Frequency Domain Magnetic Measurements

8/6/2019 Frequency Domain Magnetic Measurements

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Frequency Domain Magnetic Measurementsfrom Kilohertz to Gigahertz

John F. Gregg

Clarendon Laboratory, Oxford UniversityParks Road, Oxford, OX1 3PU, [email protected]

......we applied much prolonged labor on investigating the magnetical forces;

so wonderful indeed are they, compared with the forces in all other minerals,

surpassing even the virtues of all bodies around us. Nor have we found this

labor idle or unfruitful; since daily in our experimenting new unexpected prop-erties came to light.

William Gilbert, De Magnete, 1600

Abstract. This review deals with practical aspects of making frequency-domainmeasurements of magnetic susceptibility and magnetic losses from 200 kHz up to10 GHz. It sets out the types of measurement concerned, distinguishing resonantfrom nonresonant phenomena. The techniques available are categorized accordingto suitability for the different frequency regimes and types of investigation. Practical

recipes are provided for undertaking such experiments across the entire frequencyrange. Marginal oscillator spectrometry is discussed which is applicable across thewhole frequency range. Different instruments are presented, and particular em-phasis is placed on designs which function on the Robinson principle. Analysisof oscillation condition and signal-to-noise performance is dealt with, also sam-ple considerations such as filling factor. Practical circuits are presented and theirmerits and demerits evaluated. Layout and radio-frequency design considerationsare dealt with. Ultrahigh/microwave frequency marginal oscillator spectrometryis given special treatment and several practical designs are given. The essentialsof good microwave design are emphasized. A general discussion of resonant struc-

tures is included which treats multiple layer coil design, slow wave line structures,stripline and cavities. Unusual cavity designs such as the rhumbatron are treated.Use of striplines with microwave marginal spectrometry is described and comparedwith conventional network-analysis techniques. The use of parameter matrices forhigh-frequency analysis is alluded to. Some details of good construction practiceare given together with some practical considerations relating to skin depth andother high-frequency phenomena.

1 Introduction

Mesomagnetism is the study of magnetic systems whose physical size hasbeen engineered to dimensions comparable with or smaller than the length-scales which characterize magnetism. Such length scales include exchange

B. Hillebrands, K. Ounadjela (Eds.): Spin Dynamics in Confined Magnetic Structures I,Topics Appl. Phys. 83, 217245 (2002)c Springer-Verlag Berlin Heidelberg 2002


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218 John F. Gregg

length, domain size, domain wall width, and spin diffusion length. Engineer-ing of magnetic systems which are sufficiently tiny to enter the mesomag-netic regime is difficult and labor-intensive: the reward is the appearance ofnew and bizarre phenomena foreign to macroscopic magnetism such as per-pendicular magnetic anisotropy, superparamagnetism, and spin-dependenttransport. They also include dynamic effects related to the size dependenceof magnetization dynamics and magnetic relaxation paths. Investigating themodification of such dynamic behavior as a function of nanoscale engineeringis one of the primary challenges of nanomagnetism. This review is concernedwith frequency-domain techniques for studying such phenomena in magneticthin films and nanostructures.

2 Time-Domain and Frequency-Domain MeasurementsMagnetisation dynamics may be probed by either time-domain or frequency-domain measurements. Each approach has its merits. The former providesa direct insight into the sequential steps in the magnetization process, aselegantly demonstrated by several authors [1] see Mark Freemans chapter.On the other hand, frequency-domain measurements relate more directly tothe energetics of magnetization dynamics and yield more immediate insightinto the energy-level structure, especially in the case of resonant phenomena.

In what follows, we are concerned with the practical aspects of making

successful frequency-domain magnetic measurements at frequencies between100 kHz and 10 GHz. The general principle underlying such magnetic mea-surements consists of applying an rf magnetic field, then measuring the mag-netic response of the system being studied in terms of the real and imaginaryparts of its magnetic susceptibility from which magnetization dynamics maybe modeled. Techniques are described which include self-tracking marginal os-cillator spectrometry across the entire frequency range, measurement of scat-tering parameters of microwave stripline structures, compact uhf/microwavecavity spectrometers, and microwave ultrasonic techniques. The application

and suitability of the various systems to investigation of bulk samples, thinfilms, and nanostructures in the various frequency regimes is discussed, to-gether with the practical considerations of design, construction, and operationof such systems.

3 Resonant and Nonresonant Phenomena

The magnetic dynamics to be investigated divides loosely into resonant andnonresonant phenomena. Resonant magnetic phenomena involve transitions

between quantum states which may be those of an isolated atom or may evenbe the consequence of collective effects. They generally entail tight selectionrules which impose constraints on the way the magnetic fields should beapplied. For example, in the simplest case of spin-flipping by a magnetic field,


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Frequency Domain Magnetic Measurements from Kilohertz to Gigahertz 219

the Zeeman operator, B J, contains operators in J+, J which generate theselection rule MJ = 1 and require that the radio-frequency magnetic fieldbe applied perpendicularly to the quantization axis. The matrix elements forsuch Zeeman transitions have value:

MJ 1|J|MJ = (JMJ) (JMJ + 1) (1)which gives rise to varying spectral intensities. For example, the hyperfinespectrum of the 51Vanadium species (nuclear spin 7/2) has intensities 7, 12,15, 16, 15, 12, 7 [2]. Such magnetic spin flips may be induced by agencies otherthan a radio-frequency magnetic field. For example, electronic and nuclearresonances may be promoted by varying electric fields or acoustic waves andthe selection rules in these cases may be very different. For the particular

case of an electric field with axial symmetry acting on a nuclear spin systemvia an operator with electric quadrupole form, the Hamiltonian has the form,

3I22 cos2 + 3I2x sin

2 + 3 (IzIx + IxIz)sin cos I2 , (2)

where the radio-frequency electric field makes an angle with the quantiza-tion axis [3]. This gives rise to two different sets of electric field induced tran-sitions with operators of form IzI+ and I+2 and selection rules MI = 1and 2. By contrast with the previous example, for a 51V nucleus these tran-sitions have respective intensities:

21 16 5 0 5 16 21and

7 15 20 20 15 7

Similar effects are observable in acoustically stimulated magnetic transi-tions, for example, in enhanced nuclear paramagnets, where the symmetryof the acoustic operators leads to unusual angular variations and intensityratios between adjacent transitions [4].

Nonresonant magnetic phenomena generally have different behavior.Many arise as Sisyphus-type relaxation processes consequent upon a diag-onal perturbation which commutes the energies of two magnetic states forexample, by Zeeman interaction with an oscillating applied magnetic field.If the timescale of the applied field is comparable with the longitudinal re-laxation time, the level populations will adjust to the energy modulation.Energy dissipation results with consequent variation in for the magneticsystem. Similar considerations apply to the motion of domain walls betweentwo magnetization states which are alternately stabilized and destabilized by

commuting the applied field. The characteristic relaxation time involved inthis case is evidently related to the velocity of the domain wall motion. The


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220 John F. Gregg

general form of the dissipation associated with these Sisyphus effects is givenby

dEdt

1 + 22

, (3)

where it may be seen that the dissipation vanishes at very low and high fre-quencies and there is a pseudoresonant frequency band (which maximizes )whose location is governed by the nature and timescale of the relaxation pro-cess.

4 The Magnetic Susceptibility ()

The common feature of all the frequency-domain magnetic investigations de-scribed in this review is that, irrespective of whether the phenomena understudy are resonant or nonresonant, the parameter being measured is themagnetic susceptibility. This has two components and which are, re-spectively, its real and imaginary parts. The KramersKronig relations adviseus that these are intimately related as follows:

() = 1 +2

P

0

()

2

2

d ,

() = 2

P

0

() 12 2 d

where P means principal part (4)

Thus, a variation with frequency in one component also leads inevitably tovariation in the other. In resonant phenomena where the variations are local-ized in frequency space, their amplitudes may be pronounced. The form of

is symmetrical about the center frequency, whereas that of is antisymmet-rical.

Understanding the magnetic dynamics behind the susceptibility variationrequires measurement of and as a function of amplitude, frequency, tem-perature, nanostructure dimensions, etc. with high precision and reliability.Therefore, we will discuss various techniques for maximizing signal-to-noisein magnetic measurements on bulk, thin film, and nanostructured samples.

5 Resonant Structures

To obtain maximum sensitivity in such measurements, it is usual to employsome form of electrically (or even mechanically) resonant structure to gen-

erate the H field which interrogates the sample: the electrical resonance hasthe dual merits of maximizing the applied radio-frequency magnetic flux andengaging the quality factor of the resonant circuit to enhance the detectedsignal.


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A variety of such resonators will be discussed below. They include seriesand parallel inductance/capacitance resonant circuits for use from 100 kHzto 3 GHz, cavities (with particular emphasis on the reentrant rhumbatrondesign) for frequencies from 300 MHz to 10 GHz, microwave stripline designsfor use from 500 MHz to 10 GHz and above (which are particularly suitable forhighly sensitive work on thin film nanostructures), and microwave acousticresonators for frequencies from 300 MHz to 10 GHz.

5.1 The Concept of Self-Oscillating Detectors

As discussed, variations of or with frequency, magnetic field, etc. areclosely correlated. This implies that if a resonant circuit or cavity is being em-ployed to measure variations in , the associated variations in will cause

the electrical resonance to detune with, consequent appearance of spurioussignals. This is a well-known problem with electron spin resonance cavitiesor in Rollin-type NMR spectrometers [5], especially when highly magneticmaterials are being examined which have sharp variations in susceptibility;a variety of tracking/feedback techniques are used to overcome this, and thesein themselves introduce unwelcome complexity to the dynamic response ofthe instrumentation.

In the authors opinion, this experimental difficulty is an overriding ar-gument for the use of self-oscillating detectors which use the resonant struc-ture itself to determine the oscillation frequency at which the experiment isconducted. They have the additional merit of being markedly less sensitiveto microphonics [6]. A typical schematic for such a self-tracking spectrome-ter is shown in Fig. 1 where a low-frequency parallel resonant tank circuitis the electrically resonant element. However, as will be seen in the high-frequency spectrometer examples described later, the principle has universalapplication across the entire frequency range of 100 kHz10 GHz discussed. Ifcorrectly designed, such spectrometers constitute nice, compact, predictable,well-behaved, high signal-to-noise instrumentation which may additionally beadapted to cryogenic operation without the usual problems of phase lags and

thermal conduction generally associated with cryogenic coaxial cables andwaveguides. Moreover, self-oscillating spectrometers lend themselves to econ-omy of operation because two parameters are simultaneously extractable the operating frequency and the magnetic losses and these translate directlyinto the desired information about changes in and in the sample.

5.1.1 Marginal Oscillators and Limiting Oscillators

Self-oscillating spectrometers automatically track changes in the of the

sample, and these show up as changes in operating frequency. To measurechanges in requires detecting of the radio-frequency power losses in thesample and presenting of these losses at the spectrometer output as low-frequency signals. This is achieved by virtue of the fact that the gain of the


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222 John F. Gregg

Fig. 1. Schematic of self-tracking spectrometer

spectrometer is a function of radio-frequency carrier amplitude due to thenonlinear element in the feedback loop. When the oscillator is operating in itssteady state with constant carrier amplitude, this amplitude is such that thelosses in the resonator tank circuit are balanced exactly by the spectrometergain. Consequently, a change in the tank circuit losses caused by a change in for the sample gives rise to a change in radio-frequency carrier amplitudewhich the detector translates into a dc signal. Circuits which perform in this

fashion are known as marginal oscillators.A wide variety of nonlinear circuit elements is available. Most electronic

devices are inherently nonlinear, and these indigenous nonlinearities may beused perfectly well to make a marginal oscillator, as will be seen in the sin-gle transistor designs discussed below. It is possible, however, at the cost ofgreater circuit sophistication, to introduce carefully tailored nonlinearities tomaximize spectrometer efficiency or to reduce susceptibility to microphonicsor amplitude noise. Oscillators obeying the Van der Pol equation are partic-ularly amenable to mathematical analysis [7]. From a practical point of view,

the spectrometer type which is easiest to implement and which delivers thebest performance is the Robinson limiting oscillator [6,8,9,10]. The Robinsonnonlinear element has a voltage-to-current transfer function which rises lin-early with input up to a threshold beyond which the output is hard limitedas shown in Fig. 2 [11]. The Robinson spectrometer is particularly simple toanalyse. As has been mentioned, its susceptibility to microphonics is low com-pared to the Rollin spectrometer configuration. The overall signal-to-noise isgiven by [6,11,12,13]

V0

2 C Q

4kT F f1/2

(1/Q) , (5)


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Fig. 2. Van der Pol and Robinson characteristics

where V0 is the rf carrier amplitude, is the operating frequency, Q is theresonator quality factor, F is the amplifier noise figure, f is the operatingbandwidth and C is the resonator capacity.

6 Beating Miller Capacitance;the Cherry and Hooper Pair

The bandwidth of transistor amplifiers is usually restricted by Miller capac-itance between the base and collector (gate and drain) of individual activedevices. This restriction is overcome, at the expense of increased power railvoltage, by using cascode designs. A satisfactory alternative which affordswide bandwidth and is compatible with low voltage operation is the Cherryand Hooper Pair amplifier [14] in which the drain of the first active deviceof the pair is made a virtual ground and the gain is obtained instead atthe collector of the second device (Fig. 3). If R1, R3 R2, the gain of thisconfiguration is given by

gm1R2 (1 gm2R2)gm2R2

(6)

(where gm1 and gm2 are the respective mutual conductances of the transistorsTr1 and Tr2) from which it is seen that the component values must be chosensuch that gm2R2 > 1 for positive gain operation.

7 Practical Robinson Limiters

The limiter and detector functions of a Robinson marginal spectrometer maybe elegantly combined using a long-tailed pair design, as shown in Fig. 4.The input voltage/output current transfer function of this circuit is similarto that shown in Fig. 5 which was measured on a JFET long-tailed pair; this is


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224 John F. Gregg

Fig. 3. Cherry and Hooper pair

Fig. 4. Bipolar long-tailed pair circuit which functions as a Robinson-style detec-tor/limiter

another very satisfactory circuit option from which two things are apparent:first, the current at Tr2 is hard limited above a certain threshold to give theRobinson nonlinearity discussed above: second, the current in collector 1 isan asymmetrical function of input voltage, and collector 1 potential thereforecontains detected signal. This mode of detection is superior to straightfor-ward diode detection because the frequency response of the detector is nothampered by parasitic junction capacitance, as in the diode.

Examples of the versatility and high sensitivity of these Robinson os-

cillators are shown in Figs. 6 and 7, which, respectively, illustrate a crossrelaxation process between two different nuclear species and the NMR spec-trum of the rare (1 part in 400 abundant) 50V isotope. The Robinson circuitrydescribed functions well between 100 kHz and 500 MHz with minor compo-nent changes depending on frequency regime. Above 500 MHz, a differentapproach is needed which uses a higher frequency device and which lendsitself to a layout which invokes less parasitic inductance (see the discussionof 0 later). The author has achieved very satisfactory results [5] from thesingle GaAs MESFET Colpitts circuit shown in Figs. 8 and 9. This circuit

functions well up to about 3 GHz. The equivalent circuit of this spectrometeris shown in Fig. 10. Analysis shows that the oscillation conditions are

gm(average) 22R (7)


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Fig. 5. Transfer function of a JFET long-tailed pair

Fig. 6. NMR spectrum of praseodymium vanadate (PrVO4). The praseodymiumnucleus is enhanced and gives rise to the broad resonance lines, one of which co-incides with parts of the unenhanced 51V spectrum (narrow lines). The two 51Vlines which are on speaking terms with the praseodymium nuclei are markedlystronger due to their additional relaxation opportunities via PrV flip-flop processes(courtesy of M. R. Wells)

and

2 = 1/LC , (8)

where which in practice sets the maximum values of for a given MESFETand a coil of given quality factor Q.

8 Cavities

Spectrometers with discrete component resonators (where inductance andcapacitance are spatially separate items) become impractical above about


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Fig. 9. Circuit diagram of Colpitts MESFET spectrometer of Fig. 8

Fig. 10. Equivalent circuit of Colpitts spectrometer of Fig. 8

romagnetic resonance. However, they are large and unwieldy at the best oftimes; they are also tricky to tune and, even then, are tuneable only acrossa small frequency range. For an operating frequency of 2 GHz, they wouldbe highly impractical and their filling factors tiny. Their proper range of op-eration is in the microwave above the range of this article; the interested

reader is referred for further information to the abundant ESR literaturewhere their foibles are described in detail. Instead, an unusual design will bediscussed which combines the twin virtues of compactness and high fillingfactor, namely, the rhumbatron (Fig. 11).

The rhumbatron is a reentrant cavity design whose structure owes muchto the shorted quarter-wave transmission line resonator from which it differsonly in that its lateral dimensions are also engineered to allow additional de-sign flexibility, usually aimed at maximizing the Q factor. It has a maximummagnetic field at the shorted end and a maximum electric field at the openend. The author has found this cavity type highly satisfactory for construct-

ing of compact, well-tempered, tunable marginal oscillator spectrometers foruse from 300 MHz to 10 GHz. Figure 12 shows the rhumbatron being drivenas a marginal oscillator by a GaAs MESFET. The equivalent circuit for the


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228 John F. Gregg

Fig. 11. Rhumbatron design outline

Fig. 12. Circuit diagram of GaAsFet driving rhumbatron

spectrometer is shown (Fig. 13) where the cavity is represented by the parallelresonant circuit L1, C, and R.

The MESFET and the cavity are coupled via single loops in the gate

and drain leads which couple to the magnetic flux at the base of the stub.Spoiler chip resistors are included in series to inhibit the FET from resonatingspuriously on resonances associated with the coupling loops and the parasiticcapacitance of the transistor package. The marginal oscillator is limited bythe nonlinearities in the MESFET characteristics. Varying the Q of the cavitymodulates the dc current drawn. The MESFET is mounted in the rhumbatronbase with its source grounded to the rhumbatron ground close to the acgrounds of the coupling loops so as to minimize all rf ground return paths.Simple analysis, which ignores the end effects of the rhumbatron and treatsit like a shorted /4 transmission line, shows that, provided Q = C R

1,

the oscillation condition is given by gm > (L1/M)2/QZ0 where Z0 is thecharacteristic impedance of a transmission line with the same cross-sectionaldimensions as the rhumbatron. In practice, for a MESFET of given gm, this


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Fig. 13. Equivalent circuit of GaAsFet driven rhumbatron of Fig. 12

expression enables the coupling loop diameters to be estimated from thedesired value of M, the mutual inductance between loop and cavity.

9 Cryogenic Operation

Magnetic measurements frequently need to be performed at low tempera-tures, and this entails physical separation between the ambient temperature

electronics and the sample/resonator assembly. Such a separation is satis-factory, provided that the length of the connecting lead between the two isless than /10. For greater separations, the associated phase shift militatesagainst the performance of the oscillator. The most skilful cryostat designaffords a sample-to-ambient distance of 30 cm minimum for liquid helium op-eration, and the /10 criterion translates this into an upper frequency limitof 100 MHz.

Above this limiting frequency, the solution is to integrate the electron-ics and sample into a single cryogenic package, and several new constraintsnow appear. Evidently, components which function at 4 K are now required,and this excludes such items as bipolar transistors, silicon JFETs, tantalumand electrolytic capacitors, and carbon resistors, among others. Moreover,the active devices need to be restricted in number and power dissipation toavoid unacceptable levels of refrigerant boil-off (1 mW power dissipation inliquid helium equates about 1.2cc/ h liquid boil-off) and sample temperatureinstability. Silicon MOSFETs and GaAs MESFETs (GASFET) offer goodperformance at liquid helium temperatures indeed their mutual conduc-tance and noise performance are often better in the cold [15,16,17,18,19,20,21][22,23,24,25,26].

The single GASFET circuit described earlier (Figs. 8 and 9) translatesreadily into a satisfactory cryogenic spectrometer for frequencies of 500 MHzand higher [5]. The characteristics of the FET change somewhat on cooling


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230 John F. Gregg

usually for the better which implies a different set of bias conditions.Otherwise, operation at low and ambient temperatures is similar. To fill thefrequency gap between this and the 100 MHz upper limit for room temper-ature spectrometers, a dual silicon MOSFET design has been found verysatisfactory. Figures 14 and 15 show a frequency-tuneable implementation ofthis design. Figures 16 and 17 shows a more compact fixed-frequency circuit.Figure 18 illustrates the ambient temperature driver common to both cir-cuits. The potentiometer in the negative power rail of Fig. 14 controls thelong-tailed pair-switching current and hence the radio-frequency amplitude.The heart of this design is again a FET long-tailed pair which offers economyof power dissipation and simplicity of design by performing three functionssimultaneously amplification, limiting, and detection. The drain of transis-tor 1 is a radio-frequency ground point (though the low-frequency detected

output signal is available here), and this feature offers wide bandwidth byavoiding the Miller effect.

Fig. 14. Circuit diagram of cryogenic long-tailed pair-tunable spectrometer

10 Resonator Design

Different resonator schematics are appropriate for the different frequencyregimes and also for different sample types. At low frequencies, resonantcircuits comprising discrete inductance and capacitance are practical anddesirable. At higher frequencies, generally above a few hundred MHz, cavityor stripline designs are advised. Special considerations apply to thin filmsamples and hence also to nanostructured thin films.


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Fig. 15. Schematic of construction of cryogenic long-tailed pair-tunable spectro-meter

Fig. 16. Photograph of the fixed-frequency cryogenic spectrometer

10.1 Construction of High-Performance Resonatorsfor 300 kHz200 MHz

In (5) for the signal-to-noise of a Robinson spectrometer, the parameterswhich related to the coil/resonator were Q(1/Q), where (1/Q) is . isthe sample filling factor which is given by

=

sample

Brf d

all space

Brf d. (9)

For high sensitivity, and Q should evidently be as large as possible andherein lies the skill in winding a satisfactory resonant coil. The size of the coil


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232 John F. Gregg

Fig. 17. Circuit of the fixed-frequency cryogenic spectrometer

Fig. 18. Ambient temperature driver for circuits in Figs. 1417

is determined primarily by the volume of sample available. A useful practiceis to install the sample in a thin-walled tube of Teflon which is a low-lossdielectric material, around which the coil is wound. The inductance requiredis determined by the operating frequency and is given by the surprisinglyaccurate formula (which allegedly first appeared in the 1935 Wireless Worlddiary):

L (H) =0.2 N2d

3.5 + 8 (l/d)(10)

where N is the number of turns, l is the length of the coil and d (withapologies to protagonists of the SI system) is the coil diameter in inches.

For particularly low-frequency work in the range of 100300 kHz, double-

layered coils are sometimes required. A trap for the unwary lurks in the factthat the enamels on much commercially available copper wire make verylossy dielectrics: the interwinding capacitance for a double-layered coil ap-pears in parallel with the tuning capacitance and militates seriously against


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the drive for a high quality factor. Multiple layered coils are to be avoided,unless strenuous efforts are made to eliminate interwinding capacitance be-cause the resulting resonator circuits plus parasitic capacities have complexelectrical responses and generally exhibit multiple resonant frequencies whichmake their behavior uncertain. Given a wound coil of fixed dimensions, itsresonant frequency and filling factor may be forced up by surrounding it witha conducting screen. Evidently the conductivity of the screen should be ashigh as possible to afford the highest quality factor.

10.2 Cavity Resonator Sensitivity

As already discussed, the author has a preference for the rhumbatron stylecavity over conventional box or cylinder designs on the grounds of smaller

size for a given frequency but also because the magnetic field is concentratedat the bottom of the rhumbatron stub and much improved filling factorsare available with small samples. This is particularly important for thin filmsamples where the amount of material available for study is minute and signal-to-noise is crucially important.

11 Thin Film Samples

It is possible, at the cost of signal-to-noise, to examine thin film samples inresonators made for bulk samples, but it is evidently desirable to attempt totailor the resonator structure to give the best performance with thin mag-netic films. The most obvious resonator design to choose is that of a striplinein which the sample is trapped between the live strip and the ground plane.Layers of insulator (SiO2 for example) above and below the sample preventit from shorting the stripline. Evidently, this approach requires fabrication ofa dedicated stripline in the same process as makes the sample itself, but theextra effort and complexity is repaid by much improved signal-to-noise. How-ever there are attendant design problems which revolve around the manner

in which the stripline is to be electrically characterized.The most obvious method of analyzing a composite stripline/sample as-

sembly is to measure its scattering parameters using a network analyzer andback-calculate to extract changes in and . This has the advantage ofsimplicity and is a routine operation for which equipment may be purchasedoff the shelf. However, note that the system is now no longer resonant(as was the case for all the other configurations discussed so far), and as aresult the dual advantages of high H field and signal amplification by thequality factor have been lost. Moreover, most network analyzers are designedto measure 50 systems, and the more the characteristic impedance of thetest system strays from 50 , the lower the sensitivity of the technique tochanges in sample susceptibility. For a thin film sample of given thickness,the sample filling factor and the magnetic energy density may be maximized


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234 John F. Gregg

by reducing the stripline to ground-plane separation until it is comparablewith the film thickness. Unfortunately, because maintaining the characteris-tic impedance at 50 requires keeping the stripline width and separation ata fixed ratio for a given permittivity , this means the stripline width alsoapproaches the dimensions of the film thickness. For a magnetic film of submi-cron thickness, this also implies top class lithography to define the stripline.Even more annoyingly, the resistance per unit length of the stripline is in-versely proportional to the stripline width (and for skin depth reasons cannotbe compensated for by making the stripline thicker). Because the inductanceper unit length stays constant as the stripline dimensions are reduced, thismeans that the characteristic impedance of the line (given by R+jLG+jC) againstrays from 50 and now acquires a significant imaginary component.

To illustrate the problem, consider a gold stripline structure where the

line/ground separation is t = 1m and the stripline width is d = 2m. Theinductance per unit length is approximately

L =0t

d(11)

or approximately 0.5 H per meter: at 1 GHz, this has impedance = 3jk.The resistance per unit length is roughly

R =1

d, (12)

where is the conductivity and is the skin depth; at 1 GHz this is ap-proximately 3.5 k . This gives a resistance/reactance ratio of about unitywhich, irrespective of the overall magnitude of the impedance, cannot besatisfactorily matched to a real 50 system.

Notwithstanding these difficulties, network analysis of stripline structuresis a workable technique for examining thin film and nanostructured magneticsamples. In practice, a degree of compromise needs to be exercised in alldirections. The stripline dimensions are not pushed to the limit and are leftat, say, one or two orders of magnitude larger than the sample thickness at

the expense of filling factor. The characteristic impedance is allowed to strayfrom 50 with some loss in sensitivity. However, rather than employingthe sledgehammer network analysis technique, the author favors a resonantapproach to stripline structure measurements which is more labor-intensiveto set up, but which is more in line with the earlier discussions in this reviewand carries many of the advantages of those systems.

For example, a shorted quarter-wavelength section of stripline behaveselectrically very like the stub of a rhumbatron with the H field concentratedat the short-circuited end where the sample is located, and the open end

presents a high impedance at resonance. A reverse-biased GaAs diode (e.g.,an infrared light-emitting diode) across the open end makes a good microwavevaractor for tuning the resonance of the resonator which may now be madethe tank circuit of a marginal oscillator driven by a GaAs MESFET of suitable


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gain/bandwidth. Likewise, a closed half-wave line, again with the sample atthe closed end, presents low impedance at resonance and is ideal for use as thetank circuit of the MESFET Colpitts circuit discussed above in Fig. 9. Thevaractor diode may now be placed across the center of the stripline resonator.

Different stripline geometries are also possible which are rather easier toimplement at the expense of filling factor and sensitivity. One example is thedouble-ground stripline which consists of a substrate with a central hotstripline flanked on either side by a ground line. It differs from the designdiscussed above in that the magnetic pumping field acting on the sample(which is in the intermediate space between hot and ground lines) is nowvertical rather than in-plane.

These resonant stripline methods recover the sensitivity of the resonanttechniques described earlier and use much of the same electronics, but (unlike

network analysis) are tunable only over a restricted frequency range, outsideof which different structures must be used. They are, of course, confinedto higher frequencies where the stripline lengths needed are not unworkablylong, though their operation may be extended to low frequencies by carefullyadding high-Q lumped circuit elements.

For lower frequencies, however, there remain some tricks to exploit.Maxwells equations tell us that wherever we find some D/t, then there issurely a curlB to accompany it. If we use a specially made thin film capacitorin one of the low-frequency resonators treated above with the sample between(and suitably insulated from) the capacitor plates, the displacement currentin the capacitor will generate a magnetic field on the sample. Care needsto be applied to analyzing the results because the geometry of the H fieldwill depend on the plate geometry. Moreover, from (5), it is seen that at lowfrequencies, the signal-to-noise of a marginal oscillator falls off with decreas-ing frequency. However, on the positive side, the magnetic energy densityin the capacitor is comparatively high compared with other high-frequencystructures.

In passing, it should be mentioned that the possibility of some very ele-gant time-domain stripline experiments also exist. Rasing and co-workers [27]

evolved an attractive technique for creating ultrashort magnetizing pulseswhich are generated by using femtosecond laser pulses and optical switches toshort-circuit microwave stripline structures. See also Mark Freemans chapter.

12 Parameter Matricesfor High-Frequency Circuit Analysis

The tools for accurate, routine, high-frequency analysis of striplines and otherstructures are two-port parameter matrices. The majority transform columnvectors of voltages and/or currents. However, these relate subtly to the so-called scattering parameter (s-parameter) matrices discussed below.


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236 John F. Gregg

Linear electronic circuits whose physical dimensions are small comparedwith the wavelength corresponding to their frequency of operation are sus-ceptible to analysis by conventional matrix techniques. The small signal per-formance of the individual functional blocks of the circuit are assigned 2

2

matrices which relate input and output column vectors containing currentsand voltages. For example, the transmission properties of a two-port circuitmay be written in terms of the following matrix relation which transformsoutput voltage and current into input voltage and current:

VinIin

=

A BC D

VoutIout

. (13)

For example, the performance of three such circuits cascaded together isthen simply represented in terms of the cube of the matrix. Moreover, it maybe seen that, if the circuit is not loaded, the final Iout is zero and the overallvoltage transfer function may be determined very economically by evaluating

just the top left-hand element of the matrix cubed.Circuits consisting of cascaded blocks like this are best treated by cas-

cade or transmission parameters (which are each others inverses) becausemultiplying the individual matrices produces the overall performance of thecascaded stages, in both sets of parameters. However, a variety of other pa-rameters exists. For example, for three terminal networks which are addedin parallel, the overall performance is best calculated by using admittance

parametersI1I2

=

Y11 Y12Y21 Y22

V13V23

(14)

because the voltages are common to the two sets of terminals and the currentsinto them add. The parameters of any particular circuit may be expressedin terms of any type of parameter. Evidently, there are simple transformswhich convert the information about the circuit block from one matrix formto another.

For networks of passive components, these matrices are valid, irrespectiveof signal amplitude, and usually have the property that their determinantsare unity a consequence of the reciprocity theorem which obtains providedthat nowhere in the system is there a singularity such as a biased p-n diodewhere the local electric fields take large enough values to prompt the appear-ance of higher order terms in the electric or magnetic susceptibilities or theconductivity.

For circuitry containing active devices, the matrix treatment is capable ofregistering only the small signal behavior which is a function of the biasing

of the devices concerned.At microwave frequencies, these methods are, of course, all still valid.However, the greater prominence of the wave-propagation properties of thesignal prompts yet another style of presentation of the circuit parameters


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the so-called scattering parameters, or s-parameters. Instead of consideringinput and output voltages and currents as the column vector elements, thelatter are chosen to be the incident and reflected wave signals at the inputand output of the circuit. The scattering matrix for a circuit block has theform,

V1rV2r

=

s11 s12s21 s22

V1iV2i

(15)

where Vni and Vnr are the voltages of the incident and reflected waves atterminal n, s11 and s22 are essentially reflection coefficients at the inputand output, respectively, and s12 and s21 are transmission coefficients in theforward and reverse directions. The information in this scattering matrixis again readily transformable to the other parameter sets discussed above.However, there is a subtle difference in scattering parameters in that thescattering is defined relative to input and output transmission lines of givenimpedance, and the parameters are meaningless unless these impedances arespecified. The usual default impedances are 50 .

To calculate the s-parameters of a circuit consisting of different build-ing blocks, the s-parameters of the blocks are first converted to the canon-ical parameter sets for assembling the circuit and then back-converted tos-parameters at the end. Such transforms and assembly routines are easilyautomated into a computer program which can be invaluable in fine-tuning

the design of a microwave circuit with tightly defined performance criteria.

13 Magnetic Modulation Techniques

To obtain the best signal-to-noise from a measurement, the signal should bemoved to the region of the frequency spectrum where the data-capture elec-tronics delivers its best noise performance. This is done by modulating thesignal and collecting it via a lock-in detector which frequency shifts it backto quasi-dc. Various magnetic modulation methods are used. The simplest

applies a small sinusoidal modulation and detects the first derivative of thesignal at the modulation frequency. A more interesting modulation type isbisymmetrical modulation, as illustrated in Fig. 19, where it is shown beingapplied to nuclear quadrupole resonance (NQR). The resonance is spoiledtwice per modulation cycle (by the positive and negative field peaks, respec-tively), and thus is detected at twice the modulation frequency with a cor-responding reduction in spurious modulation pickup. A frequency of 87.5 Hzis favorable for modulation because this implies that the signal detectionfrequency is well removed from the harmonics of 50 Hz main interference.

On occasion, it is desirable to apply two different frequencies simultane-ously to a magnetic sample. Examples include dynamic nuclear polarizationor electron-nuclear double resonance. A particularly satisfactory structurefor this purpose is the slow wave line. This is a conducting helix in which


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238 John F. Gregg

Fig. 19. Bisymmetrical modulation of a nuclear quadrupole resonance. The verticalaxis is swept frequency: the horizontal axis is a magnetic modulation field applieddiagonally to the quadrupole Hamiltonian. The diagram shows how the resonancedisplacement with field switches the absorption signal at twice the modulationfrequency

the applied signal travels at the speed of light in the wire but is slowed inreal space by a factor dependent on the pitch of the helix with consequentconcentration of the applied magnetic flux [28].

14 Ultrasonic Spectrometers

Ultrasonic spectrometers are an unusual variant in magnetic instrumenta-tion which may be used for investigating material in which the magneticproperties are coupled to mechanical strain. The simplest design consists ofa substrate with polished opposite faces onto which is grown the ultrasonictransducer [29]. The sample is stuck to (or in the case of a thin film, grown on)the other face: indeed it may be the polished substrate itself. Ultrasonic pulses

are launched across the substrate by the transducer which is then switchedfrom transmit to receive mode to analyze variations in the amplitude andphase of the echoes. The transducer may be a thin film of piezoelectric mate-rial such as zinc oxide which is grown by radio-frequency sputtering. Trans-ducer film thicknesses of a micron or less give transducing action in the lowGHz regime. Modification of the sputtering parameters can be used to varythe piezoaxis of the transducer film and hence launch simultaneous mixturesof longitudinal and transverse waves. This kind of acoustic spectrometer hasan extremely high quality factor because the resonant element is mechanical

and the sensitivity of detection is consequently also very high and may beused to study direct phonon coupling to magnetic systems [30]. By admix-ing the microwave carrier frequency to perform ultrasonic interferometry, thetechnique may also be used for measuring magnetically induced ultrasonic


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velocity changes of parts in 109 [31]. By patterning the transducer electrodeinto an array, surface acoustic waves may be launched and used to examinethin film magnetic samples under, or adjacent to, the transducer.

15 Practical Construction and PCB Layout

Successful radio-frequency and microwave circuit building require close at-tention to detail and, as observed by F. N. H. Robinson, a lively awarenessof Maxwells equations. The most important factor in rf design and lay-out is careful consideration of the path taken by the rf return current toground. It is a sobering consideration that 0 is a nanoHenry per millimeter.At 1 GHz, this constitutes a reactance of 6 a substantial perturbation

on any 50- system. Therefore, it follows that ground return path lengthsshould be reduced to a minimum and should be broad tracks to minimizeskin depth impedance. Good radio-frequency design practice separates outdifferent functional blocks and constructs each one in its own special enclo-sure whose periphery is defined by a low impedance ground ring. Suchrings should be typically of the order of 1 cm 1 cm and the componentswhich couple adjacent enclosures are positioned across the ring conductorsto minimize cross talk between modules [8,9,10]. It goes without saying thatpower supplied to such modules should be separately filtered and decoupledto suppress spurious signal paths.

Virtually all electronic components have dimensions which relate to a 0.1matrix, so designing a printed circuit for an rf circuit is greatly facilitated bylaying out the design on a piece of 0.1 graph paper from which the artworkmay be prepared.

An invaluable tip for circuit faultfinding is initially to ignore the rf or low-frequency ac performance and to concentrate on getting the dc levels correctat the various circuit nodes. If the design is good and the components of goodquality, correct dc behavior will automatically produce the right performanceat higher frequencies.

16 Skin Depth Considerations

Alternating electrical current in a metal conductor flows only in a surfacelayer of thickness

=

2

r0(16)

which decreases as the square root of both frequency and bulk conductivity.A useful rule of thumb for estimating skin depth is to start from the roomtemperature skin depth in copper at 50 Hz which is 13 mm (the reason thatmains busbar cross sections are of this order) and use scaling with the root


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240 John F. Gregg

frequency to estimate it at the operating frequency. The room temperatureconductivities of gold, aluminium, and silver are, respectively, 1.42, 1.64, and0.92 times that of copper. The scaling of skin depth with 1/2 implies thatthe conductance of a square of metal surface varies as the square root of theconductivity of the bulk metal. Factors of 400 increase in the conductivity ofcopper are not unknown on cooling to 4 K (if the metal is sufficiently pure),and this in turn implies Q factor increases of the order of 20 in cavities andresonant circuits.

For ease of machining, brass is a good choice of starting material forfabricating of rhumbatron cavities; its indifferent electrical conductivity makeit advisable to electroplate the internal working surfaces of the cavity withgold to obtain a good quality factor. Likewise, cryogenic coaxial lines linkingroom temperature electronics to low temperature electrical resonators are

frequently made of German silver or stainless steel to reduce the leak andcryogen boil-off and should be electroplated with copper or gold, especiallyif the tuning capacitor is at room temperature and the resonant rf currentflows in the coaxial line.

In NQR systems and some magnetic resonance/magnetic loss detectionapparatus, frequency-sweeping the detector electronics is required. This isusually done by using an air-spaced capacitor because variable semiconductorcapacitances have neither the frequency range nor the quality factor required.Conventional air-spaced capacitors have the disadvantage that sweeping theminvolves a moving electrical contact which is invariably noisy. This problemmay be remedied by axially drilling the rotor and installing a flexible copperribbon by which noiseless contact is made [8]. Figure 20 shows a device wherethis configuration has been realized.

17 Practical Applications

The apparatus and methods described have been discussed in terms of funda-mental magnetic measurements on novel magnetic materials. However, there

is a different aspect to their use, namely, as practical sensors designed forapplication in position and motion sensing in internal combustion engines,braking systems, robotics, photocopiers, mine detection, etc. The author hasused some of the principles outlined in this review to develop a novel posi-tion sensor (Fig. 21) with the dimensions of a TO18 transistor package whichcan simultaneously detecte (1) rotating magnetic fields, (2) rotating ferroustoothed wheels, (3) rotating nonferrous metallic toothed wheels, and (4) ro-tating plastic toothed wheels. The principles used are simply detection ofchanges in the real and imaginary parts of electrical and magnetic suscepti-bilities of the various materials concerned. The principle may also be usedto detect passage of liquid drops, liquid flow, impurities in fluid flow, andmixtures of different fluids.


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Fig. 20. Capacitor modified to eliminate contact noise during frequency sweep

Fig. 21. A Mercedes V8 engine running on a novel magnetic ignition timing sensor.The sensor combines the magnetic properties of a nanotextured colossal magnetore-

sistant material with the instrumentation ideas discussed in this review to realizefast, accurate, speed-independent position sensing with high signal-to-noise and im-munity to microphonics, electromagnetic interference, and oil/dirt contamination


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242 John F. Gregg

Acknowledgments

The author is indebted to Martin Thornton for his invaluable help with themanuscript and diagrams, to Christel Martin and Will Allen for their drawing

skills, to Mike Wells for providing Figs. 6 and 7, and, above all, to the lateNeville Robinson for sharing his vast knowledge of high-frequency electronics.

References

1. R. H. Koch, J. D. Deak, D. W. Abraham, P. L. Trouilloud, R. A. Altman, Y. Lu,W. J. Gallagher, R. E. Scheuerlein, K. P. Roche, S. S. P. Parkin: Magnetisationreversal in micron-sized magnetic thin films, Phys. Rev. Lett. 81, 4512 (1998)218

2. B. Bleaney, J. F. Gregg, M. R. Wells: The ratio of the nuclear electricquadrupole moments of 50V and 51V in SmVO4, J. Phys. C 15, 349 (1982)219

3. J. F. Gregg: Radio-frequency studies at low temperatures, Disertation, Univer-sity of Oxford (1983) 219

4. B. Bleaney, J. F. Gregg: Enhanced nuclear acoustic resonance: some theoreticalconsiderations, Proc. R. Soc. London A 413, 313 (1987) 219

5. J. F. Gregg, I. D. Morris, M. R. Wells: Cryogenic GaAs MESFET magneticresonance spectrometer for use from 500 MHz to 3 GHz, J. Phys. E 20, 1223(1987) 221, 224, 229

6. F. N. H. Robinson: Nuclear resonance absorption circuit, J. Sci. Instrum. 36,418 (1959) 221, 222

7. F. N. H. Robinson: The modified Van der Pol oscillator, J. Appl. Math. 38,135 (1987) 222

8. F. N. H. Robinson: A sensitive nuclear quadrupole resonance spectrometer for260 MHz, J. Phys. E 15, 814 (1982) 222, 239, 240

9. F. N. H. Robinson: A convenient nuclear resonance magnetometer, J. Phys.E 20, 502 (1987) 222, 239

10. F. N. H. Robinson: An improved stable low-dissipation oscillator with cryogenicapplications, J. Phys. E 20, 399 (1987) 222, 239

11. F. N. H. Robinson, Noise and Fluctuations, (Oxford Univ. Press, Oxford 1974)

22212. F. N. H. Robinson: Noise in oscillators, Int. J. Electron. 56, 63 (1984) 22213. F. N. H. Robinson: The quantum mechanics of signals and noise in attenuators

and maser amplifiers, Proc. R. Soc. London A 286, 525 (1965) 22214. E. M. Cherry, D. E. Hooper: Proc. IEE 110, 375 (1963) 22315. J. F. Gregg, I. D. Morris: Cold electronics, Electron. Wireless World March,

232 (1989) 22916. R. K. Kirschmann: Cold electronics: An overview, Cryogenics 25, 115 (1985)

22917. B. Lengeler: Semiconductor devices suitable for use in cryogenic environments,

Cryogenics 12, 439 (1974) 22918. M. F. Bocko: Noise characteristics of a cryogenically cooled GaAs metal semi-

conductor field effect transistor at 4 MHz, Rev. Sci. Instrum. 55, 256 (1984)229


27/29


19. S. R. Forrest, T. M. Sanders: GaAs junction field effect transistors for low-temperature environments, Rev. Sci. Instrum. 49, 1603 (1978) 229

20. R. J. Prance, A. P. Long, T. D. Clark, F. Goodall: UHF ultra low noise cryogenicFET preamplifier, J. Phys. E 15, 101 (1982) 229

21. H. R. Wampach, N. S. Sullivan: Low-dissipation tunable rf preamplifier for lowtemperature NMR applications, Rev. Sci. Instrum. 49, 1622 (1978) 229

22. D. S. Miyoshi, R. M. Cotts: Helium cooled radio frequency preamplifier for usein NMR, Rev. Sci. Instrum. 39, 1881 (1968) 229

23. M. G. Richards, A. R. Andrews, C. P. Lusher, J. Schratter: Cryogenic GaAs-FET amplifiers and their use in NMR detection, Rev. Sci. Instrum. 57, 404(1986) 229

24. J. H. Goebel: Liquid helium-cooled MOSFET preamplifier for use with astro-nomical bolometer, Rev. Sci. Instrum. 48, 389 (1977) 229

25. S. S. Senic, G. R. Craig: Thermal effects in JFET and MOSFET devices at

cryogenic temperatures, IEEE Trans. Electron. Devices 19, 933 (1972) 22926. E. J. Veenendal, R. Hulsman, H. B. Brom: A frequency modulated Q-meter forvery low temperature NMR experiments, J. Phys. E 16, 649 (1983) 229

27. T. Gerrits: Precession dynamics in micron sized magnetic thin films caused byultra-short magnetic field pulses, Dissertation, University of Nijmegen (2000)235

28. D. S. Trenham: Dissertation University of Oxford (1953) 23829. C. H. A. Huan, J. F. Gregg, M. R. Wells, G. A. D. Briggs, W. P. Wolf: High

sensitivity ultrasonic interferometer for the detection of magnetic phase tran-sitions, J. Appl. Phys. 61, 3183 (1987) 238

30. B. Bleaney, G. A. D. Briggs, J. F. Gregg, G. H Swallow, J. M. R. Weaver:Enhanced nuclear acoustic resonance in HoVO4, Proc. R. Soc. London A 388,479 (1983) 238

31. S. J. Dawson, J. F. Gregg, J. S. Lord, M. R Wells, W. P. Wolf: Onion Skindomains in a relaxing metastable antiferromagnet, J. Magn. Mag. Mater. 104,373 (1992) 239


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Index

Q factor, 22750V isotope, 224s-parameters, 237

acoustic operators, 219acoustic spectrometer, 238acoustically stimulated magnetic

transitions, 219admittance parameters, 236air-spaced capacitors, 240

bipolar transistors, 229bisymmetrical modulation, 238braking systems, 240

carbon resistors, 229cascade parameters, 236cavity, 225cavity resonator sensitivity, 233characteristic impedance, 234Cherry and Hooper Pair, 223circuit faultfinding, 239colossal magnetoresistance, 241Colpitts MESFET Spectrometer, 227coupling loop, 229cross relaxation, 224cryogenic operation, 229

displacement current, 235domain size, 218domain wall, 219domain wall width, 218double-ground stripline, 235dynamic nuclear polarization, 237

electric field induced transitions, 219electrolytic capacitors, 229electron spin resonance cavities, 221electron-nuclear double resonance, 237

electronic resonance, 219enamels, 232enhanced nuclear paramagnets, 219exchange length, 218

femtosecond laser, 235fluid flow, 240frequency-domain magnetic investiga-

tions, 220

GaAs diode, 234GaAs MESFET, 224, 229GASFET, 229

hyperfine spectrum, 219

internal combustion engines, 240interwinding capacitance, 232

JFET long-tailed pair, 223

KramersKronig relations, 220

limiting oscillators, 221liquid helium, 229

long-tailed pair, 230

magnetic losses, 217magnetic modulation techniques, 237magnetic susceptibility, 217, 218main interference, 237marginal oscillator, 221, 222marginal oscillator spectrometry, 217Maxwells equations, 235Mercedes V8, 241

mesomagnetism, 217microphonics, 221microwave varactor, 234Miller capacitance, 223


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Index 245

Miller effect, 230motion sensing, 240multiple layered coils, 233

network analyzer, 233nonlinear element, 222novel position sensor, 240nuclear quadrupole resonance (NQR),

237nuclear resonance, 219nuclear spin system, 219

parallel resonant tank circuit, 221parasitic capacities, 233PCB layout, 239perpendicular magnetic anisotropy, 218piezoelectric material, 238position sensing, 240Praseodymium Vanadate, 225

radio-frequency power losses, 221radio-frequency sputtering, 238reciprocity theorem, 236resonant coil, 231resonator, 230

rhumbatron, 227, 228, 234Robinson limiting oscillator, 222Robinson marginal spectrometer, 223Robinson spectrometer, 222robotics, 240Rollin spectrometer, 222Rollin-type NMR spectrometers, 221

scattering matrix, 237scattering parameters, 233, 237

selection rules, 218self-oscillating detectors, 221self-tracking marginal oscillator

spectrometry, 218

self-tracking spectrometer, 221silicon JFETs, 229silicon MOSFETs, 229Sisyphus-type relaxation processes, 219skin depth, 239slow wave line, 237SmVO4, 226spin diffusion length, 218spin-dependent transport, 218stripline, 233

superparamagnetism, 218surface acoustic waves, 239

tantalum capacitors, 229Teflon, 232thin film samples, 233transmission line, 237transmission parameters, 236tuneable spectrometer, 230two-port circuit, 236

ultrasonic spectrometers, 238ultrasonic transducer, 238ultrasonic velocity, 239

Van der Pol equation, 222Vanadium, 219

Zeeman operator, 219zinc oxide, 238

Frequency Domain Magnetic Measurements

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