Ferrimagnetic echoes of magnetostatic surface wave modes in ferrite filmsF. Bucholtz, D. C. Webb, and C. W. Young Jr. Citation: Journal of Applied Physics 56, 1859 (1984); doi: 10.1063/1.334199 View online: http://dx.doi.org/10.1063/1.334199 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/56/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Phenomenological propagation loss theory for magnetostatic waves in thin ferrite films J. Appl. Phys. 59, 218 (1986); 10.1063/1.336867 Magnetostatic volume wave propagation in a ferrimagnetic double layer J. Appl. Phys. 53, 3723 (1982); 10.1063/1.331109 Magnetostatic wave precursors in thin ferrite films J. Appl. Phys. 53, 2658 (1982); 10.1063/1.330929 Characteristics of Magnetostatic Surface Waves for a Metalized Ferrite Slab J. Appl. Phys. 41, 5243 (1970); 10.1063/1.1658655 Magnetostatic Mode Echo by Subsidiary Absorption J. Appl. Phys. 37, 4077 (1966); 10.1063/1.1707979

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ferrimagnetic echoes of magnetostatic surface wave modes in ferrite films F. Bucholtz,a) D. C. Webb, and C. W. Young, Jr. Microwave Technology Branch, Electronics Technology Division, Naval Research Laboratory, Washington. DC 20375

(Received 16 February 1984; accepted for publication 27 April 1984)

This paper presents the first detailed characterization of ferrimagnetic echoes resulting from the nonlinear response of magnetostatic surface waves in a yttrium-iron-garnet film to excitation by two time-resolved rf pulses. Data showing the behavior of the echo as a function of excitation pulse separation time T, signal pulse power p., and pump pulse power Pp is presented. We also show the results of measurements of the spatial variation of the echo response which directly confirm the localized nature of the echo-producing magnetostatic modes. The data is analyzed in terms of (1) the dispersion relation for magnetostatic surface waves in a dielectric layered structure to obtain the dependence of the echo power on wavenumber and position in the sample and (2) the general properties of echoes produced by the anharmonic response of a system of oscillators to obtain the dependence of the echo power on T, p., and Pp •

I. INTRODUCTION

The discovery of ferrimagnetic echoes in cylinders and truncated spheres of yttrium-iron garnet (YIG) by Kaplan and co-workers) offered the possibility of a novel approach to performing important signal processing functions, such as nondispersive time delay and pulse correlation, in the fre­quency range 1-10 GHz. Various investigations of the cylin­drical configuration, in which the echoes result from the nonlinear interaction of magnetostatic-backward-volume waves (MSBVW), have demonstrated the feasibility of per­forming these functions over relatively modest ranges of fre­quency and time delay?-'(' The cylindrical configuration, however, presents several serious drawbacks including diffi­culty in synthesizing the desired electrical and magnetic characteristics and inability to uniformly excite the sample over an appreciable length. To overcome these difficulties we recently showed that echoes could be produced using YIG films in a magnetostatic-surface-wave (MSSW) configura­tion.7 Ferrimagnetic echoes of MSSW modes in YIG films exhibit longer time delays and considerably larger band­widths than MSBVW echoes in YIG cylinders. The MSSW configuration, therefore, optimizes those aspects of the ferri­magnetic echo phenomenon which are important for practi­cal device applications.

There exists a wide variety of physical systems which produce echoes under the proper conditions. All such sys­tems share the following two characteristics8

: (1) there is a distribution in the value of some fundamental parameter, such as resonant frequency, of the system which contains a large number of oscillators or oscillatory modes; (2) a nonlin­ear interaction of some kind is present. In a ferrite sample magnetized to saturation by an externally applied dc mag­netic field, the collection of magnetostatic modes comprises the system of oscillators and the spread in frequency results from the presence of a gradient in the static internal magnet­ic field. In a uniformly magnetized cylinder, a gradient in the internal field arises naturally due to the demagnetizing ef­fect. In a thin film magnetized in the plane, the demagnetiz-

., NRC/NRL Postdoctoral Research Associate_

1859 J. AWl. Phys. 56 (6), 15 September 1984

ing field is significant only within a few film thicknesses of the edge and, therefore, a gradient in the internal, in-plane field must be produced entirely by the externally applied magnetic field. This can be accomplished by properly shap­ing the pole pieces of the magnet.7 The nonlinear interaction required for echo formation arises from the anharmonic re­sponse of the magnetostatic mode system to high-power rf excitation.

Ferrimagnetic echoes are produced when a properly magnetized ferrite sample is excited by two transient distur­bances-a low-power "signal" pulse followed, after a time delay 7', by a high-power "pump" pulse. The pump pulse drives the system into a nonlinear, anharmonic response re­gime and an echo forms at a time 7' after the pump pulse. For the sake of clarity, we wish to emphasize that the echo does not result from the reflection of one of the pulses from a boundary in the sample, rather, the echo is a direct manifes­tation of the nonlinear response of the system of magnetosta­tic modes.

The following general properties characterize ferrimag­netic echoes.

(1) Since the time at which the echo occurs depends only on the time at which the two input pulses occur, the time delay before echo formation is totally nondispersive.

(2) The range of frequencies over which echoes can be observed depends on the strength of the field gradient and the length of the sample over which magnetostatic modes can be uniformly excited. It is totally independent of materi­al properties of the sample. MSSW echoes in YIG films have been observed over a 1250-MHz bandwidth in the range 275(}-4()()() MHz for fixed time delay and fixed magnetic field. 7

(3) The amplitude of the echo response depends strongly on the magnitude of the field gradient. There is an optimum range of gradient values over which intense echoes form and the echo amplitude decreases substantially for gradient val­ues outside this range. For a given excitation frequency the presence of a field gradient results in spatial localization of the MSSW modes.

(4) Under certain conditions, it is possible for the echo amplitude to be larger than the signal pulse amplitude. The

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ability to show amplification in this fashion is a unique and highly interesting property of the ferrimagnetic echo.

This paper presents the first detailed investigation of the behavior offerrimagnetic echoes ofMSSW in YIG films as a function of input pulse spacing 7, signal pulse power Ps '

and pump pulse power Pp • Evidence is presented which shows explicitly localization of the modes active in echo for­mation. The data in the low-power regime is in good agree­ment with the well-known behavior of echoes which result from the anharmonic response of a system of oscillators. Sec­tion n reviews those aspects of basic MSSW theory and the theory of two-pulse anharmonic echoes necessary for an un­derstanding of the ferrimagnetic echo effect. The experimen­tal apparatus, sample geometry. and measurement method are described in Sec. HI. The experimental results are pre­sented and discussed in Sec. IV and a summary comprises Sec. V.

II. THEORY

A. General MSSW relations

The magnetostatic modes in a YIG film magnetized and excited in a surface-wave configuration (Fig. 1) obey a dispersion relation of the form9

C PIPs +PHl + 1] [I-IPs -PH)B J = [l + IPs +PH)A ),

where

P = Wk/WM' PH = WH/WM' A = 1 + tanh( - kt ), B = 1 - tanh( - kt ). C= exp( - 2kd), s = ± 1 for waves traveling in the ± y direction.

(1)

Wk is the mode eigenfrequency, wM/2rr = y4rrMs ' Y = 2.8 MHz/Oe,4rrM. is the saturation magnetization (1750 Oe for YIG). wH/2rr = yH •• k is the magnitude of the wavenum­ber. dis the YIG film thickness. and t is the thickness of the dielectric substrate.

Consider a static. externally applied field with [inear gradient a of the form

~W=~+~ ~

Mlcro.trlp

Ground Plene

FIG. I. YIG sample and transducer configuration geometry for MSSW. For the static H field in the z direction and the rf H field in the x direction surface waves travel in the ± J1 direction.

1860 J. Appl. Phys .• Vol. 56. No.6, 15 September 1984

where Ho is a constant. Since the static field is z dependent, the MSSW mode eigenfrequencies are also z dependent through the quantity wH(z) = 2rryHz(z). For fixed Hz. k. and w" there exists a unique z value which satisfies the dispersion relation, Eq. (1). We shall refer to this z value as the "reso­nant position." An excitation in the form of a rf pulse of width T and center frequency Wo will excite modes in the frequency range, approximately [wo - (2rr/ Tj]<;w<;[wo + (2rr/T)] and, hence. there exists a correspond­ing range of resonant positions localized about the center position corresponding to Wo' It is clear that for fixed Hz and k, the resonant position changes as the frequency is changed. In practice, a microstrip transducer will excite modes having not a single k value but a distribution of k value. This effect will produce an additional distribution in resonant positions.

B. MSSW echo response

The behavior of the echo amplitude as a function of pulse spacing 7 (see Sec. IV) indicates that the MSSW echo belongs to the class of echo phenomena which occur in an­harmonic-oscillator systems.8,10-12 These echoes are charac­terized by an increase in amplitude as 7 increases for small 7

followed by an exponential decrease at large 7. In this section we apply the general mathematical results of two-pulse an­harmonic echoes to the ferrimagnetic echo effect. Solutions to the pertinent nonlinear equations of motion have been used extensively in the analysis of polarization echoes i.n pie­zoelectric powders 10 and only the relevent results will be presented here. We extend these previously used solutions to include higher-order terms and discuss how the dependence of echo power on input pulse power is affected.

We shaH aSf;ume that the MSSW mod.es behave in the following manner. The modes respond linearly to the appli­cation of both the signal and pump pulses as well as during the intervening time period 0<;t<;7. The mod.es are driven into a nonlinear response regime by the high-power pump pulse and the anharmonicity is present only for time t> 7.

For simplicity the pulses are assumed to have infinitesimal width.

The high-power equation of motion for a n.ormal.ized, circularly polarized. magnetostatic mode amplitude ak(t,f.tlj, including relaxation, has the form 13

a" + (r - iWjak - iJ" la" 12ak + iG,,(t ja~ k = O. (3)

Here w = (wo - w,,), Wo is the frequency of the driving rf field. w" is the mode resonant frequency as before, and r is a damping constant. The index k is the wavenumber in the plane-wave approximation and the coefficients J" and G"'t) are discussed fuil.y in Ref. 13. Since the l.inear effect .of the excitation pulses can be accounted for in the initial condi­tions. a driving term has not been explicitIy included. The term iG" (t ja*_ ", which represents time-d.epend.ent coupling with the counter-rotating mode, can lead to exponential growth (amplification) of the ak mode amplitude but, since our data is restricted to the unamplified region. we shal1 neg­lect this term. We are then left with the equation of motion

ak + (r - iWjak = 0, 0<t<7, (4)

and

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ak + (F - ito)ak - iJk Jak \2ak = 0, t> r. (5)

By integrating the individual oscillator responses over the collection of oscillator frequencies, the macroscopic re­sponse of the system is obtained. The solution will be ex­panded in terms ofthe nonlinearity parameter J k and it will be found that echoes form provided Jk #0.

and

Equations (4) and (5) have solutions

ak(t,to) = ao expI - (r - iw)(t - to)), O,t,r, (6)

ak (t,to) = ao exp [ - (r - iw)(t - toJ

Xexp{ - [Jk/(Jk -Jt)]

X In{1 - i[(Jk - Jt)/2F] Jao\2

X p - exp[ - 2r(t - to)) J), t> r, (7)

respectively. Solution (7) can be expanded in powers of J k as follows:

[adt,to)/ao ]exp[(r - ito)(t - to)]

= 1+ iJk (iaoI2/2r)f 1- exp( - 2r(t - to)3 I

-J~(laoI4/8r2H 1 - exp( - 2r(t - to)] f' + .... (8)

Assuming a linear response for times O,t,r, the mode am­plitude immediately after the application of the pump pulse is

(9)

where As and Ap are the (real) mode amplitudes induced by the signal and pump pulses, respectively. The observed mac­roscopic system response is given by

(to)

WhenJk = 0, the response of the system is completely linear and the integral (to) vanishes for all t>r. For J k #0, the integrand in Eq. (10) contains terms of the form exp[ - itodt - mr)], m = 2,3,4,.··. Since integration of these terms will yield delta functions at t = mr, these terms describe echoes in the system response resulting from the presence of the nonlinearity. For example, the term in Eq. (8) proportional to Jk produces an echo at t = 2 with

R l(2r) = (iJk!2r )AsA ;e- 2I"T(1 - e - m"). (11)

The notation Rn{mr) denotes the echo response at t = mr arising from the J ~ term in Eq. (8). The resulting echo power is given by Pe = R r R J or

P.(2r) = (Ji!4r 2)p.P;e- 4r"'(1 - e-2rI 2

, (12)

where Ps = A ; and Pp = A ;. Therefore, an anharmonicity of the form given in Eq. (5) leads, in lowest order, to an echo in the macroscopic response of the system at t = 21' with power dependence PsP;.

All higher-order terms in the expansion (8) also produce echoes. The J i term leads to multiple echoes-one at t = 21' and another at t = 31'. Here

R2(2r) = - (JJ2F)2[A.A; + A; A; e- m'l (13)

and

R 2 (3r) = - (JJ2r)2 A; A! e- m "(I- e- 2rI 2• (14)

Consider now the power in the echo at t = 21' arising from the sum ofthe n = 1 and n = 2 terms:

P.(2r) = (Jk /2rf p. [P; + (J,J2r)2(1 - e- 2r12 ~ ]e-4rT(l_ e-2r-t12

+ 2(Jk12r)4 P; P! e- 6rT(1 _ e- 2r14 + (Jk/2r)4 P; P; e- srT(1_ e-2I"14, (15)

where P.(2r) = [R J(2r) + R z(2r)]· [R)(2r) + R2(2r)]. An important consequence of the n = 2 contribution to the echo at t = 21' is found in the first term on the right-hand side in Eq. (15). Here a linear dependence on p. is accompanied not only by P; but by a weaker, higher-order P; dependence as well. This higher-order dependence will be examined more closely in our discussion of echo power as a function of pump pulse power (Sec. IV).

Although the ferrimagnetic echo data exhibits the gen­era! functional dependence shown in Eq. (12), quantitative agreement could not be obtained without introducing an off­set parameter 1'0 such that ris replaced by (1' - 1'0)' For the purpose of analyzing our data we found it convenient to work with the following expression for echo power Pe which includes only first-order nonlinear effects:

Pe = KP.P; exp[ - 4(1' - 1"0)/T2]

X{l - exp'( - 2(r -rO)/T2 JY (16)

Here the relaxation time Tz = r -1 and the prefactor K, which includes the nonlinearity parameter and the effects of coupling efficiency between the rf field and the MSSW

1861 J. Appl. Phys., Vol. 56, No.6, 15 September 1984

, modes, is independent of p. and Pp at low-power levels but becomes a strong function of these variables at high-power levels where the echo power saturates. In this paper, we shaH be concerned with the low-power unsaturated regime. In general, K, T2 and ro all depend on the field gradient a but there exists no satisfactory theoretical model to predict these dependences and it is not possible to experimentally vary a independently of other important parameters such as z and Hz. Qualitatively, the magnitude of a directly influences the degree of spatial overlap of modes localized at adjacent posi­tions within the sample so it is not surprising that details of the relaxation process and the nonlinear response depend on a.

m. EXPERIMENTAL APPARATUS

The sample configuration for exciting and detecting MSSW, in which a YIG film is placed in close proximity to a single microstrip line terminated in a short, is shown in Fig. 1. The 76-flm wide by 5.6-mm-Iong copper microstrip line on a 300-flm-thick Duroid substrate was connected to the ground plane on the opposite side of the substrate. The sam­ple consisted of a 75-flm-thick YI G film on a GGG substrate

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I j 1

I 1

II 1 i I i

with dimensions 9.0 by 2.5 mm. A 65-llm-thick plastic spac­er was inserted between the YIG film and the microstrip to improve the echo-response characteristics.7

Figure 2 is a simplified block diagram of the 2-4 GHz system. Both signal and pump pulses are derived from a sin­gle cw source modulated by rf switches and combined in a circulator. Attenuator AI reduces the power in the signal pulse relative to the pump pulse. A peak power meter was used to monitor any frequency dependence in the pump power incident on the sample. After making slight adjust­ments of the phase shifter to optimize the echo response at any particular frequency, the output of the cw source was adjusted. to bring Pp to the desired level. The ratio Pp/Ps is controlled by the attenuator and was found to be insensitive to changes in the cw source level. To further reduce the ef­fects of frequency-dependent mismatches in the system, the quantity recorded was echo gain G = (peak echo power/ peak incident signal power) rather than simply echo ampli­tude. Switch S 1 allowed the receiver to detect either the echo returning from the sample or the signal pulse reflected from the short which was used in determining G. A standard he­terodyne receiver was used. In a method similar to one used previously 14 a wire-l.oop probe was employed to measure the spatial characteristics of the echo response. The probe con­sisted of a single, rectangular loop of the inner conductor of semirigid SMA cable with loop dimensions 2.13 by 0.86 mm, oriented to be sensitive to rf fields and magnetization in the x direction. Travel of the loop in the ± z direction was con­trolled by a vernier and switch S2 allowed the receiver to detect signal.s from either the probe or the microstrip trans­ducer. The probe was main tained at a height of approximate­ly 1 mm above the top surface of the GGG substrate, a dis­tance at which the echo was not significantly affected by the presence of the probe.

In order to produce an internal field of the form given in Eq. (2), the YIG sample configuration was inserted between specially shaped. magnet pole pieces. The design and perfor­mance of these magnet pole pieces is discussed fully else­where. 7

IV. RESULTS AND DISCUSSION

In this section we present the results of measurements of the echo power gain G as a function of pulse spacing 'I, signal pulse power Ps ' and pump pulse power Pp • These re­sults are discussed in terms ofEq. (1.6). Also presented are the

,.,

I&J - .. SWITCH

PEAK POWER MmR

s:!~LOOP I PROBE

RECEIVER

* SAMPLIt

FIG. 2. Simplified block diagram of the experimental rf(2-4 GHz) system .. System operation is described in the text.

1862 J. Appl. Phys., Vol. 56, No.6, 15 September 1984

-30

o

400

Go E 10-2.2&

TO = 330 nsec T2 = 360 nsac

600 T(nsec)

MSSW ECHO 02900 MHz A 3900 MHz

a = 186 Oa/mm Pp = 11 dBm p. = -10 dBm

BOO

FIG. 3. Echo gain G (dB) as a function of pulse separation T(nsec) obtained at 2900 and 3900 MHz. The solid line is a plot of the equation [Eq. (17)] using the values shown for the parameters Go. To> and T2• a = field gradient, Pp = pump power. and P, = signal power.

results of measurements of the echo amplitude as a function of position along thez axis of the sample which show directly the localized nature of the echo-producing modes and are in agreement with predictions based on the MSSW dispersion relation Eq. (1) and the dependence of Hz on z given in Eq. (2).

We found that observable echoes would form for gradi­ents in the range 80 0e/mm<a<;200 Oe/mm. A gradient of 165 Oe/rom offered the best compromise among the com­peting requirements of strong echo response, large band­width, and long T response and this value was used in most of our measurements. In the echo amplitUde versus z position measurement, however, it was advantageous to use a lower gradient value in order to increase the spatial resolution of modes at different frequencies. Here, a = 130 Oe/rom was used. The method for varying the gradient is discussed in Ref. 7.

Equation (16) predicts, for fixed power levels, the gain G = PJP. should vary with 7' according to

G = Go{l- exp[ - 2('1- 7'O)/T2 lJ2 (l7)

where Go = KP.P~. Figure 3 shows measured values of G (dB) = 10 log G as a function of T for fixed pulse power levels and gradient at operating frequencies 2900 and 3900

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MHz. For 1'>400 nsec, the data at these two frequencies agree to within approximately 3 dB indicating that the T

behavior of the echo is independent of frequency in this range. This is an important result for device applications requiring variable time delay over large bandwidths. The solid line drawn through the data is obtained from Eq. (17) using the parameters Go = 10 - 2.25, To = 330 nsec, T2 = 360 nsee. Using Tz = l/(211"}',dB), we find 360 nsee corresponds to a linewidth,dB = 0.16 Oe, a value in agreement with fer­romagnetic resonance linewidths expected for high-quality YIG films. The need. to include an offset parameter To indi­cates that for pulse separations T < To, the system is unable to produce echoes and the model for echo formation embodied in Eq. (16) is not applicable. Failure of the simple model may be related to the finite width of the excitation pulses and to a requirement for a "settling down" period following the pump pulse before the anharmonicity described in Eq. (5) can act on the system free of strong transient perturbations. It should be noted that the time-dependence coupling term in Eq. (3), which was neglected in our analysis, is not present in piezoelectric systems and this may account in part for the need to include To in the analysis of our system. Of course, these explanations are highly speculative in the absence of further experimental data on the behavior of To as a function of a, p., and Pp • We have observed the same general depen­dence of To on a as reported for MSBVW echoes in YIG cylinders6 namely, a decrease in To with increasing a. In the range 600-700 nsec, the data deviates significanly from the predicted curve. This structure in the G vs l' curve probably results from multimode effects. That is, a variety of surface wave modes, each with slightly different k value, G vs 1', and G vs power characteristics contribute to what is observed as a single echo and produce the observed structure. However, it is clear that the data from two widely different frequencies is in good agreement with the predicted curve over a wide range of l' values.

As a function of pulse power levels for fixed T, Eq. (16) predicts the echo power should vary as

Pe =PoPsP;'

where

Po =K{l-exp [-2(1'-1'o)/TzlP

X exp [ - 4(1' - 1'O)/T2 J. Equivalently

(18)

Pe(dBm) = P.(dBm) + 2Pp(dBm) + Po(dBm). (19)

Thus, forfixedPp a plot of PeldBm) vsP.(dBm) should yield a straight line with unity slope and intercept 2Pp + Po. Simi­larly, a plot of Pe(dBm) vs Pp(dBm) should again yield a straight line but with slope 2.0 and interceptPs + Po. Recall, however, that higher-order (n>2) expansion terms in Eq. (8) will cause a deviation from strict P; dependence in the form of additonal terms proportional to P;, P!, etc. Consider a single additional PsP; term so that

Pe cc p.(P; + b 2P;), (20)

where b 2 = (Jk /Zr)2[1- exp{ - 2rTW. The effect this added term has on the expected straight line behavior of P.,(dBm) vs Pp(dBm) can be estimated crudely as follows.

1863 J. Appl. PIlys., Vol. 56, No.6, 15 September 1984

E

MSSWECHO 75lim YlG

3400 MHz

-35 a = 165 Oe/mm T=480 "sec

-40

~ -45 G ...

-~~

J 1

-~l 0

1 5

o

o

o o 0

'" 00 o

o

'" 0

o

o

o

oP.=_ 3dBm

- 9 118m o

I !

10 15 20 Pp (dBml

FIG. 4. Echo power P.(dBm) vs pump pulse power Pp(dBm) at 3400 MHz for three values of signal power P, (dBm). a = field gradient and T == pulse separation. The solid lines represent linear least-squares fits to the data in the region shown.

Arbitrarily assume the coefficient b 2 = 0.001 and calculate Pe for 11 equally spaced values of Pp in the range 0 dBm";;Pp ..;; 10 dBm. A linear least-square fit to these "data" pairs yields a correlation coefficient in excess of 0.99 but with slope 2.38. Of course, the P.(dBm) vs Pp(dBm) curve is not linear in this case but this analysis serves to illustrate that with some experimental scatter in the data and over a limited range of Pp values, the presence of higher-order terms can easily cause an apparent increase in the slope of P.(dBm) vs Pp(dbm) curve. This effect can then be accounted for either explicitly, as in Eq. (20), or indirectly by writing the power dependence as

p. C:C.P.P;,

where £;>2.0.

(21)

Figure 4 shows the results of measurements of p. as a function of Pp for three different p. 'settings at 3400 MHz. The straight-line segments result from linear least-square analyses of the data in the region shown and yield slope val­ues 2.26, 2.36, and 2.49 for p. = - 3, - 9, and - 15 dBm, respectively. The discrepancies between these values and the lowest-order value of 2.0 is attributable, we believe, to the presence of weak, higher-order nonlinearities as discussed above. The variation of s with Ps ' which could only arise from variations in the coefficient b 2, is probably not mean­ingful. As Pp is increased beyond the "linear" regime the echo power saturates, for aU Ps values, at approximately p. = - 34 dBm. Saturation of the echo output is expected since at some level the amplitude of a magnetostatic mode is

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MSSW ECHO 75/.lm VIG

3400 MHz •• •• Pp= 16 dBm -35 a: 165 Oe/mm •

T:480 nsec • • • I

• • .11 dBm

• •

-~I • • • •

• • .9d8m •

E I In

-45f-~ -I

" I II.

-501- -1

-60L -30~----~~----'----~10~------~0~~

Ps (dam)

FIG. 5. Echo power P.(dBm)asa function of signal power P,(dBml at 3400 MHz for three values of pump pulse power Pp(dBm). a = field gradient,

T = pulse separation, and h = transducer spacing. The solid lines represent linear least-squares fit to the data in the region shown.

pinned as energy is directed into other, degenerate modes. For a given sample the saturation level depends mainly on sample and transducer geometry, and field gradient.

The variation of Pe with Ps is shown in Fig. 5. As ex­pected for Ps<.Pp' Pe(dBm) varies linearly with Ps(dBm). Linear least-squares fits to the data, shown as solid lines, yielded slopes 0.97, 1.02, and 0.97 for Pp = 15, 11, and 9 dEm, respectively. For large Pp and Ps '

saturation of the echo power is evid.ent, again, at a value near p. = - 34 dBm. Although we were not able to obtain data in the region Ps > - 3 dBm, the behavior of the curves sug­gests that the echo power will eventually saturate for large enough Ps regardless of Pp but the Ps value at which satura­tion begins does, of course, depend on Pp • Using T = 480 nsec, To = 330 nsee, T2 = 360 nsec and the intercepts of the straight-line segments it is possible to extract the value of K in Eq. (1.6). We find K = - 42.7, - 42.2, and - 43.1 dEm for Pp = 15, 11, and 9 dBm, respectively. TI1ese values are in rough agreement with K = - 39.0 dBm obtained from the G vs T curve assuming Pe ex: PsP ;.4. Since K must include the effects of coupling efficiency between the rf field and the MSSW modes, and the power data and T data were obtained at different frequencies, discrepancies in the calculated val­ues of K may result, in part, from frequency dependence of the coupling efficiency.

A single-turn, wire-loop probe was used to detect the rf magnetic flux density b" = h" + 41Tm" in the region above

1864 J. Appl. Phys., Vol. 56, No .. 6, 15 September 1984

5.0

MSSWECHO a·1300e/mm

4.0

3.0

2.0

1.0

O~ ________ L-________ ~ ________ ~ ________ ~

7.0 10.0 11.0

VERNIER POSITION Imm'

FIG. 6. Echo amplitude (arbitrary units, linear scale) vs vernier position of wire-loop antenna for three different values of the operating frequency: 3650, 3800, 3950 MHz. a = field gradient.

the GGG substrate as a function of z. Since the mode reso­nant position changes with frequency we expect to observe localization of the echo-producing modes as a shift with fre­quency in the z value at which the probe response is maxi­mized. This is indeed observed as shown in Fig. 6. For this measurement, the gradient was reduced to 1300e/mm in order to increase the spatial separation of the resonant posi-

D.J ,

Z3 exp

,,- 130 Oe/mm d = 75"m t = 366 "m

D.DLI-----:-:::I ~ __ --;:::::!:__--_~;;:;!;;;----.--L--.J D 100 2DD 300 40D 500

FIG. 7. Calculated values of z) as a function of k, using Eqs. (I) and (2). for the parameters shown. The horizontal line with error bar is the observed Z3

value. a = field gradient, d = YIG film thickness, t = thickness of dielec­tric substrate.

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tions. We chose the three frequencies 3650, 3SOO, and 3950 MHz because problems stemming from close proximity of the probe to the face of one of the magnet pole pieces were encountered at lower frequencies. Note that the "vernier po­sition" in Fig. 6 is not equal to the z value in Eq. (2) and the exact offset could not be determined without accurate knowledge of the k value of the echo-producing modes. To a good approximation, however, vernier position (mm) = z(mm) + 6 mm. The width of the peaks at each fre­quency is due almost entirely to the width of the wire-loop probe in the Z direction, 0.S6 mm. In spite of this broadening, the peaks are clearly resolvable and the following peak-to­peak separations are observed:

ZI = z(3Soo) - z(3650) = 0.40 ± O.OS mm,

Z2 = z(3950) - z(3S00) = 0.42 ± O.OS mm,

Z3 = z(3950) - z(3650) = 0.S2 ± O.OS mm,

where z(f) is the resonant position at frequency f z(f), which can be calculated by solving Eq. (1) using the field expression Eq. (2), depends on both k and s. The behavior of Z3 vs k shown in Fig. 7 suggests that the echo producing modes are those having s = - 1 and k ~ 70 em - I. Modes having s = - 1 travel along the bottom surface of the YIG film in this configuration (see Fig. 1) so this observation is consistent with the expectation that modes in the surface of the film closest to the micros trip transducer should be most strongly excited.

Finally, we note that we were not able to produce ampli­fied echoes in the sample used for this study. Preliminary investigations on a 250-j£m-thick YIG slab in a MSSW con­figuration did produce amplified (G~ 10 dB) echoes so the lack of amplification is not indicative of a general property of MSSW echoes. We suspect that the ability to show echo am­plification may, in fact, depend on the total number of spins which can be excited by the rf pulses and, hence, amplifica­tion will depend on details of the sample and transducer geometry. In terms of device application, however, we be­lieve the fixed-field bandwidth and range of time delays are the most important aspects of the ferrimagnetic echo effect.

V.SUMMARY

We have produced ferrimagnetic echoes of the magne­tostatic surface wave modes in a thin YIG film and studied

1865 J. Appl. Pflys., Vol. 56, No.6. 15 September 1984

the echo behavior as a function of pulse separation 1", signal pulse power level Ps ' pump pulse power level Pp and position in the sample. Good agreement is obtained between the data and an equation for the echo power Pe of the form Pe(dBm) = Ps(dBm) + ePp(dBm) + Po(1")(dBm) where Po(1") = K {I - exp[ - 2(1" - 1"o)/T21jexp[ - 4(1" - 1"o)IT2]

and €;>2 takes into account the effect of higher-order contri­butions to the echo response. MSSW echoes are observed for time delays (pulse separation) in the range 350--1000 nsec with maximum amplitude occuring for delays in the range 400-600 nsee. As a function of pulse power levels, the re­sponse of Pe(dBm) is linear at low-power levels but saturates at high Pp and Ps levels. Measurements of the echo ampli­tude as a function of position show that the echo-producing modes are localized and suggest that the observed modes travel on the surface of the YIG film closest to the microstrip and have wavenumbers k> 70 cm -I. It is clear that the MSSW configuration optimizes those aspects of the fem­magnetic echo effect which are critical for microwave signal processing device applications: large bandwidth, large range of time delays, and ease of device design and construction.

ACKNOWLEDGMENT

J. Douglas Adam is acknowledged for helpful discus­sions and for supplying the YIG film sample.

'D. E. Kaplan, R. M. Hill, and G. F. Herrmann, J. Appl. Phys. 40, 1164 (1969).

2D. E. Kaplan, Lockheed Missiles and Space Co. Report No. LMSC­D311371 (1971) (unpublished).

3D. E. Kaplan. Lockheed Missiles and Space Co. Report No. LMSC-0457479 (1975) (unpUblished).

4D. E. Kaplan, Nav. Res. Rev. 28. I (1975). SF. Bucholtz and D. C. Webb. Proceedings of the 1982 IEEE Ultrasonics Symposium (IEEE Catalog No. 82CHI823-4. New York. 1982), p. 547.

6F. Bucholtz and D. C. Webb, J. Appl. Phys. 54. 5331 (1983). 7F. Bucholtz and D. C. Webb, Proceedings of the 1983 IEEE Ultrasonics Symposium (IEEE Catalog No. 83CHI947-1, New York, 1983). p. 221.

8A. Karpel and M. Chatterjee, Proc. IEEE 69, 1539 (1981). "W. L. Bongianni. J. Appl. Phys. 43. 2541 (1972). 'OJ(. Fossheim, K. Kajimura, T. G. Kazyaka, R. L. Melcher, and N. S.

Shiren, Phys. Rev. B 17,964 (1978). 1'K. Fossheim and R. M. Holt, in PhYSical Acoustics. Vol. XVI. edited by W.

P. Mason and R. N. Thurston (Academic. New York. 1982). p. 217. 12K. Kajimara, in Physical Acoustics. Vol. XVI. edited by W. P. Mason and

R. N. Thurston (Academic, New York, 1982). p. 295. 13E. Schlomann. Raytheon Co. Technical Report No. R-48 (1959) (unpub­

lished). 141. Awai and J.1. Ikenoue. Electron. Commun. Jpn. 58-B. 63 (1975).

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