Microwave Devices Utilizing Magnetoelectric Hexaferrite

Materials for Emerging Communication Systems

A Dissertation Presented

by

Khabat Ebnabbasi

to

The Department of Electrical and Computer Engineering

in partial fulfillment of the requirements

for the degree of

Doctor of Philosophy

in

Electrical Engineering

Northeastern University

Boston, Massachusetts

November, 2012

NORTHEASTERN UNIVERSITY

Graduate School of Engineering

Thesis Title: Microwave Devices Utilizing Magnetoelectric Hexaferrite Materials for

Emerging Communication Systems

Author: Khabat Ebnabbasi

Department: Electrical and Computer Engineering

Approved for Dissertation Requirement for the Doctor of Philosophy Degree

______________________________________________ ____________________

Dissertation Advisor: Carmine Vittoria Date

______________________________________________ ____________________

Thesis Reader: Fabrizio Lombardi Date

______________________________________________ ____________________

Thesis Reader: Matteo Rinaldi Date

______________________________________________ ____________________

Department Chair: Ali Abur Date

Graduate School Notified of Acceptance:

______________________________________________ ____________________

Director of the Graduate School: Sara Wadia Fascetti Date

i

ABSTRACT

Ferrite materials are widely used in passive and tunable electromagnetic signal

processing devices such as phase shifters, circulators, isolators, and filters. These materials

can also be used as tunable antenna substrates and EMI suppression cores. Due to their

excellent dielectric properties, ferrites possess the advantages of low loss and high power

handling relative to semiconductors. Typically, parameters of magnetic materials are

controlled by an external magnetic field thus allowing for tuning of device performance.

Magnetic fields are usually generated using permanent magnets or current driven coils,

leading to relatively large component size, weight, and cost, as well as slow response time

in comparison to semiconductor-based technologies. Magneto-electric materials can be a

practical solution to control the magnetic parameters of ferrites by electric field and/or

voltage and would eliminate permanent magnets and tuning coils to overcome most of the

disadvantages in the use of ferrites for microwave devices. A situation where ferrites are

compatible with active components based on semiconductors would become a reality.

Furthermore, key advantages of ferrites, including low insertion loss and high power

handling capability could be exploited without the penalty of added size, weight, and cost,

as well as increased response time.

Recently, magnetically induced ferroelectric materials have been discovered giving rise

to the hope that it may be feasible to tune ferrites by applying voltage. From a practical

point of view, however, their magneto-electric effects are useless because they operate

ii

only far below room temperature (for example, 28 K in TbMnO3 and 230K in CuO).

Furthermore, many such materials require a strong magnetic field, on the order of Tesla, in

order to magnetically induce ferroelectric response, rendering them impractical.

Multi-ferroic composite materials have been proposed to generate internal magnetic

fields via voltage. Multi-ferroic composites usually consisted of magnetostrictive and

ferroelectric or piezoelectric slabs in physical contact whereby magnetic field sensors have

been implied and fabricated so far. Also, small shifts in ferromagnetic resonance (FMR)

have been observed using magnetoelectric composites in the presence of an electric field.

Tuning of ferrite microwave devices by an electric field or voltage is still not practical with

present composite structures.

In this work we propose an alternative approach to this problem. A single layer of

magneto-electric Z-type, Sr3Co2Fe24O41, which has strong ME effects at room

temperature, is proposed to induce magnetic parameter changes with application of

voltage. The advantage of a single layer is that it is simpler to utilize to tune ferrite

devices. Sr3Co2Fe24O41 is identified as a Z-type hexaferrite consisting of S, R, and T

“spinel” blocks which in the T block the Fe-O-Fe bond angles were slightly deformed to

affect the super exchange interaction between the Fe ions and induce the spiral spin

configuration in Sr3Co2Fe24O41. Changes in the spin spiral configuration in the presence

of an electric field induce changes in the magnetization . This physical mechanism

for the ME effect is very different from the mechanisms applicable to multiferroic

materials in the past. This new mechanism opens up new properties or opportunities in

iii

the physics and applications of ME materials in engineering. The previously most used

technique to explore ME effects was ferromagnetic resonance (FMR). In the past FMR

frequency shifts were measured with an applied in the presence of a permanent

magnet. There has never been a report on permeability measurement in ME material with

application of an electric field, although there are many reports on FMR shifts. The

measurement of FMR frequency shifts is ineffectual in our case, because (a) the shifts are

extremely small, (b) they are strongly damped in the new mechanism, and (c) and a

permanent magnet still is needed. Hence, we have devised a new measurement method

whereby the permeability of our material is measured directly via a modified coaxial line

technique. We refer to these measurements as “converse” ME measurements and a

physical model for the effect is provided. The application of strains the material

thereby changes the physical structure of the spiral spin configuration. It is this physical

motion of the spiral response to that induces a change in magnetization . We refer

to this model as the “slinky helix” model. Our model should be contrasted with the model

for the ME effect in multiferroics as well as ferromagnetic metal films wherein the band

energies of the up and down spin are modified by the electric fields at the interface

between phase separated ferromagnetic and ferroelectric films. The change in band

splitting leads to a change in surface magnetization.

iv

Table of Contents

Chapter 1. Magnetoelectric Overview............................................................................1

1. Introduction...........................................................................................................1

1.1 Ferroic Materials.............................................................................................1

1.2 Multiferroics ...................................................................................................2

2. Magnetoelectric Coupling.....................................................................................3

3. Parity and time reversal symmetry in Ferroics......................................................7

4. Nonlinear coupling................................................................................................8

5. Indirect coupling...................................................................................................9

6. Coupling constants calculation...........................................................................10

7. Single-phase studies............................................................................................11

8. Multiferroics.......................................................................................................12

9. Devices...............................................................................................................13

References..............................................................................................................15

Chapter 2. Magnetoelectric Effects on Single Phase of Z-type and M-type

Hexaferrites at Room Temperature...........................................................20

1. Introduction........................................................................................................20

2. Sr Z-type Experimental Material Growth Procedure..........................................22

2.1 Sr Z-type Indirect Converse Magnetoelectric Experimental Analysis.........27

2.2 Orientation of Polycrystalline Sr Z-type.......................................................31

3. M-type Experimental Material Growth Procedure..............................................38

4. Z- and M-type Hexaferrites ME Effect Comparison...........................................39

4.1 Resistivity Measurements..............................................................................39

4.2 ME Effect Measurements..............................................................................40

5. Conclusions..........................................................................................................43

References...............................................................................................................45

Chpater 3. Coaxial Line Technique to Measure Constitutive Parameters in Magneto

Electric Ferrite Materials............................................................................47

1. Introduction..........................................................................................................47

2. Theory of the Design...........................................................................................49

2.1 Two port design..............................................................................................49

2.2 One port design..............................................................................................52

3. Experimental Measurements................................................................................56

4. Conclusions..........................................................................................................62

References................................................................................................................63

v

Chapter 4. Converse Magnetoelectric Experiments on a Room-Temperature

Spirally Ordered Hexaferrite......................................................................64

1. Introduction..........................................................................................................64

2. Experimental Results...........................................................................................68

2.1 Experimental Material Growth......................................................................68

2.2 Magnetoelectric Measurement Technique.....................................................68

2.3 Experimental Magnetoelectric Measurements..............................................74

3. Conclusions..........................................................................................................80

4. Appendix..............................................................................................................80

References................................................................................................................85

Chapter 5. Strong Magnetoelectric Coupling in Hexaferrites at Room

Temperature..................................................................................................87

1. Introduction..........................................................................................................87

2. Experimental Measurements................................................................................88

3. Conclusions..........................................................................................................94

References................................................................................................................95

Chapter 6. Microwave Magnetoelectric Devices...........................................................96

1. Introduction..........................................................................................................96

2. Multi-Phase Magnetoelectric Microwave Phase Shifter......................................99

3. Single-Phase Magnetoelectric Microwave Phase Shifter..................................102 3.1 Meander Line Micro-strip............................................................................103 3.2 LC Phase Shifter Theory and Design...........................................................104

References..............................................................................................................111

Chapter 7. Discussion and Conclusion.........................................................................113

vi

Table of Figures

Figure 1-1 Circular loop model of magnetic material lattice structure............................................................1

Figure 1-2 Coupling order of Ferroics and their relations and distinctions.....................................................2

Figure 1-3 Time-reversal and parity symmetry in Ferroelectric, Ferromagnetic and Multiferroic materials..3

Figure 2-1 Orientation of magnetic moment of Sr-Z, Ba-Z and BaSr-Z hexaferrites.....................................4

Figure 2-2 Planetary mono mill Pulverisette 6 to grind particles....................................................................5

Figure 2-3 X-ray diffraction pattern of the polycrystalline Sr3Co2Fe24O41 at room temperature. The black

line represents the reference peak positions for the Ba Z-type hexaferrite (Ref. ICDD # 19-0097. Space

group: P63/mmc(194)).....................................................................................................................................6

Figure 2-4 Ferromagnetic resonance measuring instrumentation...................................................................7

Figure 2-5 FMR spectrum of polycrystalline Sr3Co2Fe24O41 at room temperature for magnetic field (H)

applied parallel to slab plane............................................................................................................................8

Figure 2-6 I-E and ρ-E curves of the polycrystalline Sr3Co2Fe24O41 at room temperature after sintering in

O2......................................................................................................................................................................9

Figure 2-7 Vibrating sample magnetometer (VSM) instrumentation. The sample is placed between the

pickup coils and voltage is applied to the sample through the conductor plates............................................10

Figure 2-8 Polycrystalline Sr3Co2Fe24O41 magnetization as a function of external applied H parallel to slab

plane and perpendicular to applied E field at room temperature....................................................................11

Figure 2-9 The zoomed in change in remanence magnetization measurements shown in Figure 2-7 over

low magnetic field..........................................................................................................................................12

Figure 2-10 Polycrystalline Sr3Co2Fe24O41 remanent magnetization change vs electric feild for a typical

sample with 0.5mm thickness at room temperature.......................................................................................13

Figure 2-11 Change in temperature in the Sr Z-type sample versus electric field........................................14

Figure 2-12 Change in dielectric constant over frequency versus applied external magnetic field..............15

Figure 2-13 Polycrystalline Sr3Co2Fe24O41 powder orientation set up..........................................................16

Figure 2-14 SEM photographs of the ground particles for different milling durations.................................17

Figure 2-15 Photograph of 0.5T rotating permanent magnet........................................................................18

Figure 2-16 Schematic of orientation procedure...........................................................................................19

Figure 2-17 VSM data of Sr-Z. Red and black dashed lines represent after orientation before orientation,

respectively.....................................................................................................................................................20

Figure 2-18 X-ray diffraction pattern of polycrystalline SrCo2Ti2Fe8O19 at room temperature. The black

line represents the reference peak positions for the Ba M-type hexaferrite (PDF # 27-1433. Space group:

vii

P63/mmc(194))...............................................................................................................................................21

Figure 2-19 Current versus electric field for Sr-Z and SCTFO.....................................................................22

Figure 2-20 Change in remanence magnetization (Mr) of M-type (sintered in air) for (a) Edc perpendicular

to H and (b) Edc parallel to H..........................................................................................................................23

Figure 2-21 The change in remanence magnetization (Mr) of Z-type sintered in O2, M-type sintered in air

and O2 versus DC electric field.......................................................................................................................24

Figure 3-1 Non-reciprocal ferrite network equivalent of transmission line..................................................50

Figure 3-2 Two port coaxial line schematic for ferrite magneto-electric (ME) effect measurement............51

Figure 3-3 Circuit model of the medium in connection with the dangling wires..........................................52

Figure 3-4 One port coaxial line schematic for ferrite magneto-electric (ME) effect measurement.............53

Figure 3-5 Coaxial line parts and assembled device......................................................................................58

Figure 3-6 Measured I-V characteristic of polycrystalline Sr Z-type hexaferrite.........................................59

Figure 3-7 Measured real and imaginary parts of the ME ferrite permeability versus frequency for E=0

kV/cm.............................................................................................................................................................59

Figure 3-8 The theoretical calculation and experimental measurement of magnetic permeability change

versus frequency for E=5 kV/cm....................................................................................................................60

Figure 3-9 The magnetic permeability change versus electric field and frequency when Mr is parallel and

anti-parallel to E.............................................................................................................................................60

Figure 3-10 The magnetic permeability change versus electric field and frequency when Mr is

perpendicular to E..........................................................................................................................................61

Figure 3-11 Phase change versus electric field and frequency when Mr is parallel to E...............................61

Figure 3-12 Phase change versus electric field and frequency when Mr is anti-parallel to E......................62

Figure 4-1 (a) Crystal structure of a part of the hexagonal unit cell. (b) Spiral spin order............................65

Figure 4-2 Real and imaginary parts of the polycrystalline Sr Z-type permeability versus frequency.........69

Figure 4-3 Coaxial line schematic.................................................................................................................71

Figure 4-4 Static electric and magnetic fields bias conditions of the hexaferrite slab in (a) E parallel or

anti-parallel to Mr and in (b) E perpendicular to Mr......................................................................................73

Figure 4-5 Magnetic permeability change versus electric field over a microwave frequency range when M

is parallel and antiparallel to E. (a) Theoretical calculation and (b)experimental measurement for E = 5

KV/cm.............................................................................................................................................................75

Figure 4-6 Magnetic permeability change versus electric field over a microwave frequency range when M

is perpendicular to E.......................................................................................................................................76

Figure 4-7 (a) Applied electric field over the slab to measure strain, (b) Electrostriction strain of

polycrystalline Sr Z-type versus electric field................................................................................................77

Figure 4-8 Spin spiral configuration for different directions of E. (a) E = 0, (b) E parallel to M, and (c) E

antiparallel to M..............................................................................................................................................80

Figure 5-1 SEM micrograph of single crystal of Z-type hexaferrites, Sr3Co2O24O41....................................89

Figure 5-2 Room-temperature X-ray diffraction pattern...............................................................................89

Figure 5-3 Ferromagnetic resonance at room-temperature (derivative absorption versus Hext)....................90

Figure 5-4 Hysteresis loops change versus electric field with the magnetic field applied parallel (//) and

viii

perpendicular () to the slab plane.................................................................................................................91

Figure 5-5 Remanence magnetization change versus electric field with the magnetic field applied parallel

(//) to the slab plane........................................................................................................................................92

Figure 5-6 Change in remanence magnetization versus electric field...........................................................92

Figure 5-7 change in capacitance versus magnetic field...............................................................................93

Figure 6-1 Potential and current applications of ferrite materials and devices in communication systems

and their operating frequency range...............................................................................................................97

Figure 6-2 Schematics of fabricated magnetoelectric nonreciprocal microwave phase shifter in [10]......101

Figure 6-3 Schematics of meander line microstrip......................................................................................104

Figure 6-4 Microwave network consisting of elements connected in series...............................................105

Figure 6-5 Phase shift by applying electric field or voltage........................................................................107

Figure 6-6 Simulated phase shifter structure (a) without and (b) with the ME material introduced with

Lorentz model...............................................................................................................................................108

Figure 6-7 Insertion loss and phase simulation results................................................................................109

Figure 6-8 The fabricated phase shifter........................................................................................................110

Figure 6-9 Measured phase shift by applying voltage for the fabricated phase shifter with no capacitor..110

1

Chapter 1. Magnetoelectric Overview

1. Introduction

In this chapter, the physical concepts of single phase ferroically ordered materials and

multi-ferroic composite structures are presented. A ferroic material may be magnetically

or electrically ordered without the application of external magnetic, H, or electric, E,

fields. Combining various ferroics potentially can be used in different applications such

as sensors and communication devices and circuits. Understanding of magnetic and

electrical properties of ferroic materials helps us to take advantage of special coupling

phenomena in ferroics to push current technology toward smaller, cheaper, more compact

and more efficient devices [1].

1.1 Ferroic Materials

Here are some basic definitions of ordered ferroic materials that we plan to utilize for

various applications:

• Antiferromagnetic: magnetic moments cancel each other completely within each

magnetic unit cell for temperatures below the Neel temperature. An example is

the heavy-fermion superconductor URu2Si2. Better known examples

include chromium, alloys such as iron manganese (FeMn), and oxides such as

nickel oxide (NiO).

• Ferrimagnetic: magnetic moments cancel each other incompletely and there is a

net magnetization that can be rotated by an external magnetic field. The ordering

2

temperature is the Neel temperature which for most ferrites is well above room

temperature.

• Ferromagnetic: possesses spontaneous magnetization. Ferrites are usually

insulators for temperatures below the Currie temperature. Most ferromagnets tend

to be metallic.

• Antiferroelectric: electric dipole moments cancel each other completely within

each crystallographic unit cell. This is the analogue of antiferromagnetism.

• Ferroelectric: possesses a spontaneous electric polarization for temperatures

below the Currie temperature. It is the analogue of ferromagnetism.

• Ferroelastic: possesses a stable spontaneous deformation with hysteretically

versus an external stress.

Figure 1-1 Circular loop model of magnetic material lattice structure.

1.2 Multiferroics

Multiferroics are materials that exhibit two or more ordered ferroic phases. In most

cases of interests the multiferroics interact with each other.

• Magnetoelectric coupling: represents a change in magnetization or polarization

of a multiferroic material upon application of a magnetic or electric field.

3

• Piezoelectricity: describes the influence of an applied linear electric field on

strain, or a change in polarization as a linear function of applied stress.

• Piezomagnetism: represents a change in strain as a linear function of applied

magnetic field, or a change in magnetization as a linear function of applied stress.

• Electrostriction: describes a change in strain as a quadratic function of applied

electric field.

• Magnetostriction: describes a change in strain as a quadratic function of applied

magnetic field.

• Single Phase Multiferroic: a material possessing at least two of ferroic properties:

ferroelectricity, ferromagnetism and ferroelasticity [2].

2. Magnetoelectric Coupling

A ferroelectric crystal exhibits a stable and switchable electrical polarization in the

form of cooperative atomic displacements. A ferromagnetic crystal exhibits a stable and

switchable magnetization that arises through the quantum mechanical phenomenon of

spin exchange. The relationship between multiferroic and magnetoelectric materials is

shown in Figure 1-2. A multiferroic material is not necessarily magnetoelectric. There are

few multiferroic materials that exhibit both ferroelectric and ferromagnetic properties

without coupling between the two.

Magnetoelectric coupling can exist wherever magnetic and electrical orderings occur

in the same temperature range. Also magnetoelectricity may occur in paramagnetic

4

ferroelectrics [3]. Usually, the mediator for the coupling is strain as related to crystal

phases.

Figure 1-2 Coupling order of ferroics and their relations and distinctions.

As shown in Figure 1-2, ME materials have been classified in four categories. Type I,

is the ME materials which are multiferroic, type II, refers to ME materials being just

Ferroelectric, type III, is the analogue of type II and it represents the ME materials which

are just Ferromagnetic, and type IV, is neither Ferroelectric or Ferromagnetic.

The magnetoelectric effect in single-phase crystals is traditionally described [4-8] in

Landau theory ,see equation (1), by writing the free energy F of the system in terms of an

applied magnetic field H whose ith component is denoted as Hi, and an applied electric

field E whose ith component is denoted Ei. This convention is unambiguous in free space,

but Ei within a material includes the resultant field that a local site would experience. In a

non-ferroic material, where both the temperature dependent electrical polarization Pi(T)

(µCcm-2

) and the magnetization Mi(T) (µB per formula unit, where µB is the Bohr

5

magneton) are zero in the absence of applied fields. F may be represented in an infinite,

homogeneous and stress-free medium under the Einstein summation convention as:

,

(1)

where the SI and CGS units of the parameters and their relations are:

. !" , #$ $%&'' %( )*+

,!" ;

!" 10 )*+,!"

. /!

, #$ $%&'' %( '0%01230,!

; /!

4×1054 '0%01230

,! ( 16

4

7898:;<8 )

. =!

, #$ $%&'' %( >? ; =!

4A×1054>? ( 1B

78989CD?E? )

*It is noted that Equation (1) is in standard (SI) unit system.

The first term on the right hand side of eq.(1) describes the contribution resulting from

the electrical response to an electric field, ε0 is the permittivity of free space, and the

relative permittivity εij(T) is a second-rank tensor that is typically independent of Ei in

non-ferroic materials. The second term is the magnetic equivalent of the first term, where

µij(T) is the relative permeability and µ0 denotes the permeability of free space. The third

term describes linear magnetoelectric coupling via αij(T); the third-rank tensors βijk(T)

and γijk(T) represent higher-order (quadratic) magnetoelectric coefficients.

All magnetoelectric coefficients incorporate the field independent material response

functions εij(T) and µij(T). The magnetoelectric effects can then easily be established in

6

the form Pi(Hj) or Mi(Ej). Pi(Hj) is obtained by differentiating F with respect to Ei, and

then setting Ei = 0 and a complementary operation involving Hi establishes the Mi(Ej) as:

F G HIJK

(2)

and

L MNOP

(3)

In multiferroic materials, the above analysis is less rigorous because εij(T) and µij(T)

display field hysteresis. This is because it is then possible to account for the potentially

significant depolarizing/demagnetizing factors in finite media, and also because the

coupling constants would then be functions of temperature alone, as in the standard

Landau theory. In practice, resultant electric and magnetic fields may sometimes be

approximated by the polarization and magnetization respectively [9]. A multiferroic that

is ferromagnetic and ferroelectric is liable to display large linear magnetoelectric effects.

This follows because ferroelectric and ferromagnetic materials often (but not always)

possess a large permittivity and permeability respectively, and αij is bounded by the

geometric mean of the diagonalized tensors εii and µjj such that [10]:

Q (4)

This is obtained from Einstein summation convention free energy equation by forcing

the sum of the first three terms to be greater than zero that is ignoring higher-order

7

coupling terms. It represents a stability condition on εij and µij, but if the coupling

becomes so strong that it drives a phase transition to a more stable state, then αij, εij and µij

take on new values in the new phase. Note that a large εij is not a prerequisite for a

material to be ferroelectric (or vice versa); and similarly ferromagnets do not necessarily

possess large µij. For example, the ferroelectric KNO3 possesses a small ε = 25 near its

Curie temperature of 120 0C whereas paraelectric SrTiO3 exhibits ε > 50,000 at low

temperatures [11]. Therefore large magnetoelectric couplings need not arise in, or be

restricted to, multiferroic materials.

3. Parity and Time Reversal Symmetry in Ferroics

In Ferroelectric material the electric dipole moment p is represented by a positive

point charge that lies asymmetrically within a crystallographic unit cell that has no net

charge, R SE, where R is polarization, q is electric charge and E is the charges

distance. There is no net time dependence, but spatial inversion E T E reverses p,

shown in Figure 1-2. In Ferromagnets the magnetic moment m is represented classically

by a charge tracing dynamically an orbit, C AE US U8⁄ , where U7 AE , see

Figure 1-2, and 8 is time. A spatial inversion produces no change, since E T E,

but time reversal switches the orbit and thus m. In summary, p obeys time symmetry but

not parity. However, m obeys parity but not time symmetry. Multiferroics that are both

ferromagnetic and ferroelectric break time reversal and parity symmetries.

8

Figure 1-3 Time-reversal and parity symmetry in Ferroelectric, Ferromagnetic and Multiferroic materials.

4. Nonlinear Coupling

Most materials have small values of either εij or µij or both, so the linear

magnetoelectric effect will also be small, given that permittivity and permeability appear

as a product in equation (4). However, no such restriction applies to higher-order

couplings, such as those described by βijk and γijk. For example, in some materials terms

such as βijkHjHk can dominate the linear term αijHj in equation (2), as first shown

9

experimentally at low temperatures in the piezoelectric paramagnet NiSO4.6H2O [12]. In

order to achieve large magnetoelectric effects at room temperature through higher-order

terms, investigating magnetic materials with reduced dimensionality can be a good choice.

Indeed, two dimensional spin order associated with β(T) can persist to a temperature T2D

that exceeds the temperature T3D at which three-dimensional spin order associated with

α(T) is destroyed. This scenario arises at low temperature in BaMnF4 [13].

5. Indirect Coupling

In linear and higher-order magnetoelectric coupling the strain effects have not been

included. Such effects could be significant or even dominant. For example, the inclusion

of piezomagnetism (magnetostriction) would generate cross terms in equation (1) that are

proportional to strain and vary linearly (quadratically) with Hi. Analogous expressions

would arise from piezoelectricity or electrostriction. Furthermore, mixed terms involving

products of strain, Hi and Ej have been predicted [14]. In two-phase materials, magnetic

and electrical properties are strain-coupled by design in the quest for large

magnetoelectric effects. The strength of this indirect coupling is not restricted by equation

(4), and enhancements over single-phase systems of several orders of magnitude have

been achieved [15].

10

6. Coupling Constants Calculation

The magnetoelectric behavior of a material can only be fully understood if its

magnetic point group symmetry is known. This is because the magnetoelectric

coefficients αij, βijk and γijk possess the symmetry of the material. For example, αij is

non-zero for materials that do not have a centre of symmetry and are time-asymmetric.

Conversely, information regarding the magnetoelectric coefficients based on electrical or

optical experiments can aid the determination of magnetic point group symmetries. The

major challenge is to make samples sufficiently insulating to prevent leakage currents

contributing to the measured signal, a widespread problem undermining the measurement

of ferroelectric polarization loops [8, 16]. Another complication arises if ferroic domains

are present, and care should be taken to prepare single-domain polarization states [17].

Magnetoelectric coupling can be measured indirectly by simply recording changes in

either the magnetization near, say, a ferroelectric transition temperature or the dielectric

constant near a magnetic transition temperature. The resulting effects are described using

various terms such as magnetocapacitance or magnetodielectric response. Catalan has

recently shown that the frequently reported effects could be misleading due to

magnetoresistance effects alone, and that the signature of true magnetocapacitance effects

is persistent to high frequencies and low loss [18]. However, even magnetocapacitance

measurements may not provide insight nor yield coupling constants. Direct

measurements are more challenging. They record either a magnetic response to an

applied electric field or an electrical response to an applied magnetic field. The first way

11

typically requires placing the sample in a magnetometer apparatus. In the other method,

the electrical response can be measured in terms of either current or magnetic field. The

time-integrated current per unit area directly represents the magnetically induced change

of polarization in equation (2), that is, WF W⁄ , ignoring higher-order terms.

Measurements of voltage, however, yield empirical coupling coefficients commonly also

denoted α, assuming linearity take the form W W⁄ .

7. Single-Phase Studies

In 1957, the linear magnetoelectric coupling coefficient α was predicted to occur in

Cr2O3 [19]. Then, in the 1960s, α was experimentally observed to be non-zero below the

anti-ferromagnetic Neel temperature of 307K, peaking to a value of WF W⁄ X

4.1D7C5[20-21]. Potential fapplications of multiferroic materials include the possibility

of reversing the magnetization by applying an electric field or vice versa. In the boracite

Ni3B7O13I, magnetic and electrical ordering occurred below 60K, and a

magnetic-field-induced reversal of the magnetization was found to flip the polarization

(0.076 µCcm-2

) [17]. Alternatively, in the paramagnetic ferroelectric Tb2(MoO4)3, a

magnetically induced persistent polarization can arise in large part to applied magnetic

fields [3]. Recently, magnetoelectric switching has been observed in orthorhombic

manganites, REMnO3 or REMn2O5, where RE is a rare earth element. These are

anti-ferromagnets that display weak ferroelectricity. A small polarization appears at the

Neel temperature (~30 K) because the magnetic transition gives rise to crystalline

12

distortions. The polarization of 0.04 µCcm-2

in TbMn2O5 has been magnetically reversed

[22], and the polarization of 0.08 mCcm-2

in TbMnO3 has been magnetically rotated by

90o [23]. Similarly, in the hexaferrite Ba0.5Sr1.5Zn2Fe12O22, a polarization of 0.015µCcm

-2

may be magnetically induced and subsequently rotated 360o about the C-axis. These

changes in polarization are not persistent, and arise at low temperatures only [24].

8. Multi-Phase Studies

An alternative strategy for engineering enhanced magnetoelectric effects is to

introduce indirect coupling between two materials such as a ferromagnet and a

ferroelectric [25]. Each phase may then be independently optimized for room temperature

performance, and the coupling limit of equation (4) is lifted. Strain coupling requires

intimate contact between a piezomagnetic (or magnetostrictive) material and a

piezoelectric (or electrostrictive) material. This can be achieved in the form of composites

[25-26], laminates [15], [27-28] or epitaxial multilayers. The coupling constant depends

on the frequency of the a.c. applied magnetic field [29], and such multiferroic structures

could thus find applications in microwave frequency transducers. Epitaxial thin-film

heterostructures could permit precise magnetoelectric because crystallographic

orientation, layer thickness and interfacial roughness may be controlled accurately, but

direct measurements of an epitaxial systems have not been forthcoming. However,

ferroelectric layers can generate strains of the order of 1% in magnetic epilayers owing to

structural phase transitions. For example, the tetragonal to monoclinic structural phase

13

transition in a BaTiO3 substrate at 278K produces [30] a 70% change in the

magnetization of an epitaxial film of the ferromagnetic manganite La0.67Sr0.33MnO3.

Alternatively, one may attempt to alter the magnetic structure of a film by applying a

voltage to the underlying piezoelectric material [31-33]. Promising results [34] were

found for a thin film heterostructure of CoPd and Pb(Zr,Ti)O3 (PZT), where the

application of an electric field to the PZT layer rotated the magnetization of the CoPd

film by 90o. The ferromagnetic and ferroelectric phases may be distributed laterally in a

film while preserving an epitaxial relationship with one another and the substrate. This

has been achieved for nanopillars of CoFe2O4 in a BaTiO3 matrix, grown on a SrRuO3

electrode with a SrTiO3 substrate. However, the observed change in magnetization of the

CoFe2O4 pillars at the ferroelectric Curie temperature was just 5%, possibly due to either

clamping from the underlying epitaxial structure which is not piezoelectric, or electric

field effects associated with the ferroelectric. Nevertheless, when the matrix was changed

to BiFeO3, an electrically induced magnetization reversal in the CoFe2O4 nanopillars was

reported [35].

9. Devices

Ferroelectrics may be used to address magnetic materials in devices for two reasons

that in practice are not easy to separate [36-37]. First, their superlative piezoelectric

properties permit them to strain intimately connected layers. Second, the large

polarization can be used in field effect transistor geometry to influence the charge density

14

in a magnetic channel. Various other two-phase magnetoelectric devices that have been

explored include a heterostructure comprising PZT and a magnetic garnet between

crossed polarizers, where it is possible to electrically influence the Faraday rotation in the

garnet and thus control the optical transmission of the device [38]. Exchange bias in

Cr2O3/(Co/Pt)3 may be electrically reversed but requires thermal cycling, whereas

exchange bias in YMnO3/permalloy heterostructures can be electrically tuned directly

[39-40]. Also, tunable microwave devices with superconductor/

ferroelectric/ferromagnetic multilayers have been proposed [41]. In other devices,

strain-coupled magnetostrictive and piezoelectric layers can lead to voltage gain, and the

detection of magnetic fields [42-43]. The sensor devices seem particularly promising

compared to existing superconducting quantum interference device (SQUID) technology

because not only would they be cheaper and simpler, but also they can operate at room

temperature.

15

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Ferroelectrics 161, 43-48 (1994).

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Ferroelectrics 161, 43-48 (1994).

[5] Schmid, H. Introduction to the proceedings of the 2nd international conference on

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[8] Lines, M. E. & Glass, A. M. Principles and Applications of Ferroelectrics and

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541-544 (2004).

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[10] Brown, W. F. Jr, Hornreich, R. M. & Shtrikman, S. Upper bound on the

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2329-2331 (1977).

[14] Grimmer, H, The piezomagnetoelectric effect, Acta Crystallogr. A 48, 266-271

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properties in piezoelectric and magnetostrictive laminate composites. Jpn. J. Appl.

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ferromagnetoelectric nickel-iodine boracite, Ni3B7O13I. J. Appl. Phys. 37,

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[19] Dzyaloshinskii, I. E., On the magneto-electrical effects in antiferromagnets, Zh.

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Fiz. 38, 984-985 [Sov. Phys. JETP 11, 708-709] (1960).

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effect in Cr2O3. Phys. Rev. Lett. 6, 607-608 (1961).

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induced by magnetic fields. Nature 429, 392-395 (2004).

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(2003).

[24] Kimura, T., Lawes, G. & Ramirez, A. P. Electric polarization rotation in a

hexaferrite with long-wavelength magnetic structures. Phys. Rev. Lett. 94, 137201

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[25] van Run, A. M. J. G., Terrell, D. R. and Scholing, J. H. An in situ grown eutectic

magnetoelectric composite material. J. Mater. Sci. 9, 1710-1714 (1974).

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[27] Cai, N., Nan, C.-W., Zhai, J. & Lin, Y. Large high-frequency magnetoelectric

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18

[28] Srinivasan, G. et al. Magnetoelectric bilayer and multilayer structures of

magnetostrictive and piezoelectric oxides. Phys. Rev. B 65, 134402 (2002).

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magnetostrictive piezoelectric composites. Phys. Rev. B 68, 132408 (2003).

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Appl. Phys. 53, 2759-2761 (1982).

[31] Novosad, V. et al. Novel magnetostrictive memory device. J. Appl. Phys. 87,

6400-6402 (2000).

[32] Iwasaki, Y. Stress-driven magnetization reversal in magnetostrictive films with

in-plane magnetocrystalline anisotropy. J. Magn. Magn. Mater. 240, 395-397

(2002).

[33] Kim, S.-K. et al. Voltage control of a magnetization easy axis in piezoelectric/

ferromagnetic hybrid films. J. Magn. Magn. Mater. 267, 127-132 (2003).

[34] Zheng, H. et al. Multiferroic BaTiO3-CoFe2O4 nanostructures. Science 303,

661-663 (2004).

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columnar nanostructures. Nano Lett. 5, 1793-1796 (2005).

[36] Mathews, S., Ramesh, R., Venkatesan, T. & Benedetto, J. Ferroelectric field effect

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19

[37] Wu, T. et al. Electroresistance and electronic phase separation in mixed-valent

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heterostructures. Preprint at khttp://arxiv.org/cond-mat/0607381l (2006).

[41] Hontsu, S. et al. Preparation of all-oxide ferromagnetic/ferroelectric/

superconducting heterostructures for advanced microwave applications.

Supercond. Sci. Technol. 12, 836-839 (1999).

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piezoelectric composite. Appl. Phys. Lett. 85, 3534-3536 (2004).

[43] Dong, S., Li, J. F. & Viehland, D. Ultrahigh magnetic field sensitivity in laminates

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2265-2267 (2003).

20

Chapter 2. Magnetoelectric Effects on Single Phase of Z-type

and M-type Hexaferrites at Room Temperature

1. Introduction

Since modern technologies will require miniaturization and efficient performances

from the use of magnetic materials, inexpensive and simpler device structures must be

developed in order to be compatible with the semiconductor technology. This may be

achieved if all devices have the flexibility to be tuned by an electric field and/or voltage

only- including ferrite devices. There have been a lot of efforts in the past decade to do

away with magnetic fields and/or permanent magnets in the fabrication of microwave

ferrite devices so that they may be tuned by an electric field or voltage. Multi-ferroic

composite materials have been proposed to generate internal magnetic fields via voltage.

Multi-ferroic composites usually consisted of magnetostrictive and ferroelectric or

piezoelectric slabs in physical contact whereby magnetic field sensors have been implied

and fabricated so far. For example, small shifts in ferromagnetic resonance (FMR) fields

have been observed using magnetoelectric composites in the presence of an electric field.

Tuning of ferrite microwave devices by an electric field or voltage is still not practical

with present composite structures, because they still require fields.

We propose an alternative approach to this problem. The change in remanence

magnetization is measured by applying a DC voltage or electric field across a slab of

hexaferrite. A single layer of magnetoelectric hexaferrite is proposed to induce magnetic

21

parameter changes with application of voltage. The advantage of a single layer is that it is

simpler to utilize to tune ferrite devices.

Hexagonal ferrites of the M, Y and Z-types are of interest, since they exhibit high

permeability at wireless frequencies [1-2]. In particular, Co2Z-type ferrite, Sr3Co2Fe24O41,

is a member of the planar hexaferrite family called ferroxplana, in which the easy axis of

magnetization direction lies in the basal plane (c-plane) of the hexagonal structure at

room temperature. In this crystal, a large field is required to rotate the magnetic moments

from the c plane to the c-axis direction, but a small field is enough for the moment in the

c-plane to rotate in the plane. Hence, these materials are magnetically "soft" for H,

external magnetic field, in the c-plane. As such the magnetic moments can follow an

alternating field even in the gigahertz region, giving rise to high permeability even in the

ultra high frequency (300 MHz–3 GHz) region. Therefore, Y and Z-types materials are

regarded as promising candidates for inductor cores and electromagnetic noise absorbers

to be used in this frequency region.

In this chapter, converse magnetoelectric effects of Sr Z-type, Sr3Fe24Co2O41, and

M-type, SrCo2Ti2Fe8O19, hexaferrite materials at room temperature were measured. The

change in remanence magnetization(Mr) for M-SCTFO sintered in oxygen and sintered in

air are similar and approximately equal to ~3% in 13kV/cm electric field and for Z-type

was ~12% in ~10kV/cm E-field. The measured magnetoelectric coupling coefficient, α,

values at room temperature for Z-type and M-type hexaferrites sintered in O2 were

measured to be 7.6×10-10

sm-1

and 2.4×10-10

sm-1

, respectively. Sintering the M-type in

22

air reduced α to 1.7×10-10

sm-1

. As it is well known lack of oxygen in local oxygen sites

imply lower resistivity and a modified magnetic structures or state. However, in

magnetoelectric hexaferrites there is an additional effect due to lack of oxygen and that is

the spin spiral configuration is significantly modified to lower the induced magnetization

upon the application of a DC voltage or electric field. In magnetoelectric effects

measurements high resistivity is critical in order to reduce current flow in the hexaferrite.

The resistivity of the hexaferrite was raised to 4.28×109 Ωcm by annealing under oxygen

pressure. The measurements indicate that indeed electric polarization and magnetization

changes were induced by the application of static magnetic and electric fields,

respectively. The implications for microwave applications appear to be very promising at

room temperature.

2. Sr Z-type Experimental Material Growth Procedure

Substitution of Sr2+

for Ba2+

was reported in order to reduce the sintering temperature

from 1250 (0C) to 1210 (

0C) and oxygen partial pressure in synthesizing Co2Z-type ferrite

[3]. This substitution also increased the zero field FMR frequency and, therefore,

extended the frequency range of the permeability. These results also indicate that Sr2+

substitution would be favorable for lowering cost in manufacturing and putting this type

of ferrite material into practical uses. The magnetic cation distribution in Sr-Z is

significantly different that of Ba-Z and Ba Sr-Z hexaferrites. Magnetic moments in Ba1.5

Sr1.5 Co2Fe24O41 and Ba3Co2Fe24O41 lie in the c-plane while that in Sr3Co2Fe24O41 are at

23

oblique angle to the plane, shown in Figure 2-1, and with respect to c-axis is 52.3o [4].

Figure 2-1 Orientation of magnetic moment of Sr-Z, Ba-Z and BaSr-Z hexaferrites.

Sr3Co2Fe24O41 samples were prepared by the solid-state reaction method by our group

[5]. The calculated amount of the oxide mixtures were: SrO (99.5%), Co3O4 (99.7%), and

Fe2O3 (99.8%). 25 g of the starting reagents mixture were blended with a liquid

dispersing agent (reagent alcohol). To grind uniformly, the ball milling machine, shown

in Figure 2-2, was used with a set of agate balls with 300 rpm rotation speed for 4 hours.

The slurry was dried at room temperature and five 5(gr) pellets were made. The pellets or

discs were placed in the tube furnace in an oxygen atmosphere over the sample with 5

deg/min temperature rate and set in 1210 (0C) for 16 hours. To prevent formation of other

impurity phases, including W-, M- or/and Y-phases, it was found most favorable to

quench the sample immediately to room temperature. The X-ray diffraction pattern is

shown in Figure 2-3. The ferromagnetic resonance (FMR) measurement instrumentation

and result are shown in Figures 2-4 and 2-5, respectively. The line-width (∆H) is quite

24

high and about 2400 Oe. This is due to the polycrystalline structure of sample. In order to

obtain low line-width one needs to either improve materials homogeneity or reduce the

thickness of the slab or produce single crystals. This will be shown in following chapter

when the single crystalline of the Sr-Z type is presented.

Figure 2-2 Planetary mono mill Pulverisette 6 to grind particles.

25

Figure 2-3 X-ray diffraction pattern of the polycrystalline Sr3Co2Fe24O41 at room temperature. The black

line represents the reference peak positions for the Ba Z-type hexaferrite (Ref. ICDD # 19-0097. Space

group: P63/mmc(194)).

Figure 2-4 Ferromagnetic resonance measuring instrumentation.

26

Figure 2-5 FMR spectrum of polycrystalline Sr3Co2Fe24O41 at room temperature for magnetic field (H)

applied parallel to slab plane.

In order to increase resistivity, samples were annealed at 600 0C in an oxygen

atmosphere for 6 hours [6]. The high resistivity of the sample was required for the

magnetoelectric measurements to minimize current flow through the sample in the

presence of high electric fields. I-E and ρ-E curves of a typical sample are shown in

Figure 2-6. Increasing the oxygen pressure during anneals reduced current flow or

increased resistivity and dependence of current with voltage is almost linear. The

resistivity estimated from the experimental linear I-V characteristic is ρ = 1.43×109 Ωcm

for samples of 1mm in thickness. The preparation in oxygen leads to Fe2+

concentration

reduction which then lowers the hopping of electrons between Fe2+

and Fe3+

ions [6-7].

27

Figure 2-6 I-E and ρ-E curves of the polycrystalline Sr3Co2Fe24O41 at room temperature after sintering

in O2.

2.1 Sr Z-type Indirect Converse Magnetoelectric Experimental Analysis

In general, the linear magnetoelectric (ME) effect implies the following: the

application of a magnetic field, H, induces a change in electric polarization, P, and the

application of an electric field, E, induces a change in magnetization, M. In this work the

latter is called the "indirect converse ME effect". To measure changes in remanence

magnetization versus electric field a Vibrating Sample Magnetometer (VSM) instrument

was used, shown in Figure 2-7. In Figures 2-8 and 2-9, the magnetization, M, is plotted as

a function of H, magnetic field, for a given applied electric field or voltage. We note that

the remanence magnetization (for H=0) was indeed affected by voltage. The change in

remanence magnetization was as much as 16% with the application of an electric field of

5 kV/cm. In Figure 2-10, the percentage change in remanence versus the applied electric

field is shown. Changes in remanence magnetization scale with polarity changes of the

electric field or applied voltage. Thus, heating effects, shown in Figure 2-12, may be

28

eliminated as a source of the remanence magnetization changes, since heating effects

induce changes in remanence in one polarity sense only.

The implication to microwave properties of this material is straightforward. The

permeability expression for the Z or Y-type hexaferrite may be readily found in [8].

Typically, the zero field FMR for these materials ranges near 3 GHz. However, below the

FMR frequency the permeability is approximately for this material to be

µr ≈1+(4πMr / Hφ) (1)

where Mr is the remanence magnetization and Hφ is the c-plane magnetic anisotropy field.

Typically, Hφ is in the order of 40 (Oe) implying µr ≈3.5, since 4πMr ≈105 G. Clearly, any

changes in remanence magnetization are reflected in the microwave permeability at

wireless communication frequencies. Certainly, application of DC voltages will not affect

the Hφ.

Figure 2-7 Vibrating sample magnetometer (VSM) instrumentation. The sample is placed between the

pickup coils and voltage is applied to the sample through the conductor plates.

29

In the ME experiment where changes in the dielectric constant were measured as a

function of frequency for a given application of magnetic field, H, the measurements are

shown in Figure 2-12. Remarkably, the applied field is small in affecting changes in

dielectric constants in comparison to other reports [7]. For example, at 1 GHz and with an

applied magnetic field equal to 32 mT, the change in relative dielectric constant was

almost 3.5, a change of 16%. The measurements were performed using an

impedance/material analyzer (Agilent). According to Ref. [7], the mechanism for the ME

effect is due to a local distortion of the Co ions giving rise to a spiral spin configuration

which is a pre-required condition for this effect in hexaferrite materials to exist.

Figure 2-8 Polycrystalline Sr3Co2Fe24O41 magnetization as a function of external applied H parallel to

slab plane and perpendicular to applied E field at room temperature.

30

Figure 2-9 The zoomed in change in remanence magnetization measurements shown in Figure 2-8 over

low magnetic field.

Figure 2-10 Polycrystalline Sr3Co2Fe24O41 remanent magnetization change vs electric feild for a typical

sample with 0.5mm thickness at room temperature.

31

Figure 2-11 Change in temperature in the Sr Z-type sample versus electric field.

Figure 2-12 Change in dielectric constant over frequency versus applied external magnetic field.

2.2 Orientation of Polycrystalline Sr Z-type

In order to obtain low FMR linewidth and, therefore, higher permeability as given in

equation (1) it is required to improve materials homogeneity to increase remanence

magnetization. The grown Sr-Z material was polycrystalline and this implies that the easy

plane surfaces are randomly distributed in the crystal. The random distributions of the

c-axis needs to be aligned parallel to each other so that a much softer Z-type hexaferrite

32

can be produced. In order to align all c-axis of each particle in a powder an orientation

technique is used to orient Z-type hexaferrite particles with c-axis normal to the disc

plane. The orientation set up is shown in Figure 2-13 [15].

Figure 2-13 Polycrystalline Sr3Co2Fe24O41 powder orientation set up.

Generally in polycrystalline hexaferrites each particle has its own easy direction, free

poles are expected to appear on the grain boundaries, unless the domains are well aligned

as in single crystals. That means the grain size is the critical issue of the domain structure

in magnetic materials. The critical domain size is the largest domain size that prevents the

existence of domain wall. The only mechanism for demagnetization is rotation of the

magnetization direction, which may be critical for high anisotropy material such as

hexaferrites materials. For Sr-Z the domain size is usually 0.5-2µm. The orientation

33

procedure is as following:

Step 1- The grown polycrystalline Sr-Z disk is ground to powder. The particles are sieved

to uniform the size of 75µm or smaller.

Step 2- Using the ball milling machine with specified agate balls indicate size of the balls,

rotation speed and duration of rotation provide particle size as small as 0.5-2µm.

These parameters are experimental. To find out the duration of rotation providing

uniform particles Scanning Electron Microscope (SEM) is used. This is shown in

Figure 2-14 for different milling durations. It was found most favorable to rotate

3gr for 22 hours.

(a) 2 hours

(b) 4 hours

34

(c) 6 hours

(e) 10 hours

(f) 14 hours

(d) 8 hours

(f) 12 hours

(g) 16 hours

35

(h) 20 hours

(i) 22 hours

Figure 2-14 SEM photographs of the ground particles for different milling durations.

Step 3- The slurry is casted together with pure distilled water inside a stainless cylinder

die in the mechanical press apparatus. This is shown in Figure 2-13.

Step 4- A 0.5T permanent magnet, shown in Figure 2-15, is placed on a rotating platform

such that the direction of the applied field was in a radial direction perpendicular

to the force direction that is normal to the disk plane. The applied pressure on the

die was 500 psi and they were pressed into a disk shape to dehydrate the disc.

The schematic of the procedure has been plotted in Figure 2-16.

Figure 2-15 Photograph of 0.5T rotating permanent magnet.

36

(a) Step 1 and Step 2.

(b) Step 3 and Step 4.

(c) Pressed oriented disk.

Figure 2-16 Schematic of orientation procedure.

37

The oriented Sr-Z disks showed magnetically soft behavior for fields in the plane, as

illustrated by VSM measurements in Figure 2-17 where the horizontal axis is the external

magnetic field (kOe), and vertical axis is normalized magnetization.

Figure 2-17 VSM data of Sr-Z. Red and black dashed lines represent after orientation before orientation,

respectively.

We also note that for the external magnetic, H, applied normal () to the slab plane it

is required higher values to saturate the sample after orienting the particles. This means

that the disc plane is “made” much easier magnetically after orientation. This is further

confirmed for H in the disc plane (). For H~0, there is sufficient curvature of M versus

H curve to conclude either there is another phase of material, some local stress, or local

particles that are not completely aligned. Complete alignment implies a linear

relationship for H~0.

38

3. M-type Experimental Material Growth Procedure

We have adopted a procedure similar to that in [9] to prepare a single phase

polycrystalline M-type hexaferrite SrCo2Ti2Fe8O19 (SCTFO) and it was prepared through

conventional solid state reaction technique. The high-purity powders of SrCO3, Fe2O3,

Co3O4, and TiO2 were mixed stoichiometrically and sintered at 1200 (oC) for 10 hours

twice in air and oxygen atmosphere. The powder X-ray diffraction measurement of

SCTFO at room temperature was carried out to identify the sample as single phase and it

is shown in Figure 2-18.

Figure 2-18 X-ray diffraction pattern of polycrystalline SrCo2Ti2Fe8O19 at room temperature. The black

line represents the reference peak positions for the Ba M-type hexaferrite (PDF # 27-1433. Space group:

P63/mmc(194)).

39

4. Z- and M-type Hexaferrites ME Effect Comparison

4.1 Resistivity Measurements

Resistivity is very important in magnetoelectric materials to prevent current flow in the

sample. I-E curves of the prepared M- and Z- type hexaferrite materials are shown in

Figure 2-19. The Resistivity of the Z-type and M-type hexaferrites sintered in oxygen are

1.43×109 Ωcm and 4.36×10

10 Ω-cm, respectively [9-12].

This value for M-type sintered

in air is 1.12×107 Ωcm.

The resistivity of the Z-type sintered in air is 6×10

3 Ωcm which is

low for ME measurements, since current flow in the sample is inversely proportional to

resistivity [13].

Figure 2-19 Current versus electric field for Sr-Z and SCTFO.

40

4.2 ME Effect Measurements

The change in magnetization with the application of a DC voltage is proportional to α.

Hence, α is the most important parameter that dictates the application of the hexaferrite in

terms of sensor and/or ferrite device applications, when using magnetoelectric

hexaferrites. One emphasis in this section is our measurements of α as related to previous

section. The magnetoelectric effects on two types of hexaferrites: M- and Z-types are

presented. We measured the change in magnetization with the application of DC voltages.

The changes in permeability, µ, are due to changes in remanence magnetization.

The magnetization, M, is plotted versus H, magnetic field, for a given direction of

applied electric field or voltage for M-type hexaferrite in Figure 2-20. The remanence

magnetization is affected by DC voltage, and we measured changes as much as 3% at

16kV/cm where the electric field was applied parallel to H and perpendicular to the slab

plane. For the Z-type we measured 12% change in Mr, shown in Figure 2-9, with the

application of an electric field of 10kV/cm.

41

Figure 2-20 Change in remanence magnetization (Mr) of M-type (sintered in air) for (a) Edc perpendicular

to H and (b) Edc parallel to H.

The magnetoelectric coupling coefficient, α, for all the samples were deduced using

the formula, ∆L* ∆⁄ , and has been summarized in Table I. In CGS α may be

determined from ∆L* ∆⁄ , where ∆L* is in emu/cm3 and ∆ in esu units. The value

of α for Z-type is higher than the M-type as seen in Figure 2-21 and Table I. α=1.7×10-10

for the M-type sintered in air at room temperature is ~40 times bigger than the α value

measured in Cr2O3 (αX4.1×10-12

sm-1

) [14]. The implication to microwave applications of

these materials is straightforward. The permeability expression for the Z or Y-type

42

hexaferrite may be readily determined analytically [8].

Table I: Converse magnetoelectric coupling coefficient and resistivity for Z-type and M-type hexaferrites

at room temperature.

Material ρ[Ω cm] α [sm-1

]

Z-type (Sr3Co2Fe24O41) 1.43×109 (Ref.11) 7.6×10-10

M-type (SrCo2Ti2Fe8O19, sintered in O2) 4.36×1010 (Ref.9) 2.4×10-10

M-type (SrCo2Ti2Fe8O19, sintered in air) 1.12×107 (This chapter) 1.7×10-10

Figure 2-21 The change in remanence magnetization (Mr) of Z-type sintered in O2, M-type sintered in air

and O2 versus DC electric field.

Zero field FMR for Z-type hexaferrite is about 3GHz, but for M-type may range to

frequencies above 20GHz.

Z [

\ ]1.4 ^ 10_\`` a 4AL' (2)

43

a (Uniaxial magnetic anisotropy field), ` (six-fold magnetic anisotropy field or

azimuth magnetic anisotropy), and ] factor were measured and their corresponding

values for Sr-Z were 105 G, 25 kOe, 40 Oe, and ~2.

The difference in zero fields FMR of these two similar materials is due to the fact that

Z-type hexaferrites are planar and M-type is intrinsically uniaxial symmetry materials.

Hence, the types of microwave applications are much different for the two materials. For

the Z-type hexaferrite the permeability as given in equation (1) is approximately 3.8.

Application of DC voltages will not affect ` . Any changes in remanence

magnetization are reflected in the microwave permeability at wireless communication

frequencies. M-type hexaferrites have been used most often in self biased circulators

whereby the Mr is typically above 90% of the saturation magnetization after orienting the

particles. The bandwidth and center frequency of circulator is approximately proportional

to Mr. Here we have a unique situation whereby * is readily changed by varying Mr

with the application of a DC voltage to affect the operation of a circulator. We have

illustrated two potential applications where the special property of magnetoelectricity is

important to the applications. There are many applications that can be conceived that

depend upon the ability to change the magnetization value in a ferrite device.

5. Conclusions

In this chapter changes of remanence magnetization and magnetoelectric coupling

coefficient in polycrystalline slabs of Z-type, Sr3Co2Fe24O41, and M-type,

44

SrCo2Ti2Fe8O19 ,sintered in air and oxygen, with the application of voltage or electric

field at room temperature were measured. Sintering in oxygen increased not only

resistivity but also the magnetoelectric coupling. We believe that sintering in air reduced

the magnetoelectric effect as predicted by the "slinky helix" model which will be

demonstrated in chapter 4. We have identified two potential applications whereby the

application of a DC voltage can affect the operation of a microwave ferrite device. We

anticipate that sensor applications that depend on magnetization changes have a high

potential for success.

45

References

[1] T. Tachibana, T. Nakagawa, Y. Takada, T. Shimada, T. Yamamoto, J. Magn. Magn.

Mater. 284, 369 (2004).

[2] M. Pardavi-Horvath, J. Magn. Magn. Mater. 171.215 (2000)

[3] O. Kimura, M. Matsumoto, and M. Sakakura, J. Jpn. Soc. Powder, Powder Metall.

42, 27 (1995).

[4] Y. Takada, T. Tachibana, T. Nakagawa, T. A. Yamamoto, T. Shimada, and S.

Kawano, J. Jpn. Soc. Powder , Powder Metall. 50, 618 (2003).

[5] Y. Takada, T. Nakagawa, M. Tokunaga, Y. Fukuta, T. Tanaka, and T. A. Yamamoto,

J. Appl. Phys., 100, 043904 (2006).

[6] O.

Kimura, M. Matsumoto and M. Sakakura,. J. Am. Ceram. Soc. 78, 2857

(1995).

[7] Y.Kitagawa, Y. Hiraoka, T. Honda, T. Ishikura, H. Nakamura, and T. Kimura,

Nature Mater. 2826, 797 (2010).

[8] C. Vittoria, "Magnetics, dielectrics, and wave propagation with MATLAB codes",

(CRC press, New York 2011).

[9] Wang, D. Wang, Q. Cao, Y. Zheng, H. Xuan, J. Gao, and Y. Du, Sci. Rep., 2, 223

(2012).

[10] K. Ebnabbasi,Y. Chen, A. Geiler, V. Harris, and C.Vittoria, J. Appl. Phys. 111,

07C719 (2012).

[11] K. Ebnabbasi, C. Vittoria, and A. Widom, Phys. Rev. B 86, 024430 (2012).

46

[12] K. Ebnabbasi, Marjan Mohebbi, and C. Vittoria, Appl. Phys. Lett. 101, 062406

(2012).

[13] Y. Kitagawa, Y. Hiraoka, T. Honda, T. Ishikura, H. Nakamura, and T. Kimura,

Nature Mater. 9, 797 (2010).

[14] Schmid, H, in Introduction to Complex Mediums for Optics and Electromagnetics

167-195 (SPIE Press, 2003).

[15] Mahmut Obol and Carmine Vittoria, "Microwave permeability of Y-type

hexaferrites in zero and low fields", Journal of Magnetism and Magnetic

Materials 2004.

47

Chpater 3. Coaxial Line Technique to Measure Constitutive

Parameters in Magneto-Electric Ferrite Materials

1. Introduction

In this chapter an experimental measurement technique is presented to measure the

constitutive parameters of magneto-electric ferrite materials in the presence of high DC

voltages. The traditional coaxial line design was modified in a manner that it allowed for

the introduction of high DC voltage (~2000V) in the coaxial line and also it minimized

electromagnetic radiation loss via connections to the magnetoelectric sample in the

coaxial line. The modified coaxial line was tested from 50MHz to 10GHz.

Ferrite materials are widely used in passive and tunable electromagnetic signal

processing devices, such as phase shifters, circulators, isolators, filters, antenna substrates,

and EMI suppression cores. Due to their excellent dielectric properties, ferrites possess

the advantages of low loss and high power handling capability relative to semiconductors.

Usually, parameters of magnetic materials are controlled by an external magnetic field

and/or permanent magnets thus allowing for tuning of device performances. Permanent

magnets or current driven coils imply relatively large component size, weight, and cost,

as well as slow response time in comparison to semiconductor-based technologies. In

recent years, self biased hexagonal M-type ferrites have been utilized in circulators to

reduce or eliminate magnetic bias field requirements and permanent magnets. However,

their applicability is limited in terms of frequency range and minimum achievable

48

insertion loss. Ferrite magneto-electric (ME) materials can be a practical solution in

controlling the magnetic parameters of ferrites by tuning the electric field and/or voltage

instead of external magnetic fields and would eliminate permanent magnets and tuning

coils to overcome most of the disadvantages in the use of ferrites for microwave devices.

Circuits where ferrites and semiconductors can be used on the same integrated circuit or

chip may become a reality. Furthermore, key advantages of ferrites, including low

insertion loss and high power handling capability could be exploited without the penalty

of added size, weight, and cost, as well as increased response time.

Recently, there has been considerable interest in the nature of ME materials and, in

particular, hexaferrites which have strong magneto-electric effects at room temperature.

Most often ME materials are operational at low temperatures. In previous chapter we

prepared hexaferrite of the Z-type which are intrinsically magneto-electric at room

temperature exhibiting very high magneto-electric coupling coefficient [1]. The material

preparation is similar to the method used in [2]. Previous papers on ME hexaferrite

materials reported on the DC properties of these materials upon the application of DC

magnetic field for example, the low frequency (~1 kHz) permittivity as a function of DC

magnetic field. Since these materials are ME we conceived that the converse must hold.

That is, the application of DC voltage (electric field) must necessarily affect the

permeability. Indeed, we applied a DC voltage and measure the permeability, µ, as a

function of frequency (50MHz-10GHz) utilizing a coaxial line. This measurement

implied the introduction of a DC voltage in the coaxial line apparatus. Coaxial line

49

techniques to measure µ (permeability) and ε(permittivity) have been around for many

years. These measurements were never performed in high DC voltage, since there was

never a need for that.

High DC voltage could easily damage delicate microwave testing instrumentation.

Conventional measuring technique does not permit the use of high DC voltage in testing

or characterization of microwave parameters, since there is no provision to isolate high

voltage from the instrumentation. ME materials respond to the application of an electric

field or DC voltage and, as such, the tested ME sample was necessarily in electrical

contact with an external DC voltage. It was required to make electric contact to the

sample and simultaneously prevent radiation loss in the connections. We were able to

eliminate wire contacts with the sample and, therefore, eliminate radiation loss through

the wires. Also, radiation loss was minimized by shorting out a small gap on the coaxial

line using a novel use of capacitors in the gap. As a result of these we could measure

permeability and permittivity of ME hexaferrite toroidal sample as a function of

frequency, DC voltages, and magnetic fields.

2. Theory of the Design

2.1 Two Port Design

In conventional coaxial line measurement technique mostly the two port or

transmission through lines are used to measure the constitutive parameters. In this case as

shown in Figure3-1 these parameters can be calculated as follows [3]:

50

1 1 4 1

the + or - sign selection is based on the rule that the reflection coefficient should not

exceed 1.

Figure 3-1 Non-reciprocal ferrite network equivalent of transmission line.

1 2ln !"# $1 1 % ln $1 % 2

& & & 1 ln 2 1!"# $1 1 % ln $1 % 3

where b and a are the outer and inner diameters of the coaxial line, respectively.

51

Figure 3-2 Two port coaxial line schematic for ferrite magneto-electric (ME) effect measurement.

The advantage of this method is that the S-parameters can be collected by the network

analyzer at one time in comparison with the one port measurement which is done in two

steps. And the phase adjustment can be performed by providing the sample thickness and

its distance from port1. However, with the introduction of high DC voltage it might be

very complicated to apply external DC voltage to do the same measurement. If a very

thin wire is put in the coaxial line, see Figure 3-2, such that the thickness is very small in

comparison with the skin depth it results in antenna radiation and, therefore, uncertainty

in the accuracy of the measurement. The circuit model of the wire in contact with the ME

material is given in Figure 3-3. The wires influence the measurement precision, although

it is possible to cancel out its effect through calibration techniques. However, the

dangling of the wires and their position is not fixed and we cannot consider it as a fixed

52

object to remove its effect precisely from calibration runs. In order to properly

characterize ME ferrite materials the material should just experience the DC voltage

without external radiation effects due to contacts to the sample.

Figure 3-3 Circuit model of the medium in connection with the dangling wires.

2.2 One Port Design

In the case of one port transmission line which is used in this work the analysis makes

use of the matrix representation given in Figure 3-1 [3]. The port1 S-parameter is:

!"( !" !"(!" !"( !" !"(!" 4

where the (a) matrix in the case of a material with the thickness of t is [3]:

$)* % $)* %, where

, - cos 1# !2341#! sin 1# cos 1# 6.

53

The permeability, µ, can be calculated from the reflection coefficient, S11, as [3]:

!#41# !" 81 91 9 : 5

where Z=< &⁄ and 1 √&.

Figure 3-4 One port coaxial line schematic for ferrite magneto-electric (ME) effect measurement.

Here 9 is the reflection coefficient for the shorted port of the coaxial transmission

line, Z is the coaxial line characteristic impedance of the sample, k is the propagation

constant and is equal to 2 ?⁄ , and Z0 is characteristic impedance of the coaxial line

which is 50. The permeability may then be determined from:

@ !" $ 1#% 81 91 9 : 6

54

where is 2πf and f the frequency. We should notice this is an approximate formula and

it is valid as long as kt << 1. The advantage of this approach is that the permittivity, ε,

does not enter in the analysis in this limit of approximation. This is extremely important

point in that dielectric changes can not influence the changes in µ as measured by this

technique, see (6). In the same way ε can be calculated independent from µ:

& @ 1!" $ 1#% 81 B1 B : 7

where B is the reflection coefficient for the open port of the coaxial transmission line.

It should be noticed that there is no longer wire connections in this design, see Figure 3-4,

and capacitors are used to short out radiation losses in the gap.

In general µ and ε may be deduced from:

1 <DDDE 8

& 1 <DE/DD 9

where

D !" 81 B1 B : D !" 81 91 9 : , and

55

DE K 12# ln 1 <D D⁄1 <D D⁄ L .

Let’s now address the accuracy of the measurement for µ and ε, in (8) and (9). We require

the thickness of the toroidal sample to be much less than the wavelength of the coaxial

line. The thickness of the toroid was 0.1cm and the wavelength exceeded 10cm.

Nevertheless, we compared µ obtained from (8) and (9) to conventional techniques using

(2) and (3). The error was less than 2%. Other concerns are explained below.

1) Skin depth: As shown in Figures 3-2 and 3-4, in order to connect the DC voltage to

the toroidal sample it is required to cover at least one side of the ME ferrite material with

a conductor so that the electric field is perpendicular to the toroidal plane. Clearly, the

conductive plating might reflect the electromagnetic wave and affect the precision of

Eqs.8 and 9. If the thickness of the conductor metallic surface is well below the skin

depth, most of the electromagnetic energy is coupled to the toroid. We used a conductor

with as low conductivity as possible and still make electrical contact at DC voltage. We

used liquid silver paint for this purpose. The paint was convenient to apply on the toroid,

be removed from the surface by acetone, and control the thickness. Furthermore, the

resistivity was increased by diluting the silver paint in acetone with 1:3 ratio.

2) Isolator and shorting capacitor: It is desirable to measure the constitutive

parameters of the ME material while maintaining isolation of the DC voltage from

56

coaxial line and instrumentation. For this purpose, as shown in Figure 3-4, the DC

voltage is applied outside of the coaxial line. Thin Teflon slabs separate the DC voltage

between the two terminations of the DC power supply. The gap (10 mils) introduced by

the Teflon sheets was filled with 0.22µF capacitors. The purpose of the capacitors was to

short out at high frequencies the coaxial line across the gap. In this design wire

connections were eliminated and isolation between the DC voltage and microwave

equipment was achieved. We compared our results using (8) and (9) (when no DC

voltage was applied) with conventional coaxial line technique using (2) and (3) and the

accuracy in measurement is 2%.

3. Experimental Measurements

A toroidal shaped sample in a coaxial line was inserted (the material was a hexaferrite

Z-type, Sr3Co2Fe24O41 [1]). One side of the toroid was shorted to the coaxial line

termination as well as to the DC ground voltage. The other side of the toroid was coated

with a thin film of silver paint and then connected to a high DC voltage power supply,

shown in Figure 3-4.

There are three precautions that need to be exercised: (1) the high DC voltage needed

to be isolated from the microwave signal of the Network Analyzer (NA) instrumentation,

(2) reduce antenna effects from dangling wires connected to the toroidal sample. The

VNA was used to measure the electrical scattering S-parameter. Antenna effects were

prevented by connecting high frequency capacitors to electrically short out any

57

microwave signals and connect the DC isolated plate to the grounded body of the coaxial

line, and (3) the thickness of the silver paint film was sufficiently small compared to the

skin depth(10µm- 200µm) so that the reflected signal from the toroid was notdominated

by pure metallic reflections from the silver paint. For example, initially we inserted the

toroidal sample without any wire attachments, silver paint and capacitors attached to any

wire. We then loaded the toroidal sample with all the attachments (silver paint, capacitors,

etc.), but no DC voltage applied and measured µ again. We were again able to obtain the

same µ curve within 3% accuracy. At this point we applied the DC voltage to the toroidal

sample and measured changes in µ due to the DC voltage.

The fabricated coaxial line assembly is shown in Figure 3-5. High resistivity is critical

in order to minimize current flow through the hexaferrite sample in the presence of high

electric fields. The I-V curve of the hexaferrite material is shown in Figure 3-6 The

resistivity estimated from the experimental linear I-V characteristic measurement, shown

in Figure 3-6, was ρ = 1.4×109 Ω.cm for a toroid with 1mm thickness. The real and

imaginary parts of µ versus frequency for E=0 kV/cm are shown in Figure 3-7. For E≠0

(application of DC voltage) the theoretical calculation and experimental measurements

for the change in permeability is shown in Figure 3- 8. The calculated formula for the

changes in µ (∆N ) is:

58

∆N0 @ PQ RSRRSR T U ∆VNVN W X!"1 Y 10

with respect to the direction of E to M, direction of magnetization.

Figure 3-5 Coaxial line parts and assembled device.

The plot in Figure 3-8 is for E=500 kV/cm and similar curve may be obtained for any

electric field. The material is anisotropic and it is expected that ∆N to reflect the relative

directional dependence on E. Since we cannot change the mechanical structure of the

designed device, shown in Figure 3-5, the ferrite sample was magnetically poled before

applying the DC voltage or E. We chose Mr to be parallel, anti-parallel, and

perpendicular to the applied electric field direction, E . For E-field parallel and

perpendicular to the magnetization ∆N plots are given in Figures 9 and 10, respectively.

The FMR frequency is about 3GHz and also ∆N is about zero for frequencies above

3GHz. However, this technique is applicable for frequencies up to 10GHz and DC

59

voltage up to 2000V.

Figure 3-6 Measured I-V characteristic of polycrystalline Sr Z-type hexaferrite.

Figure 3-7 Measured real and imaginary parts of the ME ferrite permeability versus frequency for

E=0KV/cm.

60

Figure 3-8 The theoretical calculation and experimental measurement of magnetic permeability change

versus frequency for E=5KV/cm.

Figure 3-9 The magnetic permeability change versus electric field and frequency when Mr is parallel and

anti-parallel to E.

61

Figure 3-10 The magnetic permeability change versus electric field and frequency when Mr is

perpendicular to E.

Figure 3-11 Phase change versus electric field and frequency when Mr is parallel to E.

62

Figure 3-12 Phase change versus electric field and frequency when Mr is anti-parallel to E.

4. Conclusions

A coaxial line measurement technique was presented to measure the constitutive

parameters of the magneto-electric ferrite materials in the presence of high DC voltage

(Z 2000V) and for frequencies up to 10GHz. The measurement technique yields

measurements of µr versus frequencies which are in general agreement with theory. This

technique can be equally applied in measuring the dielectric constant as a function of

frequency in the presence of DC voltage or magnetic field.

63

References

[1] K. Ebnabbasi, Y. Chen, A. Geiler , V. Harris, and C. Vittoria, Magnetoelectric

effects on Sr Z-type hexaferrite at room temperature, Applied Physics 111,

07C719 (2012).

[2] Y. Kitagawa, Y. Hiraoka, T. Honda, T. Ishikura, H. Nakamura and T. Kimura,

Low-field magnetoelectric effect at room temperature, Nature Mater. 9, 797

(2010).

[3] C. Vittoria, Elements of Microwave Networks, World Scientific (1998).

[4] C. Vittoria, "Magnetics, dielectrics, and wave propagation with MATLAB codes",

CRC press, New York (2011).

[5] M. Soda, T. Ishikara, H. Nakamura, Y. Wakabayashi, and T. Kimura, Magnetic

Ordering in Relation to the Room-Temperature Magnetoelectric Effect of

Sr3Co2Fe24O41, Physical Review Letter, 106, 087201 (2011).

64

Chapter 4. Converse Magnetoelectric Experiments on a

Room-Temperature Spirally Ordered Hexaferrite

1. Introduction

In this chapter magnetoelectric properties of room-temperature spirally ordered

Sr3Co2Fe24O41 hexaferrite slabs have been measured. A physical model in this paper

referred to as the “slinky helix” model is presented to explain the experimental data. The

measured properties include the magnetic permeability and the strain, all as a function of

the electric field E. Upon application of an electric field to slabs of Sr Z-type hexaferrite,

it exhibits broken symmetries for time reversal and parity. This is the central feature of

these magnetoelectric materials.

There has been considerable recent interest in the nature of magnetoelectric (ME)

materials [1]. Of interest in this work is spirally ordered hexaferrites [2–5] which have

strong ME effects at room temperature. Neutron scattering experiments [5,6] revealed a

spiral spin configuration responsible for the ME effect at room temperature in

Sr3Co2Fe24O41 hexaferrite. Sr3Co2Fe24O41 is identified as a Z-type hexaferrite consisting

of S, R, and T “spinel” blocks [4,5]. It was further revealed that in the T block the

Fe-O-Fe bond angles were slightly deformed to affect the superexchange interaction

between the Fe ions and induce the spiral spin configuration [7] in Sr3Co2Fe24O41 as

shown in Figure 4-1. Changes in the spin spiral configuration in the presence of an

electric field E induce changes in the magnetization M. In a polycrystalline sample such

65

as ours it induces changes in the remanent magnetization. This physical mechanism for

the ME effect is very different from the mechanisms applicable to multiferroic materials

in the past. This new mechanism opens up new properties or opportunities in the physics

and applications of ME materials.

Figure 4-1 (a) Crystal structure of a part of the hexagonal unit cell. (b) Spiral spin order.

The previously most used technique to explore ME effects was ferromagnetic

resonance (FMR). In the past FMR frequency shifts were measured with an applied E.

There has never been a report on permeability measurement in ME material with

66

application of an electric field, although there are many reports on FMR shifts. The

measurement of FMR frequency shifts is ineffectual in our case, because (a) the shifts are

extremely small and (b) they are strongly damped in the new mechanism. Hence, we have

devised a new measurement method whereby the permeability of our material is

measured directly via a modified coaxial line technique. We refer to these measurements

as “converse” ME measurements.

Although previous authors [1–5] have established a strong correlation between the

spiral configuration and the ME effect, we provide a physical picture, i.e., model for the

effect. Our measurements reveal that Sr3Co2Fe24O41 is electrostrictive. As such, the

application of E strains the material, thereby changing the physical structure of the spiral

spin configuration. It is this physical motion of the spiral response to E that induces a

change in magnetization M. We refer to this model as the “slinky helix” model. Our

model should be contrasted with the model for the ME effect in multiferroics as well as

ferromagnetic metal films wherein the band energies of the up and down spin are

modified by the electric fields at the interface between phase separated ferromagnetic and

ferroelectric films. The change in band splitting leads to a change in surface

magnetization [8].

The thermodynamic enthalpy per unit volume ω(s, E, H, σ) determines all of the

spirally ordered hexaferrite thermodynamic equations of state [9] via the thermodynamic

minimum principle:

67

, , , min , , , , . . . . : (1)

Here, T, P, M, and e represent, respectively, the temperature, polarization,

magnetization, and strain, while s, E, H, and σ represent, respectively, the entropy per

unit volume, electric field, magnetic intensity, and stress. Other thermodynamic quantities

of interest include the adiabatic dielectric constant tensor

1 4" #$$%&,,' 1 4"(, 2

the adiabatic permeability tensor

* 1 4" #$$%&,,' 1 4"(, 3

and the adiabatic ME tensor

, #$$ %&,,' #$$%&,,' . 4

Conventional experiments probing ME effects measure elements of the ME tensor αij

= (∂Mi/∂Ej )s,H,σ. In the converse experiments reported in this work, the ME effect is

probed by measuring elements of the magnetic permeability tensor µ and the strain tensor

e, while noting the manner in which these tensors depend on E and H. Direct

measurements of the magnetization M were also employed.

68

2. Experimental Results

2.1 Experimental Material Growth

In chapter 2, the material growth procedure was presented. We have adopted a

procedure similar to that in Ref. 5 to prepare a single phase of Sr3Co2Fe24O41 except for

the following preparation steps. In order to prevent the formation of other impurity

phases, including W-, M- and/or Y-type phases, it was found most favorable to quench

the sample immediately to room temperature after annealing. Our x-ray data are

consistent with a Z-type hexaferrite structure [11]. Also, for the ME measurements it is

important to minimize conductance current flow or heating effects through the sample in

the presence of high electric fields. As such, the resistivity was increased by annealing the

samples at 600 C in an oxygen atmosphere for 6 hours. The resistivity estimated from

the experimental linear I-V characteristic was ρ = 1.43 × 109 Ω cm for samples of 1-mm

thickness. The preparation in oxygen leads to an Fe2+

concentration reduction, which then

lowers the hopping of electrons between Fe2+

and Fe3+

ions [5,10].

2.2 Magnetoelectric Measurement Technique

Typically, coaxial lines are used to measure permeability and dielectric constants as a

function of frequency, but never in the presence of an electric field or a dc voltage as high

as 2000 V.

69

Figure 4-2 Real and imaginary parts of the polycrystalline Sr Z-type permeability versus frequency.

In chapter 3, the measuring fixture apparatus was presented. In order to minimize the

risks to the instrumentation, the termination of the coaxial line was electrically separated

from the rest of the coaxial line by ∼10 mil. Software was developed in order to calculate

the effects of the separation on the measurement of µ. The technique was calibrated or

standardized against well-known coaxial line results where the line was not split. We

inserted a toroidal-shaped sample in a coaxial line. One side of the toroid was shorted to

the coaxial line termination as well as to the dc ground voltage. The other side of the

toroid was coated with a thin film of silver paint and then connected to a high dc voltage

power supply. Three precautions need to be exercised, as follows. (i) The high dc voltage

must be isolated from the microwave voltage of network analyzer instrumentation. (ii)

Antenna effects from dangling wires connected to the toroidal sample must be reduced.

The vector network analyzer was used to measure the electrical scattering S-parameter.

70

Antenna effects were reduced by connecting high-frequency capacitors to electrically

short out any microwave signals in the dangling wires. (iii) Finally, the thickness of the

silver paint film must be sufficiently small compared to the skin depth (10 µm < 200 µm)

so that the reflected signal from the toroid is not dominated by pure metallic reflection

from the silver paint. For example, initially we inserted the toroidal sample without any

wire attachments, silver paint, or capacitors attached to any wire. In short, a conventional

coaxial line measurement was performed to measure µ as a function of frequency (see

Figure 4-2). We then loaded the toroidal sample with all the attachments (wires, paint,

capacitors, etc.) but no dc voltage applied and measured µ again. We were again able to

obtain the same µ curve as in Figure 4-2. At this point we applied the dc voltage to the

toroidal sample so we measured changes in µ due to the dc voltage. Using conventional

scattering S-parameter analysis, µ may be calculated from the reflection coefficient, S11

(see Figure 4-3). The analysis is simplified considerably if the thickness of the toroidal

sample is less than the wavelength in the sample (1 mm . 6cm). The calculated S11

scattering coefficient was calculated as follows [14]

/00& 123 cos78 92:;7823 cos78 92:;78 < 928=;78. 5

where 2 ?*/ and 7 √*.

71

Figure 4-3 Coaxial line schematic.

Here /00& is the reflection coefficient for the shorted port of the coaxial transmission

line; Z is the coaxial line characteristic impedance of the sample; k is the propagation

constant, which is equal to 2π/λ; t is the sample thickness; and Z0 is the characteristic

impedance of the coaxial line, which is 50Ω. The permeability may then be determined

from

* B 23 # 198% 11 /00&1 /00& <, 6

where ω is 2πf and f is the frequency. Note that this formula is an approximate formula

and it is valid as long as kt . 1. The sample thickness was 1mm and the approximation

is valid up to 3 GHz. The advantage of our approach or calculation technique is that the

permittivity, ε, does not enter into the analysis in this limit of approximation. This is an

extremely important point in that dielectric changes cannot influence the changes in µ as

measured by this technique, as there is no dependence on ε in Eq. (6).

72

Microwave experiments were performed under the following conditions: for a given

direction of the remanent magnetization, Mr, the electric field was applied parallel,

anti-parallel, and perpendicular to Mr. Prior to the experiments the remanence direction

was poled with a permanent magnet. The direction of the remanence magnetization, Mr,

is fixed by applying a DC magnetic field in the direction perpendicular or parallel to the

sample’s slab plane prior to the application of a static electric field as shown in Figures

4-4 (a) and (b). The removal of the DC magnetic field leaves the ferrite in the remanence

state, Mr, or simply magnetically poled.

In Figure 4-2, we illustrate the complex relative magnetic permeability µ(ω-j0+) for

low microwave frequencies, on the scale of the ferromagnetic resonant frequency. In the

limit ω→0, we expect the permeability, µ(0), to be of the order of [14]

*0 1 14"EFGH <, 7

where Mr is the remanence magnetization and Hφ is the six fold magnetic anisotropy field.

We measured 4πMr = 105 G and thereby Hφ ≈ 40 Oe, as in Figure 4- 2. This result is

typical of Z-type hexaferrite [7]. The permeability µ(ω) as a function of the frequency is

given as [14]

* 1 # 4"EFG0G0GJ J/KJ%, 8

73

where 4πMr is the remanence magnetization, H1 = H + Hφ + 4πMr + Hθ , H is the external

magnetic field, Hφ is the six-fold magnetic anisotropy field, Hθ is the polar angle uniaxial

magnetic anistropy field, H2 = H + Hφ, γ = g(MJNO) P 1.4g × 10

6, and g ≈ 2.

Magnetic damping may be included by making ω complex for example (∆RS ) ≈ 100

Oe at X-band frequencies for Z-type hexaferrites, where ω → ω -jω (magnetic damping)

and for H > 0 such that magnetization saturation occurs, 4πMr is replaced by 4πMs, Ms

saturation magnetization.

Figure 4-4 Static electric and magnetic fields bias conditions of the hexaferrite slab in (a) E parallel or

anti-parallel to Mr and in (b) E perpendicular to Mr.

74

In our experiments H = 0 and thus there is no magnetic saturation. All of the magnetic

parameters in Eq. (8) were measured by us in Ref. 11. This means that for a given value

of 4πMr, µ may be plotted as a function of frequency. The plot in Figure 4-2 applies for H

= 0 and E = 0. However, as E was varied in our experiment, 4πMr also varied. This

implies that from the knowledge of 4πMr alone as determined at zero frequency, one may

indeed infer µ as a function of frequency. Hence, a family of curves of µ versus frequency

may be plotted where 4πMr or E is the third variable parameter, since 4πMr is related to E

via the ME effect of these materials. This was an important clue in the performance of

our experiment at microwave frequencies. We chose to measure the change in µ, ∆µ,

relative to the value of µ at E = 0 and H = 0, as a function of frequency. We do not report

the imaginary component of µ, since there is no FMR line width measurement on these

materials.

2.3 Experimental Magnetoelectric Measurements

Figures 4-5 and 4-6 show the changes in permeability when an electric field is applied

parallel or antiparallel and perpendicular to the magnetization, respectively. Under a

change in parity, E→−E and Mr → Mr. Under time reversal, E → E and Mr →−Mr the

data indicate both broken parity and broken time reversal symmetry. This represents the

fundamental broken symmetry expected of ME effects. The measurements in Figure 4-5

correlate very well with the vibrating sample measurements whereby Mr scales as E,

changing polarity with the direction of E [11]. The quadratic ME interaction in the

75

conjugate enthalpy of Eq. (1) is given by

T UV. V. , 9

where n is a unit vector in along the spiral axis.

(a)

(b)

Figure 4-5 Magnetic permeability change versus electric field over a microwave frequency range when M

is parallel and antiparallel to E. (a) Theoretical calculation and (b)experimental measurement for E = 5

KV/cm.

76

Figure 4-6 Magnetic permeability change versus electric field over a microwave frequency range when M

is perpendicular to E.

The total driving fields Ed and Hd have a reversible and an irreversible thermodynamic

part [12,13]. There are two ways to calculate the change in µ with frequency and E. One

way is to apply Eq. (8) for different values of Mr of E. It is somewhat tedious but possible.

The other way is to go back to the magnetic dynamic equation of motion (after

linearization).

1K XYdt \ ] ^ Y ] \ 10

where m is the microwave dynamic magnetization, M0 is the average static internal

magnetization =Mr , h is the microwave magnetic field, and H0 is the static internal field

=Hφ. The ME coupling to the magnetic motion modifies the above equation

77

1K XYdt \ ] ^ #1 αχaωZ3χa0χd0% Y ×××× \ 11

where α is the ME coupling ≈0.5 × 10−2

[5], χe(0) is the dc electric susceptibility, χm(0) is

the dc magnetic susceptibility, and Z0 is the characteristic impedance of the medium.

(a)

(b)

Figure 4-7 (a) Applied electric field over the slab to measure strain, (b) Electrostriction strain of

polycrystalline Sr Z-type versus electric field.

78

The ME effect manifests itself as a change in the dynamic magnetic field at microwave

frequencies. After much algebra as developed in Ref. 14, we obtain

T*Fe*0 B 1χNe fχd0 . ∆MhMh < 1χMe fχa0 . ,Z3<, 12

where χNe f and χMe f are the real parts of the magnetic and electric susceptibilities,

respectively. For example, the complex magnetic susceptibility is defined as [14]

(Nf χNe f 9χNee f 4"EFG0G0GJ J/KJ 13

where H1 = Hφ + Hθ, γ = 2π g 1.4×106 Hz/Oe, ω=2πf, and Mr is the remanence

magnetization. Magnetic damping may be included in the expression for (Nf by

assuming ω to be complex. Mr, Hθ (uniaxial magnetic anisotropy field), Hφ (six-fold

magnetic anisotropy field), and i factor were measured [11] and their corresponding

values were 105 G, 25 kOe, 40 Oe, and ~ 2, respectively. The zero magnetic field FMR

frequency, f0, may be easily deduced from the expression for (Nf as f0 = i1.4 ]10j?GHGH Gk B 2.51 GHz. Clearly, f0 is well above the frequencies where T*Fe is

maximum (l 0.5 GHz). Thus, there is no correlation between the zero magnetic field

FMR and Δ*Fe , but according to Eq. (7) there is a direct correlation between Δ*Fe and

ΔMr induced by the application of an E field [11]. The relationship between E and ΔMr

is given as TMr = α E, where α is the linear ME coupling. Mr also implies an internal

79

change in magnetization via the spin spiral reconfigurations. Since Δ*Fe is maximum at

relatively low frequencies compared to f0, we can approximate Eq. (7) by neglecting

magnetic damping. Magnetic loss or damping is the maximum at FMR frequency,

T*Fe*0 B n GHG0GHG0 J/KJ . ∆EFEF o # ,231 JpJ%, 14

where ω is real (no magnetic damping), τ is the electric relaxation time, and Z0 is the

characteristic impedance of the ME medium (~250). Thus, Eq. (8) is applicable for

frequencies below f0. From Eq. (8), it is predicted that the decrease or "roll-off" of Δµhe

with frequency is due to electric damping or relaxation rather than magnetic damping.

The experimental data in Figure 4-5 are compared with the theoretical plot of Δµhe as a

function of frequency and E = 5kV/cm. Other theoretical plots scale the same with

frequency at other values of E. The relaxation parameter τ was assumed to be 3.2 × 10-10

s,

which compares with the τ ≈1.5 × 10-10

s deduced from the measured frequency

dependence of ε (see data in Refs. 4 and 11). Assuming that , 60 ] 10rs, Z0 ≈250 ,

and ∆EF/EF= 0.16, we estimate ∆EF= 0.96, compared to the experimental value of 1.2

at E = 5 kV/cm. Finally, in Figure 4-7 the strain induced by an electric field is exhibited

as a function of the electric field. The strain is quadratic in the electric field strength,

which indicates that Sr3Fe24Co2O41 is neither ferroelectric nor piezoelectric material.

Hence, the material exhibits electrostriction, and therefore, it may not be classified

80

strictly as a multiferroic material.

Figure 4-8 Spin spiral configuration for different directions of E. (a) E = 0, (b) E parallel to M, and (c) E

antiparallel to M.

3. Conclusions

The material hexaferrite Sr3Fe24Co2O41 exhibits broken symmetries for both time

reversal and parity. This is a central feature of these ME materials. Measurements have

been made in order to verify this feature, but in a novel manner. The measurements

involve the magnetic permeability and strain, both as a function of the electric field E.

The field dependence on strain indicates that the material is electrostrictive, which

distinguishes this material from a pure multiferroic material. The application of an

electric field induces a change in the spin spiral configuration of the hexaferrite via

81

electrostriction. This spin reconfiguration manifests itself as a change in the remanence

magnetization Mr and, therefore, as a change in the permeability. The changes in Mr were

confirmed by vibrating sample measurements, and changes in permeability were

measured using a modified coaxial line technique. This physical picture may be detailed

in a sketch we refer to as the “slinky” model (see Figure 4-8). With the application of E

the angle θ or the angle of the spin within the cone is affected by the direction of E. As

the angle θ is varied with E, the size of the “slink” changes, as well as the “net” internal

magnetization along E and, therefore, Mr. It is well known that hexaferrites are

mechanically hard along the c-axis and easier to strain in the azimuth plane

(perpendicular to the C axis). Figure 4-7 represents the average strain along the

component of E in the azimuth plane rather than along the c-axis, since the hexaferrite is

polycrystalline. Figure 4-8 shows the average change in magnetization along the

component of E in the c-axis of each crystallite, in agreement with Figure 4-5. Hence, the

strain along the c-axis or the change in magnetization is not at all correlated with the

strain as measured in Figure 4-7. As such, from practical considerations this simplifies

the design of ferrite devices and applications, since µ is the principal quantity that

governs the performance of a microwave ferrite device, for example. Hence there would

be less need for permanent magnets in microwave device applications, since only E is

applied.

82

4. Appendix

In this section the theoretical calculation derivation of equation (8)-(12) are presented.

(I) FMR condition may be derived from magnetic dynamic equation of motion (after

linearization):

1K dmttttttudt Mtttu ] Httu wM3tttttu mtttux ] H3ttttu htu

1K dmttttttudt M3tttttu ] htu mtttu ] H3ttttu I

where H3 B H and M3, is average static magnetization.

(II) Assuming shape of particle as polycrystalline, µ may be calculated as

* 1 | s~rR/S ; G0 GH Gk; GJ GH II

(III) Introducing magnetoelectric effect,

~ , Httu. Ettu ,e Mtttu. Pttu ,e(3NHttu. (3MEttu , 3 1 , ,e(3N (III)

(3is the DC susceptibility.

(IV) Calculation of internal magnetic field, Httu Httu tttttuF ,ePttu ,eP3tttu ptu (IV)

83

P3 Static polarization

p Dynamic polarization

---------------------------------------------------------------------------

Considering (I), (II), (III) and (IV) the equation of motion becomes

1K dmttttttudt M3tttttu ] htu1 αχaZ3 mtttu ] H3ttttu yielding

*f 1 4"EFG01 ,eχaZ3G0GJ JKJ ; EF EF3 TEF *f *3 T*F

hence,

T*Ff*0 4"TEFG0,eχaZ3G0GJ JKJ

where from Mtttu tttttuF αEttu or simply TEF ,. Thus,

T*Ff*0 4"TEFG0,eχaZ3 TEFEFG0GJ JKJ ; TEF , . T*Ff*0 (Ne f ,3EF ,23 (Me f (Ne 0 (Me 0

or T*Ff*0

n(Ne f(Ne 0 ,3EF o n(Me f(Me 0 ,23o V

84

(Ne f(Ne 0 GHG0G0GJ JKJ and (Me f(Me 0 11 JpJ Replacing in (V),

T*Ff*0 GHG0G0GJ JKJ ,3EF # ,231 JpJ%.

85

References

[1] M. Fiebig, J. Phys. D 38, R123 (2005).

[2] G. Srinivasin, V. Zavislyak, and A. S. Tatarenko, Appl. Phys. Lett. 89, 152508

(2006).

[3] T. Kato, H. Mikami, and S. Noguchi, J. Appl. Phys. 108, 033903 (2010).

[4] M. Soda, T. Ishikura, H. Nakamura,Y.Wakabayashi, and T.Kimura, Phys. Rev.

Lett. 106, 087201 (2011).

[5] Y. Kitagawa, Y. Hiraoka, T. Honda, T. Ishikura, H. Nakamura, and T. Kimura,

Nature Mater. 9, 797 (2010).

[6] Y. Takada, T. Nakagawa, M. Tokunaga, Y. Fukuta, T. Tanaka, and T. A. Yamamoto,

J. Appl. Phys. 100, 043904 (2006).

[7] W. Martienssen (ed.), Landolt-B¨ornstein: Numerical Data and Functional

Relationships in Science and Technology (Springer-Verlag, Berlin, 1970).

[8] C.-G. Duan, J. P. Velev, R. F. Sabirianov, Z. Zhu, J. Chu, S. S. Jaswal, and E. Y.

Tsymbal, Phys. Rev. Lett. 101, 137201 (2008).

[9] L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media

(Pergamon Press, Oxford, UK, 1984).

[10] O. Kimura, M. Matsumoto, and M. Sakakura, J. Am. Ceram. Soc. 78, 2857

(1995).

[11] K. Ebnabbasi,Y. Chen, A. Geiler, V. Harris, and C.Vittoria, J. Appl. Phys. 111,

07C719 (2012).

86

[12] A. Widom, S. Sivasubramanian, C. Vittoria, S. Yoon, and Y. N. Srivastava, Phys.

Rev. B 81, 212402 (2010).

[13] L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Elsevier

Butterworth-Heinemann, MA, 1984).

[14] C. Vittoria, Magnetics, Dielectrics, and Wave Propagation with MATLAB Codes

(CRC Press, New York, 2011).

87

Chapter 5. Strong Magnetoelectric Coupling in Hexaferrites

at Room Temperature

1. Introduction

In this chapter, the magnetoelectric effect in single-crystalline Sr Z-type hexaferrite

materials is presented. The measurements include material characterization and change in

remanence magnetization (Mr) versus electric field. In a very low electric field equal to

3.75 V/cm, 14% change in Mr was observed. We deduced a magneto-electric coupling of

55.4 in CGS units or 2.32×10-6

sm-1

(SI units) which is the highest value measured to date.

There have been a number of publications dealing with the magneto-electric properties

of M- and Z- type hexaferrites [1-6]. These hexaferrites are special ferrite materials,

because they exhibit high magneto-electric coupling coefficient at room temperature. This

means that the application of an electric field or DC voltage induces magnetization changes

and the application of a magnetic field induces electric polarization changes. The common

denominator of recent publications was that the tested materials were poly-crystalline. The

application of these types of materials still is not possible along with semiconductors.

And converse measurements have shown that very high voltage or electric field in the

range of 1-5 kV/cm is required for high magneto-electric coupling effect [3].

The magnetic properties of single crystals of Z-type hexaferrites, Sr3Co2Fe24O41,

exhibiting the strongest magnetoelectric effect at room temperature is presented. High

88

ME coupling, α, at very low voltage or electric field was observed in converse

measurements. This is quite promising in terms of being able to induce magnetization

changes with as little as 15 mV compared to polycrystalline materials requiring hundreds

of volts affecting the same change in magnetization. We believe that changes in

magnetization at low voltages places ferrite and semiconductor devices in the same range

of required voltages for modern multi-functional applications.

2. Experimental Measurements

SEM (Scanning Electron Microscope) photograph, XRD (X-ray Diffraction) material

characterization, and FMR (Ferromagnetic Resonance) measurements are shown in

Figures 5-1, 5-2, and 5-3, respectively, consistent with a hexagonal crystal structure.

From VSM measurements we measured 4πMs≈3100 G and Hc=14.14 Oe. From FMR

measurements, we deduced the following parameters: g = 2, ∆H=750 Oe (9.53 GHz),

Hθ=12 kOe, and Hφ=60 Oe where 4πMs, Hc, ∆H, Hθ, and Hφ are the saturation

magnetization, coercive field, the FMR linewidth, the uniaxial magnetic anisotropy field,

and the azimuth anisotropy field (six fold symmetry), respectively.

89

Figure 5-1 SEM micrograph of single crystal of Z-type hexaferrites, Sr3Co2O24O41.

Figure 5-2 Room-temperature X-ray diffraction pattern.

90

Figure 5-3 Ferromagnetic resonance at room-temperature (derivative absorption versus Hext).

The internal field (Hi) is equal to HextNM, where Hext, N, and M are external applied

magnetic field, the demagnetization factor, and the magnetization, respectively. As it is

well known in the non-saturation regime (Hext NM; Ms is the saturation magnetization)

Hi=0 and typically Hext is linear with M. In the saturation regime (Hext NM) the internal

field is finite and pointing along the saturation magnetization direction. As shown in

Figures 5- 4 and 5-7, for external fields up to 700 Oe the measured magnetization scales

as the external field implying non-saturation of the magnetization and, therefore, zero

internal magnetic field.

91

Figure 5-4 Hysteresis loops change versus electric field with the magnetic field applied parallel (//)

and perpendicular () to the slab plane.

The change in remanence magnetization versus DC electric field when the applied

magnetic field is parallel and perpendicular to the material slab in an electric field equal

to 3.75 V/cm, is given in Figure 5-4. The observed change in Mr, remanence

magnetization, is 14%. This is given in Figure 5-5 for the external magnetic field

perpendicular to applied electric field and parallel to slab plane. The change in Mr versus

electric field when it is applied parallel, anti-parallel and perpendicular to the

magnetization is given in Figure 5-6. The magnetoelectric phenomenon is explained in

terms of spin spiral order of the magnetic structure referred by us previously as the

"slinky helix model" in chapter 4 and [3].

92

Figure 5-5 Remanence magnetization change versus electric field with the magnetic field applied

parallel (//) to the slab plane.

Figure 5-6 Change in remanence magnetization versus electric field.

93

Figure 5-7 change in capacitance versus magnetic field.

These measurements show the ME effect at very low electric fields. The

magnetoelectric coupling was measured to be in the order of ~55.4 in CGS units or

2.32×10-6

sm-1

(SI units) at room teperature and there is no other material that exhibits

such high coupling at any temperatures. In poly-crystalline Sr-Z α was measured to be

1×10-10

sm-1

and at ~30 Oe reached a maximum value of 2.5×10-10

sm-1

[4]. In the convers

magnetoelectric this value was measured to be 7.6×10-10

sm-1

[7]. The ⁄ peak

values in single phase materials usully are small. For instance, α=4.1×10-12

sm-1

(Cr2O3) at

307K, and ⁄ ~10-9

sm-1

(Tb2(MoO4)3) [8-9]. Giant magnetoelectric effects equal to

α=2.3×10-7

sm-1

in single epitaxial interface in ferromagnetic 40 nm La0.67Sr0.33MnO3

films on 0.5 mm ferroelectric BaTiO3 substrate has been observed near room temperature

with low magnetization [10]. This is almost 10 times smaller than our measured value

94

reported here in single crystalline Sr-Z hexaferrite. Also, the magnetoelectric effect

observed by us was measured at very low electric fields ~3.75 V/cm.

3. Conclusions

We measured a magnetoelectric coupling, α, of 2.32×10-6

sm-1

in Sr3Co2O24O41 single

crystals. The α value measured by us represents the highest value measured at room

temperature. For example in La0.67Sr0.33MnO3 films α=2.3×10-7

sm-1

at room temperature.

The implications of high values of α are immense especially at room temperature. It

means that one can affect significant changes in magnetization in the millivolt range

rather than hundreds of volts range (for thickness in the order of 1mm, for example). We

envision many applications in sensor and microwave devices.

95

References

[1] K. Ebnabbasi,Y. Chen, A. Geiler, V. Harris, and C.Vittoria, J. Appl. Phys. 111,

07C719 (2012).

[2] M. Soda, T. Ishikura, H. Nakamura,Y.Wakabayashi, and T.Kimura,Phys. Rev. Lett.

106, 087201 (2011).

[3] K. Ebnabbasi, C. Vittoria, and A. Widom, Phys. Rev. B 86, 024430 (2012).

[4] Y. Kitagawa, Y. Hiraoka, T. Honda, T. Ishikura, H. Nakamura, and T. Kimura,

Nature Mater. 9, 797 (2010).

[5] L. Wang, D. Wang, Q. Cao, Y. Zheng, H. Xuan, J. Gao & Y. Du, Nature, 2, 223

(2012).

[6] K. Ebnabbasi, Marjan Mohebbi, and C. Vittoria, Appl. Phys. Lett. 101, 062406

(2012).

[7] K. Ebnabbasi, Marjan Mohebbi, and C. Vittoria, J. Appl. Phys., Accepted (2013).

[8] Folen, V. J., Rado, G. T. and Stalder, E.W., Phys. Rev. Lett. 6, 607–608 (1961).L.

D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon

Press, Oxford, UK, 1984).

[9] Ponomarev, B. K., Ivanov S. A. et al., Ferroelectrics 161, 43–48 (1994).

[10] W. Eerensteini, M. Wiora, J. L. Prieto, J. F. Scott and N. D. Mathuri., Nature

Letters, 6, 348 (2007).

96

Chapter 6. Microwave Magnetoelectric Devices

1. Introduction

Ferrite materials are widely used in passive and tunable electromagnetic signal

processing devices. In Figure 6-1, potential and current applications of ferrite materials and

devices in communication systems and their operating frequency range are shown. Due to

their excellent dielectric properties, ferrites possess the advantages of low loss and high

power handling relative to semiconductors. Magnetic fields are usually generated using

permanent magnets or current driven coils, leading to relatively large component size,

weight, and cost, as well as slow response time in comparison to semiconductor-based

technologies.

Magneto-electric materials can be a practical solution to control the magnetic

parameters of ferrites by electric field and/or voltage and would eliminate permanent

magnets and tuning coils to overcome most of the disadvantages in the use of ferrites for

microwave devices. A situation where ferrites are compatible with active components

based on semiconductors would become a reality. Furthermore, key advantages of ferrites,

including low insertion loss and high power handling capability could be exploited without

the penalty of added size, weight, and cost, as well as increased response time.

In this chapter a single layer of poly-crystalline magneto-electric Z-type,

Sr3Co2Fe24O41, which has strong ME effects at room temperature, is proposed to induce

magnetic parameter changes with application of voltage. It is very important that in this

97

type of material there is no need of an external magnetic field to control the parameters of

magnetic material and simplify the tune of device performance.

Figure 6-1 Potential and current applications of ferrite materials and devices in communication systems

and their operating frequency range.

Traditionally, most of ferrite devices and elements were used in defense and military

applications such as phase array systems and search and missile radars, shown in Figure

6-1. In these applications, phase shifters and circulators play key role. The magnetoelectric

material studied in this work has good performance in low frequencies (< 4GHz) with no

magnetic bias field and hence, very compact devices can be designed. This is quite

98

important since there are a lot of commercial applications like cellular mobile, medical

applications and GPR (Ground Penetration Radar) in this frequency range.

In terms of phase array in wireless communication systems, in L and S frequency bands,

phase shifter has found its way into applications such as digital television, mobile

networking, GPS (Global Positioning System), RFID (Radio Frequency Identification),

and even anti-collision systems. Additionally, phase shifters are utilized in high data rate

communication systems and test equipments to implement mixer, VCOs (Voltage

Controlled Oscillators), phased locked loops, frequency synthesizers, and etc.

There are different types of phase shifters with different materials and design

techniques. In most cases, phase shifting functions are realized using digital semiconductor

devices that offer small size, fast switching times, and low power consumption. These

devices, however, suffer from high insertion loss (> 5 dB), poor power handling

capabilities (<1 W), and high cost (GaAs substrate). Other technologies, including MEMS

and ferroelectric phase shifters, have emerged over the years but none of them deliver the

same exceptional insertion loss, power handling, and reliability as ferrite devices. One

issue with MEMS phase shifters is that packaging is perhaps more critical than with

alternative technologies. Hydrocarbon contamination may compromise MEMS reliability

so hermetic seals and careful processing are required. In Table I, a summary of different

technologies in the design of phase shifters are provided for comparison [1].

99

2. Multi-Phase Magnetoelectric Microwave Phase Shifter

Multi-phase and multiferroic composite materials have been proposed to generate

internal magnetic fields via voltage. These composites usually consisted of

magnetostrictive and ferroelectric or piezoelectric slabs in physical contact whereby

magnetic field sensors have been implied and fabricated so far. Also, small shifts in

ferromagnetic resonance (FMR) have been observed using magnetoelectric composites in

the presence of an electric field.

The ME effect is observed in two classes of materials: single phase multiferroic

materials possessing simultaneously both ferroelectric and ferromagnetic properties and

composites consisting of ferroelectric and ferromagnetic phases. The ME effect in the

single-phase materials [3] arises from the long-range interaction between the atomic

moments and electric dipoles in ordered magnetic and ferroelectric sublattices. In previous

single-phase materials the problem was the realizable ME coefficient is very small (1–20

mV/cm Oe) and not sufficient for practical applications. Moreover, ME effect in most of

these single-phase materials is observed only at low temperatures as either ferromagnetic

(or antiferromagnetic) or ferroelectric and transition temperature is very low.

Traditional ferrite phase shifter use magnetic tuning systems that are slow, demand high

power, and are not miniature in size. A desirable alternative is the latching ferrite phase

shifter that operates at the remanent magnetization for the ferrite element and requires

current pulses for switching the magnetization state [4].

100

Table I. Comparison of phase shifter technologies (The ferrite type is non-ME) [1].

Type

Feature

Ferroelectric Semiconductor

/MMIC Ferrite MEMS

Cost Low Expensive Very expensive Low

Reliability Good after 106 to

40V/µm bias cycle

Very good (if

properly packaged) Excellent

Good after several

billion cycles

Power

handling Good, >1W

Very Good, tens of

watts Very high (kW)

Low power,<50mW

for high reliability

Switching

speed

Intrinsically fast

(~ns)

Fast at low power

(<10-9S)

Slow

(inductance 10

to 100µs)

Slow (mechanical 10

to 100µs)

Radiation

tolerance Excellent

Poor (good if

radiation hardened) Excellent

Excellent

(mechanical; no solid

state junction)

DC power

consumption Low (<<1µA) µW

Low (10mW:

diodes,~0: FETs)

High (large

current)~10W negligible

RF loss ~5dB/36o

@K-band

2dB/bit @ Ka

band=8dB

<1dB/360o

@X-band

~2.3dB/337.5o @ Ka

band

Size Very small (mm2) Small (~10mm2 @

Ka band) Large

Smalle (compared to

MMIC)

Linearity IMD interest

+60dBm

IMD intersect +35

to +40dBm --------

IMD intersect

+80dBm

Phase shifts could also be realized through magnetostatic wave propagation or

ferromagnetic resonance FMR in planar ferrites in microstripline structures [5]. The MSW

wavelength and group velocity are two to three orders of magnitude smaller than that of

electromagnetic waves of the same frequency. This makes possible a phase shift of decades

of π for propagation distances of several millimeters. In the case of phase shifters operating

close to FMR, a rapid change in the permeability and phase shift can be achieved by tuning

the bias magnetic field [6]. But all of the above ferrite phase shifters, in general, require

101

high electrical power for operation and cannot be miniature in size or compatible with

integrated circuit technology. Ferroelectric phase shifters, on the other hand, can be tuned

with an electric field [7]. But such phase shifters are very lossy at frequencies above 1–5

GHz. With a ferrite-ferroelectric layered structure, it is possible to achieve both magnetic

and electric field tunabilities of the phase shift [8,9]. In [10], the design and

characterization of a new tunable electric field phase shifter based on ferrite-piezoelectric

layer composite has been published. The electrical control of the phase shifter is realized

through microwave magnetoelectric effect. The phase shifter is capable of rapid tuning and

compact size. However, the disadvantage of this design is the multi-layer of the device and

the required magnetic field to bias the material leading to heavier and bigger component.

Figure 6-2 Schematics of fabricated magnetoelectric nonreciprocal microwave phase shifter in [10].

102

In Figure 6-2, the schematics of fabricated ME microwave phase shifter and ME

resonator of YIG film on GGG bonded to PMN-PT is shown [2, 10].

The base of the phase shifter is a microstrip transmission line on alumina substrate (εr

= 9.8, thickness =1mm). Ferrite phase shifters maximize phase shift over a given

distance by producing circularly polarized microwaves to interact with the magnetic

dipole moments in. the biased ferrite material. In the past this was typically done by

placing a longitudinally (i.e., in the direction of propagation) biased ferrite rod in the

center of a waveguide. Although this technique produced the desired phase shift, it was

costly to manufacture because the cross-section of the structure was a fraction of the

operating wavelength. In [10], the designed phase shifter consists of a YIG-PZT resonator,

and microstrip loops of lengths λ/8 and 3λ/8 that produce a circularly polarized

microwave magnetic field in the resonator. By this phase shifter the differential phase

shifts of 90°–180° could be obtained with nominal electric fields on the order of 5kV/cm.

The device shows an insertion loss of 1.5–4 dB at 5–10 GHz.

3. Single-Phase Magnetoelectric Microwave Phase Shifter

The design in [10] has two main disadvantages. First the multi-layer or multi-phase

structure of the device and second the required external biasing magnetic field. Both

make the device pretty big and non-compact. The design of the phase shifter in this

section is based on a single phase or single layer of the poly-crystalline Sr Z-type

hexaferrite which was presented in previous chapters and studied in detail in terms of

103

material characteristics change versus electric field with no external biasing magnetic

field. It was found that the change in remanence magnetization for E=5kV/cm is ~13%.

Here in our design we will refer to this change in permeability to design the phase shifter.

First the desirable structure of the phase shifter is analyzed and studied and then it is

simulated and compared to experimental results.

3.1 Meander Line Micro-strip

Here the meander line structure is studied to see if we can get reasonable phase shift. If

we suppose εr=8 and µr=3for the ME substrate, the phase constant at 1GHz for a

micro-strip with 1cm length will be:

3 10√µε 10 6 360

1 3606 60

By applying voltage if we have 10% change in both εr and µr, the phase shift will be:

∆φ = φ(E)- φ(0)≈7o

By utilizing meander line microstrip, shown in Figure 6-3, for 180o, we should use 25

lines which make the device big and for that number of lines the insertion loss will

increase and lossy devices is resulted.

104

Figure 6-3 Schematics of meander line microstrip.

A solution to use less number of meander lines is using high dielectric materials like

"D-100 Titania" as a substrate which has dielectric constant equal to 100. If sandwich

microstrip is designed, the overall permittivity will be between 32 and 100. And 10%

change in εr and µr will result in higher value in phase shift. For example, at 1GHz for

1cm length the phase shift will be roughly 90o. Although this is high value, the substrate

is expensive and fabrication of microstrip on that requires special fabrication process.

And also to get higher phase shift we need to use more microstrips and insertion loss gets

higher.

3.2 LC Phase Shifter Theory and Design

In this section a method is presented that prevents the big loss and size problems.

These disadvantages are resulted since the change in permeability in high frequencies

(>1GHz) is small and hence the phase shift by applying voltage is small. To achieve

higher shift we can use LC circuit in our design. L can be realized by the ME material

and microwave capacitors can be used in either of series or parallel with the L. And we

105

can design the L and C values to be set in the resonance frequency at required value and

by a small change in voltage the S21 phase change for ~180o. The series microwave

network is shown in Figure 6-4.

Figure 6-4 Microwave network consisting of elements connected in series.

S21 in this case is:

11 2

1

If Z is a pure inductor (Z=jLω) then

11 2

!"#$ 2 2

0%/ !"#$ '02 ( !"# '02)×10

100 (

5+%/ !"#$ '5+%/ 2 ( !"# '0.902)×10

100 (

.

/ 5+%/ 0%/ !"#$ ' 0.102)×1001 0.902)×100 (

if 02)×100 1 1 then

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/ !"#$ 2 10.902)×100 3

for an square spiral inductor with 2 turns with 1cm length the L(0) will be

0 4 5#6 6.28 10$0

which results in

/ 4.19:;. Since L is proportional to µr any change in permeability is reflected in L. Considering

this and 10% change in L @ 1GHz the change in phase for a spiral inductor with 10 turns,

as shown, will be ~ 4 degrees.

For pure inductor the phase change is small. Instead of that a series LC is used where

Z=jLω+1/jCω. In this case one can calculates the S21 as:

2<1 < 2< 3

/ !"#$ = 2<> ?1 2< <>? < ?@ 4

Here L and L' are the inductance values in 0 and E (V/cm), respectively. The phase

shift is direct proportional to frequency and change in inductance.

In Figure 6-5, the change in phase for an example series LC is given (L=2.838µH,

C=15fF→fr= 0.77GHz). In this technique we can obtain more shifts in phase for small

changes in remanence magnetization of the ME material in microwave frequencies and

hence in inductance.

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Figure 6-5 Phase shift by applying electric field or voltage.

L in the design is realized as spiral inductor. This is shown in Figure 6-6. CST

microwave studio was used to simulate the designed device. The problem with the

software simulators such as HFSS was there is no material in their component library to

be introduced to the software. The beauty with CST MWS is the user can model the

material such as Debye and Lorentz models. In this work we used Lorentz model and we

replaced the values by the experimentally measured results presented in previous chapters.

In the Lorentz model, as given below, it is required to put the resonance frequency and

static and relaxation permeability values.

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5A 1 4)BACCC D ; D F

D 1 G, G IJ KIL:6! 9M#"I N"6":!:6

C C CO 4)BA CP

C C CO

Here H=0.

If we re-write these equations

5A 1 4)BQ/C1 1CC D F 5R 5QSTSUV

1 D

D

In the simulation it was supposed 5QSTSUV 3.8, 5R 1 , W 2.51KCX and

2)W1 G.

(a)

(b)

Figure 6-6 Simulated phase shifter structure (a) without and (b) with the ME material introduced with

Lorentz model.

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The simulation results for the S21 amplitude and phase in dB and degrees, respetively,

are given in Figure 6-7. As shown, the resonance frequency is close to 1GHz and there is

~180 phase shift. If the resonance frequency is shifted by applying voltage, this phase

change can be achieved. This is a reliable method to broaden the phase change for small

value change in permeability.

Figure 6-7 Insertion loss and phase simulation results.

The fabricated device and measure change in phase by applying voltage are shown in

Figures 6-8 and 6-9, respectively. We should notice that the measured values are for pure

inductor and without connecting the capacitor. The value is close to the calculation.

110

However in 300V it gets bigger and that is because by increasing voltage the permittivity

also changes and the overall change is bigger than what we expect for pure inductor. This

is required result and it can be an advantage because for a desire change we can apply

lower DC voltage.

Figure 6-8 The fabricated phase shifter.

Figure 6-9 Measured phase shift by applying voltage for the fabricated phase shifter with no capacitor.

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4. Conclusions

In this chapter a compact DC voltage tunable microwave phase shifter with no external

biasing magnetic field was presented. It was shown that with a single phase

magnetoelectric poly crystalline Sr Z-type we can design an LC phase shifter with almost

180 degrees phase change although the change in permeability is not that big to

implement the design using the convention meander line microstrips. The designed

device is compact and small in the frequency range of L and S bands.

112

References

[1] Robert R. Romanofsky, "Array Phase Shifters: Theory and Technology",

NASA/TM-2007-214906.

[2] A. S. Tatarenko and M. I. Bichurin, "MicrowaveMagnetoelectric Devices",

Advances in Condensed Matter Physics vol. 2012.

[3] M. I. Bichurin and V. M. Petrov, “Magnetic resonance in layered

ferrite-ferroelectric structures,” Soviet Physics -Technical Physics, vol. 33, p.

1389, 1989.

[4] C. R. Boyd, Jr., IEEE Trans. Microwave Theory Tech. 18, 1119 (1970).

[5] H. Chang, I. Takenchi, and X.-D. Xiang, Appl. Phys. Lett. 74, 1165 (1999).

[6] H. How, W. Hu, C. Vittoria, L. C. Kempel, and K. D. Trott, J. Appl. Phys. 85,

4853 (1999).

[7] H. Chang, I. Takenchi, and X.-D. Xiang, Appl. Phys. Lett. 74, 1165 (1999).

[8] W. J. Kim, W. Chang, S. B. Qadri, H. D. Wu, J. M. Pond, S. W. Kirchoefer, H. S.

Newman, D. B. Chrisey, and J. S. Horwitz, Appl. Phys. A: Mater. Sci. Process. 71,

7 (2000).

[9] Y. K. Fetisov and G. Srinivasan, Electron. Lett. 41, 1066 (2005).

[10] A. S. Tatarenko, G. Srinivasan, and M. I. Bichurin, “Magnetoelectric microwave

phase shifter,” Applied Physics Letters, vol. 88, no. 18, Article ID 183507, 2006.

113

Chapter 7. Discussion and Conclusion

In this dissertation we developed a new class of ferrite materials which exhibit the

highest magnetoelectric coupling ever measured at room temperature. The results gave

rise to the hope that magnetic materials along with semiconductors can be integrated

together in circuits and chips.

The material growth, characterization and converse ME effect in Z- and M- types of

hexaferrites were studied in chapter 2. The ME coupling coefficient at room temperature

were sufficiently high to explore the utilization of these new generation of ferrite

materials in applications such as phase shifter, filter, sensors, DC voltage variable

inductor, variable resonance frequency in printed antenna substrates and etc.

A coaxial device was developed to measure directly the microwave permeability

versus electric field which has been done for the first time. This was presented in chapter

3.

Chapter 4 covered the introduction of a physical model and theory of the converse ME

effects to explain and illustrate the ME coupling and it was referred to as the “slinky helix”

model. The application of strained the material thereby changing the physical

structure of the spiral spin configuration. It is this physical motion of the spiral response

to that induces a change in magnetization . Our model should be contrasted with

the model for the ME effect in multiferroics as well as ferromagnetic metal films wherein

the band energies of the up and down spin are modified by the electric fields at the

114

interface between phase separated ferromagnetic and ferroelectric films.

In chapter 5 the ME effect of single crystalline of single phase Sr Z-type hexaferrite

was presented and it was found that this material had the highest ME coupling coefficient

ever measured. Measurements were performed for both direct and indirect or converse

ME effects. This is quite promising in the use of magnetic materials in integrated devices

along with semiconductors. In addition to the compact devices advantages these materials

possess they can handle high power where semiconductor cannot.

In the last chapter a ME microwave phase shifter was designed and the compact

structure of the device was presented in L band. This is extremely important since this

gave rise to the hope to use these devices in commercial and personal applications where

a lot of those can be found in L and S bands.

This is the beginning of a new generation of microwave components for RF

communications and medical applications. Currently, research is in progress to develop

thin film of these types of materials and results have been obtained in ME M-type

hexaferrite growth to apply very small value of voltage to be comparable to

semiconductor biasing voltage and decreasing the DC power consumption. The materials

are currently bulk and can be utilized mostly in discrete circuits.