz.
For all practical analysis, the demagnetization effects in lengths of magnetostrictive wires
used in ME composites, ranging from 2 cm to 10 cm, are negligible. This effect is also seen in
Figure 49, which plots magnetostriction as a function of length for the iron-nickel wire.
Similarly, and for all practical purposes, the demagnetization factor is not responsible for causing
any changes to magnetostriction. It is believed that the primary factor dictating behavior in
Figure 49 is physical clamping of the wire due to the strain gauge. As the wire becomes shorter
the clamping effect becomes more pronounced. In Figure 50, the derivative of the
magnetostriction curves, dλ/dH, for 13 cm, 9 cm, and 5 cm lengths of iron-nickel wire is shown
as a function of applied magnetic field. This plot was generated in an attempt to see if the peak of
the dλ/dH curve was changing as a function of wire length. Due to the low-resolution
experimental setup, which exhibited excessive drift over time, shown in Figure 51, the results are
75
unclear. However, ignoring initial and low-field data, it is observed that the peak in the dλ/dH
curves shifts from ~65 Oe for the 5 cm wire, to ~50 Oe for the 9 cm wire, to ~ 20 Oe for the 13
cm wire. The importance of this trend will be considered in the sensitivity vs. ME composite
length studies presented in the upcoming sections.
Figure 49: a) Magnetostriction as a function of magnetic field applied from 0 Oe, to +500 Oe, to -500 Oe,
and then to +500 Oe. Hysteresis effects are observed. b) Notional magnetostrictive data generated by
averaging data points at equal bias, per wire.
76
Figure 50: dλ/dH as a function of applied magnetic field for different lengths of iron-nickel wire.
Figure 51: Drift in the magnetostrictive measurement as a function of time. Drift is presented as a
percentage-change, relative to the full scale range of collected data.
77
Based on this analysis, there does not seem to be any significant effects caused by
demagnetization on the lengths of wire used in the ME composites. The quasi-one dimensional
geometry maintains an axial demagnetization factor at near-zero.
2.5.2. Active-Region Effects
The active region, as previously described, is the interface layer between piezoelectric
and magnetostrictive materials and it is quantified in terms of area. A uniform piezoelectric
material undergoing uniform strain will generate a constant separation-of-charge density across
its faces. Increasing the amount of surface area where charge is collected is therefore a linear
function. According to the equation for the area of the wall of a cylinder, 2 where r
is radius and l is the length, it is simple to see that wall area scales linearly with cylinder length.
Therefore, the area of the active region scales linearly with ME composite length and it can be
postulated that the ME sensitivity does so accordingly. The volume of this structure,
, also scales linearly with length. Therefore the active-region-density (active area / total
volume) is a constant, 0.7 mm-1. In laminate structures the active-region-density term is simply
1/t, where t is the thickness, and is 5 mm-1 for the D31 Sensor and 2.5 mm-1 for the D33 sensor.
It can be generally understood that by reducing the thicknesses of piezoelectric and
magnetostrictive materials, a higher active-region-density can be achieved. However, it has been
shown, in Figure 52, that optimal thickness does exist for certain composite types, and
maximizing the active-region-density is not necessarily preferred.[65] In addition, it is also
observed that modifying this ratio can cause shift in optimal magnetic bias field magnitude; an
important consideration for designing devices customized for a specific application. Although
78
brief, this discussion of the active region is important for understanding optimization methods in
fabricating ME composites.
Figure 52: ME coupling coefficient as a function of applied magnetic bias for
Metglas®/PZT/Metglas® heterostructural laminates for different N, where N denotes the number of
Metglas® layers.
2.5.3. Galfenol Length Study
The Galfenol wire batch WB21 was fabricated into four sensors consisting of lengths of
1.5, 2.5, 5, and 7.5 cm. Sensitivity of each sensor was measured using experimental setup 1. For
this set of measurements, a 100 Hz, 1 Oe RMS, magnetic test field was applied while the DC
bias field was swept over the following steps: 0, 1, 2.5, 5, 7.5, 10, 15, 20, 30, and 50 Oe.
79
Sensitivity vs. magnetic bias measurements for four lengths of ME composites fabricated using
FG WB21 are shown in Figure 53. Zero-bias sensitivity is observed to increase with length. In
addition, it can be envisioned that the optimal magnetic bias field magnitude reduces as sensor
length increases. Unfortunately, this behavior is unable to be characterized because of the upper
bias field limit of the experimental setup. However, interpretation of the data suggests the 1.5
cm, 2.5 cm and 5 cm length devices have an optimal bias field > 50 Oe. Based on trajectory, it
can be inferred that the bias field maximizing sensitivity for the 1.5 cm device is greater than the
field requirement of the 5 cm device. Additionally, a reduction in sensitivity is shown for the 7.5
cm device at bias field values greater than 20 Oe, implying that the behavior of each device is
that, initially, sensitivity increases with applied bias field, peaks at some optimal bias field
magnitude, and then decreases as bias field continually increases. In theory, the slope of the
magnetostriction curve, as previously discussed, can explain this behavior. Peak performance is
demonstrated by the 7.5 cm device that exhibits a zero-bias sensitivity of 0.886 mV/Oe, and an
optimal-bias sensitivity of 12.97 mV/Oe at 20 Oe.
80
Figure 53: Sensitivity vs. applied magnetic bias field for various lengths of tube-topology ME
composites made using Galfenol wire batch WB21.
Sensitivity as a function of length for different bias fields is shown in Figure 54 along
with two fit curves. The polynomial fit lines, applied to the 0 Oe and 50 Oe sensitivity curves as
in Figure 54 provide excellent agreement between fit and measured data suggesting a third-order
polynomial relationship. Coefficients A, B, C, and D were solved on a per-case basis however
modeling and defining equations for the coefficients has not yet been completed.
(2.13).
81
Figure 54: Sensitivity vs. length for varying DC magnetic bias applied to composites fabricated using the
Galfenol wire batch WB21.
The Galfenol wire batch WB14 was fabricated into three sensors consisting of lengths of
1, 2.5, and 5 cm. Due to slight cracking of the PZT tube on the 5cm device, a second 5cm device
was made. Results from both devices are included. Again, sensitivity of each sensor was
measured using experimental setup 1, and a stimulus field of 100 Hz, 1 Oe RMS, served as
magnetic test field. The same DC magnetic bias steps were applied. Sensitivity vs. magnetic bias
measurements for three lengths of ME composites fabricated using FG WB14 are shown in
Figure 55. Similar behavior is exhibited with this wire batch to the WB21 batch in that at zero-
bias, sensitivity increases with length. Again, the same effect showing a reduction to the optimal
magnetic field bias magnitude as length increases is observed. For the 5 cm device it is observed
that peak biasing occurs at 20 Oe and that sensitivity decreases at higher bias field. Peak
performance is demonstrated by the 5 cm device that exhibits a zero-bias sensitivity of 0.362
82
mV/Oe, and an optimal-bias sensitivity of 12.52 mV/Oe at 20 Oe, making the 5 cm WB14
device comparable to the 7.5 cm WB21 device under optimal bias.
Figure 55: Sensitivity vs. applied magnetic bias field for various lengths of tube-topology ME
composites made using Galfenol wire batch WB14.
Sensitivity as a function of length at different bias fields is shown in Figure 56 along with
third order polynomial fit functions applied to the 0 Oe and 50 Oe sensitivity curves. Again the
fit function is a close match suggesting the system is governed by the equation in (2.13).
83
Figure 56: Sensitivity vs. length for varying magnetic DC bias applied to ME composites made using
Galfenol wire batch WB14. The cracked 5cm sensor is excluded.
Comparing device performance between Galfenol wire batches provides interesting
insight relating to material properties. VSM data, for magnetic field applied parallel and
perpendicular to the length of the wire, is shown in Figure 57, for both Galfenol wire batches.
WB14 exhibits a saturation magnetization of ~2000 emu/cc whereas WB21 saturates at 1300
emu/cc. In addition, the zoomed-in VSM plot, shown in Figure 58a, shows that WB14 is
significantly more magnetically soft, meaning that the slope of the magnetization curve vs. H is
steeper, than the WB21 material.
84
Figure 57: Vibrating-sample magnetometer (VSM) data comparing Galfenol wire batches WB14, (a) left,
and WB21, (b) right.
Figure 58: (a) VSM comparison at low applied field for WB14 and WB21 Galfenol wire samples. WB14
is shown to be magnetically softer than WB21. The effect of this is shown in (b) which demonstrates
sensitivity vs. applied magnetic field for 5cm long devices.
Peak sensitivity for the 5cm WB14 sensor is 12.5 mV/Oe, shown in Figure 58b, and
occurs at a magnetic bias field of 20 Oe. The 5cm WB21 sensor exhibits a peak sensitivity of
85
9.55 mV/Oe at 30 Oe. In addition, the entire WB14 curve exhibits higher sensitivity at lower bias
fields, except for the 0 Oe and 50 Oe field points, appearing to have shifted towards H = 0. These
results imply that it is possible to shift and enhance ME composite sensitivity by engineering the
magnetostrictive material. The trend is such that use of a magnetically soft magnetostrictive
material will shift the optimal magnetic bias field towards zero, and magnetically harder
materials will shift away from zero.
2.5.4. Iron-Nickel Length Data
The 5cm iron-nickel (FN) ME composite demonstrated the highest zero-bias sensitivity,
shown in Figure 44, of 3.15 mV/Oe, compared to devices made using from other
magnetostrictive wire types. In addition, it exhibited a peak sensitivity of 5.26 mV/Oe at a bias
field of 7.5 Oe. The FN wire effectively resulted in a 62.5% and 75% reduction of optimal
magnetic bias field for WB14 and WB21 sensors, respectively. This type of improvement
translates to energy savings in an electromagnet-driven application, or weight and volume
savings in a permanent magnet-driven application. Accordingly, the largest ME composite
fabricated for these experiments was made using an 11cm piece of FN wire and an 8cm PZT
tube. Sensitivity of the 8cm FN device is compared with that of the 5cm device in Figure 59 for
a 10mOe, 25 Hz magnetic test field. Experimental setup version 2 was used and magnetic bias
field was swept from 0 to +50, then -50, and then +50 Oe to generate the butterfly-shaped curve.
Note that the hysteretic nature of the magnetostrictive wire works in favor of maintaining high
sensitivity as external bias returns to zero. Zero-bias performance significantly increases from
2.84 mV/Oe, exhibited by the 5cm device, to 13.1 mV/Oe exhibited by the 8 cm device,
86
representing a ~360% increase in sensitivity due to a 60% increase in length. Optimal-bias
sensitivity increased from 4.7 to 18.1 mV/Oe, demonstrating a 285% improvement. Due to its
high performance, the 8cm FN composite is further studied in various ways in the following.
Figure 59: Sensitivity as a function of magnetic bias field for 8 cm and 5 cm lengths of ME composites fabricated using magnetostrictive iron-nickel wire.
87
2.6. Test Field Amplitude and Frequency Study
Off-the-shelf components are engineered to operate within a set of amplitude limits for
static fields and within a bandwidth for alternating fields. In most cases, the limits are put in
place because a device falls into non-linear or unpredictable behavior when operating beyond
them and may even self-destruct. As there is always an underlying effort to commercialize new
technology, specific limitations to the technology must be identified in order to target
applications. As such, characterizing the behavior of the tube-topology ME composites with
respect to applied field amplitude and frequency is important. In this section, the sensitivity
(mV/Oe) is evaluated as a function of magnetic field amplitude and frequency, within the
limitations of the experimental setup.
2.6.1. Amplitude Study
Amplitude characterization is performed on these devices to understand trends in sensor
behavior and to identify, if any, a linear operational range. Due to magnetic and magnetostrictive
saturation, these devices will inherently exhibit non-linear behavior at saturation-onset field
amplitudes. In this study a conventional DC magnetic-biasing technique, applied using
experimental setup version 1, is employed to characterize the amplitude linearity of tube-
topology ME magnetic sensors.
This section focuses on measurements of ME sensors constructed with iron-nickel
magnetostrictive wire and fabricated to lengths of 5 and 8 cm. A 100 Hz test field was used for
reference, which was characterized using a LakeShore 421 Gaussmeter, with amplitude varying
88
from 0.1 to 1.2 Oe. Sensitivity response as a function of magnetic bias for varying test field
amplitude is shown in Figure 60. It is observed that ME sensitivity increases as magnetic test
field decreases from 1.2 to 0.1 Oe. Both sensors present similar trends in sensitivity with bias
field, yielding a maximum in sensitivity at a bias field of 7.5–15 Oe, which is related to a
maximum in the dλ/dH vs. H curve. In contrast, the 8-cm sensor shows sensitivity (22 mV/ Oe)
twice that (10.5 mV/Oe) of the 5-cm sensor at a bias of 10 Oe for a 100 Hz Hac test field of 0.1
Oe. This length-dependent enhancement in sensitivity is significant and assumed to relate mostly
to increased active PZT/wire interface area. It is observed that the zero-bias sensitivity also
increases more than 200%, from 8 to 16.5 mV/Oe, at 0.1 Oe signal amplitude.
Remarkably, these tube-topology ME composite sensors have demonstrated very high
sensitivity (6-17 mV/Oe) at zero DC bias field with variable 100 Hz test field amplitude of 0.1 to
1.2 Oe rms. There is clearly a linear relationship between sensitivity and signal field for both 5
and 8 cm FN sensors as depicted in Figure 60b. It is observed that the 8 cm device exhibits a
slightly steeper slope than the 5 cm device as Hac approaches 0 Oe RMS. This trend suggests that
output sensitivity increases with device length while test field amplitude decreases. Therefore,
the FN tube sensors have greater potential to work with small sensing signals, which is justified
by the linear increase in sensitivity with decreasing sensing field.
89
Figure 60: (a) Sensitivity as a function of magnetic bias for different amplitudes of test field. (b)
Sensitivity vs. test field amplitude under zero external magnetic bias.
Two Galfenol ME composites, 5 cm and 7.5 cm, were characterized as a function of test
field amplitude under a fixed 20 Oe bias. A 25 Hz test field was applied and its amplitude swept
from 0.1 to 1.2 Oe RMS. Interestingly, the Galfenol devices, shown in Figure 61, exhibit the
opposite sensitivity vs. field amplitude trend as the FN devices. Here, sensitivity is shown to
increase linearly with magnetic field amplitude. This behavior can be attributed to the WB21
magnetostriction curve that demonstrates a relatively flat, but positively sloped, strain vs. H
curve at low applied fields. Presumably, this linear relationship deteriorates at test field
amplitude increases due to the nonlinear behavior of magnetostriction.
90
Figure 61: Sensitivity vs. test field amplitude for 5 and 7.5 cm WB21 devices. The test field was fixed at 25 Hz. A fixed 20 Oe DC magnetic bias was applied during testing.
For practical purposes, discovering that the WB21 and FN composites exhibit linear but
opposite trends in sensitivity vs. test field amplitude is an exciting result. This study has
revealed that the WB21 wire is preferential for detective larger amplitude fields whereas the FN
wire preferably detects lower amplitude fields. Limitations in the test setup prevented
characterization at higher field amplitudes where magnetostrictive saturation effects are expected
to occur.
2.6.2. Frequency Study
Frequency response is an important characteristic of any sensor that detects alternating
fields. The bandwidth of magnetic field sensors is of great importance at low and ultra-low
frequencies due to numerous magnetic field signatures of interest that exist in the range of 10-1
91
thru 103 Hz. Unfortunately, the low-frequency range is plagued by 1/f noise which becomes the
dominating signal as the frequency-of-interest approaches 0 Hz. ME composite sensors designed
to detect alternating fields usually exhibit wide linear regions on either side of a magneto-electro-
mechanical resonance. The resonance frequency of most ME composites is typically in the range
of 10 KHz to 100 KHz, and sometimes higher. The general trend, as demonstrated in the
literature, is that as sensor dimensions decrease resonant frequency increases. However,
sensitivity response measurements over this wide range of frequencies is beyond the limitations
of our experimental setup which, for experimental setup version 1, has an upper bandwidth of
400 Hz and for version 2, an upper bandwidth of 5 KHz.
In this study, the low-frequency sensitivity was measured for the WB21 Galfenol wire
type, at lengths of 5 and 7.5 cm, and for the FN wire type, at lengths of 5 and 8 cm. Figure 62
shows a linear relationship between sensitivity and frequency between 50 and 250 Hz. The 5cm
length device exhibits a slightly steeper slope than the 7.5 cm device. Projection of the slope
reveals intersection at ~400 Hz which suggests that above 400 Hz, the shorter device exhibits
higher sensitivity, whereas below 400 Hz, the 7.5 cm device exhibits higher sensitivity.
Sensitivity in Figure 62 was captured for fixed test field amplitude of 0.25 Hz and a fixed DC
bias field of 20 Oe.
92
Figure 62: Sensitivity as a function of frequency for 7.5 cm and 5 cm WB21 device. A 20 Oe bias field
was applied constantly. The test field was maintained at 0.25 Oe RMS.
Sensitivity as a function of test field frequency for the 8cm FN device is shown in Figure
63 for test field amplitudes of 0.1 and 1 Oe. These conditions were characterized at 0 and 1 Oe
DC bias fields. The frequency response for this device is measured to be nearly perfectly flat,
exhibiting a slope of ~0, from 25 Hz thru 400 Hz, for each condition. In comparing the 0.1 and 1
Oe RMS measurements, the lower amplitude test field demonstrates higher sensitivity, which
agrees with the results in Figure 60b.
Figure 64 displays sensitivity vs. frequency for a 5cm FN device for both 0.1 and 1 Oe
RMS test field amplitudes, under a fixed 10 Oe DC magnetic bias. A similar slope trend is
observed between the longer 8cm device in Figure 63, and the 5cm device in Figure 64, in
comparison with Figure 62, exhibiting that the shorter device has slightly positive slope. This
93
trend suggests that smaller devices are better suited for higher-frequency applications whereas
longer devices are more sensitive at lower frequencies.
Figure 63: Sensitivity as a function of frequency for the 8 cm FN device. Test field amplitudes of 0.1 and
1 Oe RMS were measured at zero bias and 1 Oe DC bias conditions.
94
Figure 64: Sensitivity vs. frequency for the 5 cm FN device. Test field amplitudes of 0.1 and 1 Oe RMS
were measured at zero bias and 10 Oe DC bias conditions.
An interesting overlapping trend shows that the shorter devices, such as 5 cm WB21 and
5 cm FN, shown in Figure 62 and Figure 64, respectively, exhibit a slightly positive slope
demonstrating that sensitivity increases with test field frequency. The longer devices, such as 7.5
cm WB21 and 8 cm FN, shown in Figure 62 and Figure 63, respectively, exhibit a slope closer to
zero, demonstrating a flatter sensitivity frequency response at these frequencies. Presumably this
behavior is due to the longer devices exhibiting a lower resonance frequency than the shorter
devices. As such, the shorter devices exhibit a response that rolls off more quickly as f
approaches 0 Hz which agrees with the trend show here.
95
2.7. Array Study
It was hypothesized that use of multiple identical devices wired in series would increase
the output voltage in a similar manner as series connection of batteries, or voltage sources. In
this way, the output voltage was theorized to increase by a factor of n, where n is the number of
devices. In this study, three identically manufactured, 5cm iron-nickel ME tube sensors are
fabricated and series performance is investigated.
The ME sensors were positioned in parallel to each other within the dual Helmholtz coil.
The devices were spaced ~5.5 mm apart and subjected to a 100 Hz, 0.25 Oe RMS reference field
superimposed on a 10 Oe static bias field using experimental setup version 1. Twisted-pair wire
leads for each sensor were routed out of the Gauss chamber such that the array wiring could be
manipulated. A diagram showing the three devices aligned in a parallel manner and wired in
series is shown in Figure 65.
Figure 65: Diagram showing three identically-manufactured 5 cm FN tube sensors connected in series.
96
Figure 66: Sensitivity measurements for individual and series configurations for three 5cm FN devices measured at 100 Hz, 0.25 Oe RMS under a 7.5 Oe magnetic bias field.
The output sensitivity was measured for sensors FN1, FN2, and FN3, individually, then
for sensors 1 and 2 wired in series, and finally for all three sensors wired in series as shown in
Figure 66. Individual sensitivity for sensors FN1, FN2, and FN3 was measured to be 11.3, 10.7,
and 10.7 mV/oe, respectively. Sensors 1 and 2 wired in series exhibited a sensitivity of 15.8
mV/Oe demonstrating a 45% enhancement, on average, compared to individual devices.
Sensitivity was measured to be 18.5 mV/Oe for all three devices wired in series, demonstrating a
~70% enhancement. These results do not show the anticipated increase in sensitivity as a
function of device count, n. For instance it was assumed that use of two devices would double
the output sensitivity, however only a 45% increase is measured. The reason for this behavior is
believed to be due to inconsistencies in the construction between devices which causes phase
mismatch between individual devices of the array. The phase mismatch, caused by non-
97
symmetrical motion of piezoelectric materials between devices, leads to destructive interference
of charge generated on each device.
The noise floor at 100 Hz was measured to be extremely low, ~ 2 nT/√Hz, for devices
measured both individually and in series. Negligible difference between configurations was
observed. These results indicate that increased sensitivity can be realized by using the tube-
topology devices in arrays. In addition, these ME composites, which requires no external power
supply, are ideally suitable for use in large passive arrays. Due to the small scale diameter, these
devices can be tightly packed to increase spatial resolution and used in magnetic mapping
applications to provide high detail at mm scale. Moreover, the arrays of magnetoelectric
FeNi/PZT tube sensors hold promise for use in low cost, scalable, magnetic detection systems
with nano-Tesla sensitivity.
2.8. 8cm FN ME Composite Highlights
The 8cm FN device exhibits the highest reported zero-external bias sensitivity as of this
writing. Depending on applied test field and frequency, device sensitivity as high as 16.5 mV/Oe
(1.65 V/cm-Oe) has been demonstrated, as in Figure 60.[66] This achievement has warranted
further characterization of the 8cm FN device in regards to sensitivity, noise floor, and frequency
response.
Sensitivity as a function of bipolar magnetic bias field is shown in Figure 67. This plot
reveals the true nature for high sensitivity under zero-external bias. The device prefers to exhibit
a net magnetization, even prior to application of a magnetic field, as exhibited by the first few
98
data points of the virgin curve. Here the virgin zero-bias sensitivity is ~13.5 mV/Oe, and after
returning to 0 Oe from an applied +50 Oe, the zero-bias sensitivity increases only to ~14 mV/Oe.
By decreasing the magnetic field in the - Oe direction, demagnetization of the wire occurs until
~4 Oe at which point magnetic domain reversal occurs and settles under increasing - Oe. The
difference between minimum sensitivity values is ~ 7.5 Oe indicating that under no applied bias
field, hysteresis effects, specifically, magnetic remanence and coercivity, “lock” the device in a
partially magnetized state, effectively equal to externally applying ~7.5 Oe, as shown in Figure
68. Interestingly, peak sensitivity of this device is exhibited under a magnetic bias field of 7.5
Oe. It is presumed that if the remanence and coercivity of iron-nickel wire could be increased, a
shift in the sensitivity dependence on bias field would occur. This shift can be engineered such
that the peak sensitivity intersects at zero bias. In other words, engineering of effective magnetic
remanence and coercivity may act as substitute to magnetic bias field for enabling a maximum in
dλ/dH where peak ME sensitivity is exhibited. Here, peak sensitivity is exhibited under a 7.5 Oe
bias field to be ~ 18 mV/Oe, demonstrating a ME coupling coefficient of 1.8 V/cm-Oe.
99
Figure 67: Sensitivity vs. magnetic bias field for the 8cm FN device. A 25 Hz, 10 mOe test field served as
reference.
Figure 68: Single-polarity plot of sensitivity vs. magnetic bias field to emphasize effect of hysteresis on
low-bias sensitivity.
100
Numerous efforts towards reducing the low-frequency noise floor of ME composites
have been undertaken, namely by a DARPA effort called HUMS (Heterostructural Uncooled
Magnet Sensors). As previously mentioned, great interest exists in measuring low-frequency
magnetic signatures in the picoTesla range that correlate with biomagnetic fields in the abdomen
or in the brain, generated by neurons firing. As such, measurement of the noise floor, or pseudo-
noise floor, of the 8 cm device at low frequency was carried out. Figure 69 shows that this
sensor exhibits an average noise floor less than 2 nT/√Hz at frequencies between 1 and 30 Hz. A
25 Hz, 10 mOe test signal was applied for reference.
Figure 69: Magnetic spectral density plot from 1 Hz thru 30 Hz demonstrating low-frequency pseudo-
noise floor response of the 8cm FN wire with applied bias of 7.5 Oe.
101
Frequency response from 0.001 Hz thru 5 KHz is shown in Figure 70 for an applied test
field of 1 Oe RMS. No external bias is applied to the sensor. A flat frequency response is
exhibited between 500 Hz and 5 KHz. Below 500 Hz, sensitivity rapidly rolls off. As no
magneto-electro-mechanical resonance (EMR) is observed in this figure, it is assumed that the
EMR occurs at higher frequencies. The slightly positive slope of the frequency response curve
further validates this point. Frequency response behavior of ME composites shows that below
EMR frequency, the slope is positive whereas above EMR frequency, slope is negative as the
upper bandwidth limit of the device is reached.
Figure 70: Zero-bias frequency response from 0.001 Hz thru 5 KHz of the 8cm FN sensor. The test field
was set at 1 Oe RMS and frequency was swept. Log-plot (inset) is shown to emphasize low-frequency
response.
102
The 8cm FN composite represents the flagship device developed in this work in terms of
high sensitivity at zero bias and low noise floor. In future developments, this sensor holds the
figures of merit for which new tube topology designs are compared with.
2.9. D15 Operational Mode Device
Recently, investigation of fundamental piezoelectric properties has found that the shear
piezoelectric coefficient d15 is ~440 pC/N for a c-axis oriented thin film of PZT and as high as
~494 pC/N for bulk ceramic samples.[67] These results shown an astonishing ~180% increase
as compared with the d31 (-175 pC/N) piezoelectric coefficient, which serves as the operational
mode for the vast majority of ME composites, including the tube-topology devices in this work.
As such, ways to utilize the d15 piezoelectric coefficient to harness the greatest amount of charge-
generation per input-force are being considered. The d15 coefficient describes the shear, or
torsional, charge displacement caused by an input strain, and it is also equal to its reciprocal term
d51.[68] In the case of a PZT cylinder, or tube, the d15 piezoelectric coefficient can be obtained
by detecting differential charge at short-length intervals along the shear y-direction of the
exterior surface of the tube as it undergoes axial strain in the x-direction which is illustrated in
Figure 71. Technically, the device operates in a d15 mode which is achieved through reciprocal
elemental and material action. Polarization in the shear-yaxis (5) direction is illustrated below.
The use of helical electrodes, placed perpendicular to the polarization vector and at a 45-degree
angle to the y-axis, is required. It is important to note that as of this writing no ME composite has
been fabricated to utilize the piezoelectric component in a d15 mode. An initial attempt to realize
ME tube-topology composites operating in a d15 mode is described here.
103
Figure 71: Nomenclature for describing directions in a PZT crystal for a 3D system on the left and the XY
plane on the right. The shear-y axis (direction 5) is shown by the polarization vector in the XY plane.
The d15 device was fabricated using an iron-nickel magnetostrictive wire according to the
same methodology as all other tube-topology composites except that no outer silver paint
electrode was applied. Instead, to capture the separation of charge along the PZT outer surface
area, a double-helical electrode was fabricated on the tube as shown in Figure 72. The electrodes
were made by tightly winding 20-micron diameter gold wire around the tube. Great care was
taken to keep the wires uniformly spaced, at 45 degrees, and tightly wound around the tube;
however inconsistencies are apparent due to the nature of working with such small materials by
hand. Pinhead sized drops of rubber cement were applied at opposite sides of the tube to prevent
wire from unraveling. Otherwise, no additional adhesive was used. The device was polarized
according to the same polarization procedure for d31 devices and checked for shorts using a
digital multimeter.
104
Figure 72: D15 mode device fabricated using iron-nickel magnetostrictive wire and PZT tube. a) Diagram
showing the double helical electrode structure that was fabricated, (b), using 20 um gold wires tightly
wrapped around the tube exterior.
The d15 device was characterized using experimental setup version 2. A 400 Hz, 1.8 Oe
RMS field served as the test field and reference. Standard bipolar sweeping of magnetic bias
field was done and device sensitivity captured at each step. The same butterfly-shaped curve is
observed in Figure 73, indicating hysteresis effects enable a boost to the zero-external bias state.
In addition, the device exhibits enhancement to sensitivity at an optimal bias of 7.5 Oe which
agrees with other iron-nickel wire type devices. The device exhibits a zero-bias sensitivity of
10.9 μV/Oe and an optimal-bias sensitivity of 11.2 μV/Oe, both of which are significantly
smaller than the sensitivity values exhibited by the 5cm d31 FN sensor of 2.84 and 4.7 mV/Oe,
respectively. However, this result demonstrates the world’s first ever ME composite to operate
in a d15 mode and therefore serves as a proof-of-concept.
105
Figure 73: Sensitivity vs. magnetic bias field for the D15 sensor. A 1.8 Oe RMS test field alternating at
400 Hz was used for reference.
Despite the low sensitivity of this device, the noise floor was characterized within the
limitations of the experimental setup for completeness. Note that there exist significant
limitations in the ability to measure noise floor pertaining only to the device, which is detailed
later in this chapter. Voltage spectral density measurements were captured while applying a 0.01
Oe RMS, 400 Hz reference field to the 5 cm FN d15 device. The frequency span was set to 50Hz
(clipped in plot), centered at 400 Hz. Conversion between voltage spectral density and magnetic
spectral density data results in the magnetic noise spectra as shown in Figure 74. The 400 Hz, 1
μT reference signal is shown to be approximately one order of magnitude above the noise floor,
which is, on average, ~400 nT/√Hz.
106
Figure 74: Magnetic spectral density plot for the D15 sensor. A 400 Hz, 0.01 Oe RMS magnetic field is
applied for reference.
The first-ever realization of a d15 magnetoelectric composite exhibits low figures of merit
compared with its d31 ME counterparts. However, the proof-of-concept design may be improved
upon in the following ways. Due to the difficulty in tightly winding the PZT with gold wire, it is
suggested that electrodes be painted or applied lithographically. Secure contact between PZT and
electrodes will ensure maximum charge collection and therefore boost sensitivity. The electrodes
must be fabricated at a 45 degree angle to the y axis in order to detect the d51 coefficient. Ideally,
the electrode would consist of symmetrical, equally spaced, helixes that spiral the entire length of
the PZT tube at 45 degrees. An optimization study on electrode density may also be required.
107
This initial ME sensor holds promise to realization of improved ME composites utilizing the d51
mode and encourages future development of such devices.
2.10. Experimental Setup Considerations
The list of resources available at CM3IC is extensive, albeit incomplete. Mentioned
throughout this dissertation was the phrase “within limitations of the experimental setup”. Since
no standardized magnetoelectric characterization platform exists, an experimental setup was
designed at CM3IC from the ground up using available equipment. An initial design was first in
use in late 2009. By 2011, the experimental setup had then gone through several evolutions
before settling on design version 1 which was used to capture the majority of data presented
here. However, as noise floor measurements became increasingly of interest, the system had to
be modified to allow for an extra Gauss chamber and generation of uniform magnetic fields over
greater lengths.
It wasn’t until version 2 that the first major noise floor contributions was able to be
characterized as shown in Figure 75. Sensitivity measurements at CM3IC had been challenging
to capture and repeatable within a high margin of error. Typically certain times of the day, or
night, were best to capture data. As demonstrated in Figure 75, environmental noise was the
major noise contribution, preventing accurate characterization of the device’s noise floor. After
several stop-gap attempts to reduce the effects of background noise, the entire testing platform
was moved to a quiet environment outside of Boston.
108
Figure 75: Sensitivity vs. elapsed time for 5 days. Periodic background environmental noise is apparent
during day. 10mV/Oe variations observed during daytime, 4 mV/Oe at night.
Noise floor measurements were resumed with minimal effects from background noise at
which point the second major factor contributing to overall noise floor was discovered. After
several attempts to detect sensor-specific noise floor, an analysis of the equipment’s electronic
noise was undertaken. Electronic noise of the SR770 in two different state, shorted-input and
open-input was modeled and measured.
109
For the shorted-state, Johnson-Nyquist noise of the resistance of the short (~50 mOhms)
at room temperature were calculated and added to the noise floor specified in the instrument
along with 1/f noise. Johnson-Nyquist noise was modeled using equation (2.14) where the
voltage spectral density is a function of temperature (T) and resistance (R), and kB denotes
Boltzman’s constant.
√4 (2.14)
The vendor specified noise floor of the SR770, as specified in the user manual is 5
nVrms/√Hz. The 1/f noise was simply calculated in equation (2.15) where C, the DC offset
constant is divided by frequency.
√∗ (2.15)
Modeling of the shorted-input condition is compared with experimental data and shown
in Figure 76. The total modeled noise was calculated by summing noise contributions of
Johnson-Nyquist, vendor specified, and 1/f sources. Two shorted-input cases were measured to
exhibit excellent agreement with the modeled curves. One shorted-input case was for a 3 foot
long BNC cable where the clip leads were simply shorted together. The other case involved
shorting the BNC input jack with aluminum foil. In both cases the resistance contribution was so
110
minimal (~50 mOhms) it wasn’t included on the plot. Clearly, the modeled noise accurately
predicts the electronics noise floor exhibited for the shorted-input case.
Figure 76: Modeled and measured noise for the shorted-input case. Contributing factors for
modeled noise are shown along with total noise (sum).
Next, the open-input case was modeled. The same equations were used and the same
three contributing factors accounted for. The only change was the new contribution of the 1
MOhm input resistance. The input impedance of the SR770 is specified, and measured, to be 1
111
MOhm. Therefore, the Johnson-Nyquist noise contribution now becomes a dominant factor in
the total electronics noise. Modeled and measured data is shown in Figure 77 for the open-input
state. Again, excellent agreement between modeled noise and measured noise is observed. The
open-input noise floor was measured for two conditions; open at the BNC jack input on the front
panel of the SR770 and open 1meter long BNC cable attached to the front panel jack.
Figure 77: Modeled open-input state noise contributing factors and total, consisting of sum.
Measured data is overlaid.
These results demonstrate that the noise floor will be limited by the electronics when
measuring devices that exhibit impedance greater than 1MegaOhm. It is well known that
112
magnetoelectric devices are fabricated to exhibit very high impedances, > 20 MOhms, in order to
prevent leakage current, which causes reduction in output sensitivity. Therefore, the noise floor
of this experimental setup is limited to the electronics noise floor which sits at ~130 nVrms/√Hz.
To confirm this limitation, the 8cm FN device was connected to the SR770 and its output
compared with previous measured and modeled data as shown in Figure 78.
Figure 78: 8 cm FN wire voltage output noise floor is shown to be limited by the electronics noise
floor, with exception to a few spurious environmental noise peaks.
The conclusions drawn upon these results are such that the true noise floor of the ME
composites cannot be fully characterized unless the entire noise floor profile is >130 nVrms/√Hz.
For the majority of these devices, the noise floor bottoms out at the limit demonstrated by the
113
electronics such that only an effective, or pseudo-noise floor, can be measured. With that in
mind, it can be stated that the noise floor measurements presented in this work show a high-limit,
worst-case-scenario figure.
Some consideration has gone into solving this issue and two main solutions are
suggested. The dominant electronics noise contribution is due to the 1MOhm input impedance
which generates large amounts of JN noise for ME composites connected directly to that port.
The first potential solution is to build an impedance matching network that converts the high
impedance of the ME composite to low output impedance (lower the better) which can be input
to the SR770. This method would reduce electronics noise by approximately 1 order of
magnitude to exhibit a noise profile as seen in Figure 76. The second solution, and preferable, is
to use a low noise charge amplifier which has a low output impedance in line with the ME
composite and SR770. Charge detection instead of voltage detection is common practice in
piezoelectric devices.
A rudimentary battery powered charge amplifier based in Linear Technology’s LTC6240
amplifier was fabricated, as shown in Figure 79, which successfully reduced the 1 Hz noise floor
from 1.33 nT/√Hz to 428 pT/√Hz for the zero-biased condition, representing a 67% decrease in
noise floor as shown in Figure 80. Similarly, the charge amp reduced the 7.5 Oe bias, 1 Hz noise
floor from 1.16 nT/√Hz to 578 pT/√Hz, demonstrating a 50% reduction in noise. It is suggested
that use of a professional-grade charge amplifier will result in lower noise floor figures of merit.
114
Figure 79: Schematic of charge amplifier circuit (left) used to fabricate battery powered charge amplifier
used in noise floor measurements (right).
Figure 80: Low frequency noise floor measurements for zero-biased and 7.5 Oe biased 8cm FN sensor
with and without charge amplifier.
115
Chapter 3. Conclusion
The tube-topology magnetoelectric magnetic field sensors described in this work have
achieved several exciting figures of merit. The highly sensitive zero-external bias operation
demonstrated by these devices is the most exciting and technologically important achievement
this work contributes to the field. A summary of additional contributions is shown in the
following.
3.1. Research Summary
The tube-topology ME composite offers numerous advantages over similar technologies
and ME topologies as shown in Table 3. D31 and D33 Sensors were measured in-house using
experimental setup version 1 and offer the most accurate direct comparison. Performance metrics
of ME devices published by groups and institutions around the world is also included.
116
Table 3: Overview and Comparison of Device Performance
Device Zero-Bias Sensitivity (mv/Oe)
Volume (cm3)
Zero-Bias Sensitivity
Density /
Zero-Bias 1-Hz Noise Floor
(nT/√Hz)
Cost Feature
8cm FN 16.5 0.274 60.2 ~2 $ Miniature,
Directional, Low Freq.
5cm FN 8.1 0.160 49.1 ~2 $ Miniature,
Directional, Low Freq.
7.5 cm WB21 9.8 0.245 40.0 ~2 $ Miniature,
Directional, Low Freq.
D31 Sensor 0.46 0.01132 40.6 ~100,000 $$ Miniature,
Planar
D33 Sensor 1.5 0.41 3.66 ~2000 $$
High optimally biased output
MEMS Cantilever[69]
~0.0129 ~9.296E-7 ~12000 ~775,000 $$$ High
Sensitivity Density
PZT/Metglas®[70] <~2 >~0.084 ~23.8 >~2 $$ D33,
Requires Charge Amp
PMN-PT/Metglas®[70]
<~5 >~0.084 ~59.5 >~0.75 $$ D33,
Requires Charge Amp
PZN-PT/Metglas®[70]
<~1 >~0.084 ~11.9 >~0.5 $$ D33,
Requires Charge Amp
In this table, the tube-topology composites are compared with D31 Sensor, D33 Sensor
and several others that represent types of state-of-the-art heterostructural composites. The FeNi
wire type tube-topology composites outperform in nearly every category, except for volume.
However, the FN devices exhibit higher sensitivity density than the miniature D31 Sensor. The
WB21 device has a slightly lower sensitivity density than the D31 device.
117
The tube-topology composites hold immense potential for use as magnetic field sensors,
as justified by this work. Most excitingly, they exhibit high sensitivity at zero-external bias field.
This feature gives way toward realization of magnetoelectric magnetic field sensing platforms
that, unlike hall-effect, flux gate, and SQUID magnetometers, operate completely passively. No
bulky electromagnets, permanent magnets, or conditioning circuitry is required. The
transduction of magnetic field energy to electric field energy occurs through a unique and
cleverly engineered way that utilizes intrinsic material properties.
In this work, the tube-topology ME composites are considered for use as magnetic field
sensors, and characterized accordingly. However, these composites hold tremendous potential
for use in numerous creative ways. For instance, the magnetization in the wire may be controlled
by application of voltage across PZT tube thickness, via strain. In this way, a voltage controlled
magnetic field generator may be realized and fabrication of such devices have already begun.[71]
Similarly, voltage control of magnetization can be applied to devices that exhibit strong
dependence on permeably, such as inductors and transformers. It is simple to envision a voltage-
tunable RF or chip inductor that utilizes the magnetoelectric effect to vary permeability. In an
opposite manner, high frequency and RF capacitors that are magnetically tunable may also be
realized.
Global interest in magnetoelectric devices is growing. It is with great optimism that these
works helps build upon the scientific community’s knowledge base to ultimately improve the
technology.
118
3.2. Improvements for Future Development
In brief, the following points, suggestions, and comments are listed here as logical next-
steps towards for progressing the research within.
1) The full dynamic range, especially upper limit, has not been evaluated. Devices show
linear response with test field amplitude up to 1.25 Oe, however saturation effects are
inherent to these devices. Characterizations of these effects are of interest.
2) A broadband frequency sweep has not been applied to these devices. Devices thus far
have shown relatively flat frequency response up to 5 KHz, however, for audio
applications, characterization up to 20 KHz is required. Evaluation of sensor EMR
may reveal interesting sensitivity figures of merit.
3) Pulse time response characterizing lag time between application of magnetic field and
generation of output charge has not been evaluated. Such results are of great interest.
4) Thermal response characterizing an operational temperature range is valuable.
5) Directionality testing of these devices should be done. Presumably the tube-topology
design preferentially reacts to axially applied fields. Evaluation of this may show that
these devices are ideally suited for vector-magnetometry and be used in GPS and
compass applications.
6) Investigation of application beyond magnetic field sensing, as previously mentioned,
may reveal novel use for these composites.
119
Appendix
A.1. Experimental Setup 1 – Equipment List
1) Dual-nesting Helmholtz coil.
2) Dual-layered Gauss chamber.
3) Stanford Research Systems SR770 FFT Spectrum Analyzer.
4) Stanford Research Systems SR830 Lock-in Amplifier.
5) Sorensen DCR 80-12B DC Power Supply.
6) Lakeshore 421 Gauss meter.
a. Hall Probe Model # MNT-4E04-VH.
b. Gamma Probe Model # MLA-5006-HJ.
7) Keithley DMM 199.
8) Fluke DMM 87V.
9) Non-magnetic table-top vice grip with tweezers for mounting devices (or similar).
A.2. Experimental Setup 2 – Equipment List
1) Solenoid Coil.
2) Triple-layered Gauss chamber.
3) Stanford Research Systems SR770 FFT Spectrum Analyzer.
4) Sorensen DCR 80-12B DC Power Supply.
5) AMREL PS30-1.2D Programmable DC Power Supply.
6) Lakeshore 421 Gauss meter.
a. Hall Probe Model # MNT-4E04-VH.
b. Gamma Probe Model # MLA-5006-HJ.
7) Keithley DMM 199.
8) Fluke DMM 87V.
9) Non-magnetic table-top vice grip with tweezers for mounting devices (or similar).
120
A.3. LabView Program
User Interface:
121
Block Diagram:
122
A.4. MATLAB Demagnetization Factor Calculator
% S. Gillette % 11/11/2013 % Demagnetization Factor Calculator %========================================================================== % Cleaning Services clear close all clc %========================================================================== % User Input a = 0.1; % Enter dimension along x axis. b = 0.1; % Enter dimension along y axis. c = 0:0.001:10; % Enter dimension along z axis. %========================================================================== l = (a.*b)./(a+b); Nx = 4*pi*((c./a)./(1+(c./l))); Ny = 4*pi*((c./b)./(1+(c./l))); Nz = 4*pi*((1)./(1+(c./l))); figure(1) plot(c,Nx./(4*pi),'r','LineWidth',4) hold on plot(c,Ny./(4*pi),'g','LineWidth',2) plot(c,Nz./(4*pi),'b','LineWidth',2) title('Demag Factors - Linear Scale','Fontsize',12) xlabel('Wire Length (cm)','FontSize',10) ylabel('Demag Factor (*4\pi)','FontSize',10) legend('Nx','Ny','Nz','Location','Best') figure(2) semilogy(c,Nx./(4*pi),'r','LineWidth',4) hold on semilogy(c,Ny./(4*pi),'g','LineWidth',2) semilogy(c,Nz./(4*pi),'b','LineWidth',2) title('Demag Factors - Log Scale','Fontsize',12) xlabel('Wire Length (cm)','FontSize',10) ylabel('Demag Factor (*4\pi)','FontSize',10) legend('Nx','Ny','Nz','Location','Best') Sum = 4*pi Total = Nx+Ny+Nz
123
References
1. Curie, P., [Transl.] On symmetry in physical phenomena. Symmetry of an electric field of a magnetic field. Journal De Physique, 1894. 3e series 3.
2. Lifshitz, L.D.L.E.M., Electrodynamics of Continuous Media. Vol. 8. 1960, Oxford, London, New York, Paris: Pergamon Press.
3. Dzyaloshinskii, I.E., Sov. Phys. JETP, 1959. 10. 4. Spaldin, N.A. and M. Fiebig, The Renaissance of Magnetoelectric Multiferroics. Science,
2005. 309(5733): p. 391-392. 5. Nan, C.-W., et al., Multiferroic magnetoelectric composites: Historical perspective,
status, and future directions. Journal of Applied Physics, 2008. 103(3): p. 031101-031101-35.
6. Fiebig, M., Revival of the magnetoelectric effect. Journal of Physics D: Applied Physics, 2005. 38(8): p. R123.
7. Wang, Y., et al., Multiferroic magnetoelectric composite nanostructures. NPG Asia Mater, 2010. 2: p. 61-68.
8. Zhai, J., et al., Magnetoelectric Laminate Composites: An Overview. Journal of the American Ceramic Society, 2008. 91(2): p. 351-358.
9. Kimura, T., et al., Magnetic control of ferroelectric polarization. Nature, 2003. 426(6962): p. 55-58.
10. Mochizuki, M. and N. Furukawa, Mechanism of Lattice-Distortion-Induced Electric-Polarization Flop in the Multiferroic Perovskite Manganites. Journal of the Physical Society of Japan. 78(Copyright (C) 2009 The Physical Society of Japan): p. 053704.
11. Kitagawa, Y., et al., Low-field magnetoelectric effect at room temperature. Nat Mater, 2010. 9(10): p. 797-802.
12. Wang, W., et al., Room-Temperature Multiferroic Hexagonal LuFeO_3 Films. Physical Review Letters, 2013. 110(23): p. 237601.
13. Gehring, G.A., On the microscopic theory of the magnetoelectric effect. Ferroelectrics, 1994. 161(1): p. 275-285.
14. Srinivasan, G., Magnetoelectric Composites. Annual Review of Materials Research, 2010. 40(1): p. 153-178.
15. Kambale, R.C., D.-Y. Jeong, and J. Ryu, Current Status of Magnetoelectric Composite Thin/Thick Films. Advances in Condensed Matter Physics, 2012. 2012: p. 15.
16. Fang, F., Y.T. Xu, and W. Yang, Magnetoelectric coupling of laminated composites under combined thermal and magnetic loadings. Journal of Applied Physics, 2012. 111(2): p. -.
124
17. Ryu, J., et al., Effect of the Magnetostrictive Layer on Magnetoelectric Properties in Lead Zirconate Titanate/Terfenol-D Laminate Composites. Journal of the American Ceramic Society, 2001. 84(12): p. 2905-2908.
18. Lopatin, S., I. Lopatina, and I. Lisnevskaya, Magnetoelectric PZT/ferrite composite material. Ferroelectrics, 1994. 162(1): p. 63-68.
19. Nan, C.W., et al., A three-phase magnetoelectric composite of piezoelectric ceramics, rare-earth iron alloys, and polymer. Applied Physics Letters, 2002. 81(20): p. 3831-3833.
20. Shuxiang, D., et al., A strong magnetoelectric voltage gain effect in magnetostrictive-piezoelectric composite. Applied Physics Letters, 2004. 85(16): p. 3534-3536.
21. Dong, S., J.-F. Li, and D. Viehland, Characterization of magnetoelectric laminate composites operated in longitudinal-transverse and transverse–transverse modes. Journal of Applied Physics, 2004. 95(5): p. 2625-2630.
22. Dong, S., et al., Extremely low frequency response of magnetoelectric multilayer composites. Applied Physics Letters, 2005. 86(10): p. 102901.
23. Liu, Y.X., et al., Effect of magnetic bias field on magnetoelectric coupling in magnetoelectric composites. Journal of Applied Physics, 2003. 94(8): p. 5118-5122.
24. Van Den Boomgaard, J., A.M.J.G. Van Run, and J.V. Suchtelen, Magnetoelectricity in piezoelectric-magnetostrictive composites. Ferroelectrics, 1976. 10(1): p. 295-298.
25. Ohno, H., et al., Electric-field control of ferromagnetism. Nature, 2000. 408(6815): p. 944-946.
26. Eerenstein, W., N.D. Mathur, and J.F. Scott, Multiferroic and magnetoelectric materials. Nature, 2006. 442(7104): p. 759-765.
27. Kadomtseva, A.M., et al., Phase transitions in multiferroic BiFeO3 crystals, thin-layers, and ceramics: enduring potential for a single phase, room-temperature magnetoelectric ‘holy grail’. Phase Transitions, 2006. 79(12): p. 1019-1042.
28. Yuan, G.L., et al., Structural transformation and ferroelectromagnetic behavior in single-phase Bi1−xNdxFeO3 multiferroic ceramics. Applied Physics Letters, 2006. 89(5): p. -.
29. Rivera, J.P., A short review of the magnetoelectric effect and related experimental techniques on single phase (multi-) ferroics. The European Physical Journal B, 2009. 71(3): p. 299-313.
30. Dragan, D., Ferroelectric, dielectric and piezoelectric properties of ferroelectric thin films and ceramics. Reports on Progress in Physics, 1998. 61(9): p. 1267.
31. Gautschi, G., Piezoelectric Sensorics: Force, Strain, Pressure, Acceleration and Acoustic Emission Sensors, Materials and Amplifiers. 2002: Springer.
32. Engdahl, G., Handbook of Giant Magnetostrictive Materials. 2000, San Diego: Academic Press.
33. Callen, E. and H.B. Callen, Magnetostriction, Forced Magnetostriction, and Anomalous Thermal Expansion in Ferromagnets. Physical Review, 1965. 139(2A): p. A455-A471.
34. Bozorth, R.M. and J.G. Walker, Magnetic Crystal Anisotropy and Magnetostriction of Iron-Nickel Alloys. Physical Review, 1953. 89(3): p. 624-628.
35. Valasek, J., Piezo-Electric and Allied Phenomena in Rochelle Salt. Physical Review, 1921. 17(4): p. 475-481.
36. Zhang, J.X., G. Sheng, and L.Q. Chen, Large electric field induced strains in ferroelectric islands. Applied Physics Letters, 2010. 96(13): p. -.
125
37. Huber, J.e., et al., A constitutive model for ferroelectric polycrystals. Journal of the Mechanics and Physics of Solids, 1999. 47(8): p. 1663-1697.
38. Landis, C.M., Non-linear constitutive modeling of ferroelectrics. Current Opinion in Solid State and Materials Science, 2004. 8: p. 11.
39. Bailoni, M., Mathematical Modeling and Simulation of Magnetostrictive Materials, in Comsol Conference 2008 Worldwide. 2008: Hannover.
40. Artec. Surface-Adhesive Piezo Pickup. Retrieved 2 16, 2011]; Available from: http://www.artecsound.com/acou/index.html.
41. PI. P-855 Miniature Piezo Actuator. Retrieved 2 16, 2011]; Available from: http://www.physikinstrumente.com/en/products/prdetail.php?sortnr=100650.
42. FeONIC. FeONIC F1.3 DML AUDIO DRIVE. Retrieved 2 16, 2011]; Available from: http://www.feonic.com/#f13Info.
43. Sensors, M. Linear-Position Sensors. Retrieved 2 16, 2011]; Available from: http://www.mtssensors.com/products/linear-position-sensors/index.html.
44. Hu, B., et al., Piezoelectric properties of epitaxial Pb(Zr0.525, Ti0.475)O3 films on amorphous magnetic metal substrates. Journal of Applied Physics, 2012. 111(7): p. -.
45. Hu, B., et al., Epitaxial growth of Pb(Zr0.53Ti0.47)O3 films on Pt coated magnetostrictive amorphous metallic substrates toward next generation multiferroic heterostructures. Journal of Applied Physics, 2012. 111(6): p. -.
46. Deng, C., et al., Magnetic-electric properties of epitaxial multiferroic NiFe2O4 & BaTi03 heterostructure. Journal of Applied Physics, 2007. 102(7): p. 074114-074114-5.
47. Junyi, Z., et al., Giant magnetoelectric effect in Metglas/polyvinylidene-fluoride laminates. Applied Physics Letters, 2006. 89(8): p. 083507-083507-3.
48. Gillette, S.M., et al., Improved Sensitivity and Noise in Magneto-Electric Magnetic Field Sensors by Use of Modulated AC Magnetostriction. Magnetics Letters, IEEE, 2011. 2: p. 2500104-2500104.
49. Das, J., et al., Enhancement in the field sensitivity of magnetoelectric laminate heterostructures. Applied Physics Letters, 2009. 95(9): p. 092501-092501-3.
50. Park, G., Overview of Energy Harvesting Systems, T.F.E.I. Workshop, Editor. 2005, Los Alamos National Laboratory: Engineering Institute of Engineering Sciences & Applications.
51. Phillips, J.R., Piezoelectric Technology Primer, CTS Wireless Components: Albuquerque.
52. Lenz, J. and A.S. Edelstein, Magnetic sensors and their applications. Sensors Journal, IEEE, 2006. 6(3): p. 631-649.
53. Phan, M.-H. and H.-X. Peng, Giant magnetoimpedance materials: Fundamentals and applications. Progress in Materials Science, 2008. 53(2): p. 323-420.
54. Jia, Y., et al., Magnetoelectric effect in laminate composite of magnets/0.7Pb(Mg1⁄3Nb2⁄3)O3–0.3PbTiO3 single crystal. Applied Physics Letters, 2006. 88(14): p. -.
55. Chen, Y., et al., Time domain analyses of the converse magnetoelectric effect in a multiferroic metallic glass-relaxor ferroelectric heterostructure. Applied Physics Letters, 2009. 95(18): p. -.
56. Liu, M., et al., Giant Electric Field Tuning of Magnetic Properties in Multiferroic Ferrite/Ferroelectric Heterostructures. Advanced Functional Materials, 2009. 19(11): p. 1826-1831.
126
57. Geiler, A.L., et al., Multiferroic heterostructure fringe field tuning of meander line microstrip ferrite phase shifter. Applied Physics Letters, 2010. 96(5): p. 053508-053508-3.
58. Castel, V. and C. Brosseau, Magnetic field dependence of the effective permittivity in BaTiO3⁄Ni nanocomposites observed via microwave spectroscopy. Applied Physics Letters, 2008. 92(23): p. -.
59. Castel, V., C. Brosseau, and J. Ben Youssef, Magnetoelectric effect in BaTiO3/Ni particulate nanocomposites at microwave frequencies. Journal of Applied Physics, 2009. 106(6): p. -.
60. Chen, Y., et al., Microwave magnetoelectric coupling and ferromagnetic resonance frequency tuning of a Co_2MnSb/GaAs/PZN-PT heterostructure. Physical Review B, 2011. 83(10): p. 104406.
61. Corp., S.M. 11/5/13]; Available from: http://www.smart-material.com/PZTFiber-product-main.html.
62. Li, M., et al., Enhanced Sensitivity and Reduced Noise Floor in Magnetoelectric Laminate Sensors by an Improved Lamination Process. Journal of the American Ceramic Society, 2011. 94(11): p. 3738-3741.
63. Vittoria, C., ed. Magnetics, Dielectrics, and Wave Propagation with MATLAB Codes. 2011, CRC Press: Boca Raton. 450.
64. Balanis, C.A., ed. Advanced Engineering Electromagnetics. 1989, John Wiley & Sons, Inc.: Hoboken.
65. Li, M., et al., Theoretical modelling of magnetoelectric effects in multi-push–pull mode Metglas/piezo-fibre laminates. Journal of Physics D: Applied Physics, 2012. 45(35): p. 355002.
66. Chen, Y., et al., Quasi-one-dimensional miniature multiferroic magnetic field sensor with high sensitivity at zero bias field. Applied Physics Letters, 2011. 99(4): p. 042505-042505-3.
67. Isaku Kanno, e.a., Evaluation of Intrinsic Shear Piezoelectric Coefficient d15 of c-Axis Oriented PZT Films. Applied Physics Express, 2009. 2.
68. Gaudenzi, P., Smart Structures: Physical Behaviour, Mathematical Modelling and Applications. 2009: Wiley.
69. Stephan, M., et al., MEMS magnetic field sensor based on magnetoelectric composites. Journal of Micromechanics and Microengineering, 2012. 22(6): p. 065024.
70. Gao, J., et al., Comparison of noise floor and sensitivity for different magnetoelectric laminates. Journal of Applied Physics, 2010. 108(8): p. -.
71. Fitchorov, T., et al., Tunable fringe magnetic fields induced by converse magnetoelectric coupling in a FeGa/PMN-PT multiferroic heterostructure. Journal of Applied Physics, 2011. 110(12): p. 123916-123916-4.
