3428 IEEE TRANSACTIONS ON MAGNETICS, VOL. 29, NO. 6, NOVEMBER 1993

Characteristics of Magnetostatic Surface Waves Propagating In Thin Metal Film CoatedFerrimagnetic Layered Structure

Y .Okamura, K.Kitatani, and S.Yamamoto Department of Electrical Engineering Faculty of Engineering Science

Osaka University 1- 1 Machikaneyama-choy Toyonaka, Osaka 560 Japan

Absbact -This paper is concerned with a theoretical and experimental study on magnetostatic surface waves (MSSW) propagating in a thin metal fllm covered ferrimagnetic layer structure. We have focused on the effect of a finite mn&wtivity of the metal coated on the ferrimagnetic layer. The dippersion characteristics of the magnetostatic waves, whose propagation constanls an? complex, have been discussed. Agreement between calculated and experimental values for the propagation h w and the transmbion bandwidth of the surface waves is generally @

I. INTRODUCTION

A thin metal film coated on one face of a ferrimagnetic layered structure affects the characteristics of the magnetostatic surface waves (MSSW) propagating in the magnetic slab, which l ads to nonreciprocal propagation. With a finite electrical umductivity of the metal, the sutface wave dispersion depends upon the thickness of the coated metal film. De Wames and Wolfram, and other researchers theoretically and experimentally investigated the finite conductivity problem on the metal film covered ferrimagnetic layer structure. They have mainly concentrated on resonance frequencies of the overlayered magnetic systems [1],[2]. In this paper we have focused on the actual propagation characteristics of the magnetostatic surface waves propagating in the metal coated ferrimagnetic system instead of the resonauce frequencies; Le., we have investigated the behavior of the complex propagation constant by regarding with the thickness of the metal thin f h the propagation loss and the transmission bandwidth. Furthermore, we have considered the nonzero magnetic linewidth of the ferrimagnetic material as well as the finite conductivity of the metalfilm.

II. CONFIGURATION AND ANALYSIS

In Fig.1 is shown the waveguide configuration considered here, which consists of a nonmagnetic substrate, a ferrimagnetic layer of thickness d. a thin metal film of thickness t. The fenimagnetic layer is magnetized along the z-axis. This magnetic layered structure supports magnetostatic surface waves propagating in the y-direction. With a finite electrical conductivity of the metal thin film. the wave electric field carmot be neglected in the metallic region. Many reports concerning this finite conductivity problem

Manuscript received February 15,1993.

give the following dispersion relation for the d a c e waves propagating in the positive and the negative directions, the derivation of which is based on the magnetostatic field analysis [3].

P f K - 1

/ . 4 T K + 1 exp(2pd) =-

Q + E a ) ( P r K - l / E l ) e x P ( 2 B I r ) + O - E I ) ( P r K + 1 / E , )

Q + E a )(P * K + )exP(2 B-t + 0 - )(P * K -1/e- )

(1) In this equation the upper and the lower signs correspond

to positive and negative propagation, respectively. /3 is the complex propagation constant of the magnetic surface wave, and p and K are teusor components of the permeability of the ferrimagnetic material. Other parameters are given by

112 8, - (c2 I 2 r W p ) ,

(3)

(4)

where ue is the electrical conductivity of the metal, o is the angular frequency of the wave of interest, and c is the velocity of light in vacuum. 6p is the skin depth of the metal. According to (3). the propagation constant indicates a complex quantity; the imaginary part of it represents the propagation loss.

De Wames and Wolfram solved (1) by regarding the complex frequency, the result of which shows the variation of the complex angular frequency with different parameters.

Fig 1. Thin metal film coated ferrimagnetic layer structure.

0018-9464/93$03.00 Q 1993 IEEE

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He= we solve (1) directly for the propagation constant. The result gives more easily understandable characteristics of the magnetic surface waves. We also consider the nonzero magnetic linewidth of the femimagnetic material, the effect of which was neglected in the previous papers [1],[2]. Equation (1) was solved with a Downhill method which has been originally used to figure out the complex transcendental equations in the optics [4]. Here we chose the solution to meet the criterion cited in PI. *

III. NUMERICAL RESULTS

As a numerical example we choose a structure consistiug of a lanthanum and gallium substituted yttrium iron garnet (LaGaYIG) ferrimagnetic layer and an aluminum thin film. The nonmagnetic substrate is a gadolinium gallium garnet (GGG) crystal. The model pertains to an experiment in the following section. The thickness, the saturation magnetization (4- ) , and the magnetic linewidth of the iron garnet film are 19.1 pm, 1220Gauss. and 1.10e, respectively. The internal magnetic field in the iron garnet and the electrical conductivity of the aluminum are 5000e and 3.72x105S/an, respectively.

Fig.2 shows the variation of the propagation constant for propagation in the +ydirection with respect to the frequency for various values of the thickness of the aluminum frlm. In Fig.2(a) is illustrated the real part of the propagation constant; i.e., the phase constant. In Fig.2(b) is shown the imaginary part of the propagation constant; i.e.. the attenuation constant. We also plot the result for the perfect conductor coating in these figum.

It is seen that two branches appear in accord with the thickneas of the metal f h . The first one is in the frequency region ranging from 2.6GHz to 3.1GHz. which is noted as branch 1. and the second one is in the region from 2.6GHz to 4.8GHz. which is marked as branch 2. Concerning with the wave in the branch 1. the phase and the attenuation constants grow with increasing the frequency. The metal thickness largely affects the p q " loss. As the metal thickness tends to zero, the phase constant grows towards infinity with increase in the frequency; i.e., the resonauce ocmrs. On the other hand, the wave in the branch 2 behaves in a different way. The propagation constant approaches to the constant value as the frequency is increased, and the maximum occurs, the frequency of which shifts from the smal l value to large one as increasing the metal film thickness. The result indicates that the surface wave group velocity chauges from positive to negative with increasing the thickness of the metal fh. This is similar to the numerical result shown by Awai, who considered the interaction of the magnetostatic waves with drifting carries [5].

Next we illustrate the dependence of the propagation Constant on the frequency for propagation along the negative y-axis in F ig3 In this case them also appear two different branches; however, these two are in the same frequency range as that of the branch 1 for propagation in the +y- direction. The variation of the phase constant of these modes behaves similarly with increasing the frequency. On the contrary. the dependence of the attenuation constant on the frequency is quite different for the metal film thickness. In

Branch 1

M, lnm

Branch 2 -

nL 2.5 3.0 3.5 4.0 4.5 5.0 1

Frequency, GHz (a) Phase constant

- Branch 1

I I I I 2.5 3.0 3.5 4.0 4.5 5.0

Frequency, GHz (b) Attenuation constant

Rg2. Frequency dependence of the propagation constant for the wave propagating in the +y-direction in the metal thin film coated

ferrimagnetic layered structure The thickness of the coated film is the variable parameter.

the case of the very thin film and the thick film coating, their characteristics are similar; however, the variation of the attenuation is quite different for the intermediate film thiclcness.

These results can be explained in terms of the field distribution of the surface wave. For propagation in the +y- direction the field of the wave propagating in the very rhin metal film structure is localized on the boundary between the fenimagnet and the metal: the so-called femte-air mode, on the contrary, that of the wave propagating in the thick metal structure is localized on the boundary between the ferrimagnet and the nonmagnetic substrate: the so-called ferrite-metal mode. The characteristics of the former wave are largely determined by the presence of the metal film. For propagation along the -y-axis the fields of the modes in the thin and thick metal fitm stnactures are both localized on the lower surface of the ferrimagnet; that is. their characteritica have not been largely affected by the presence of the metal.

IV. EXPERIMENT

De Wames and Wolfram investigated the effect of the finite electrical conductivity of the metal theoretically and experimentally. They concentrated on the magnetostatic

.

3430

26 2.7 2.8 29 3.0 3.1

(b) Atknuatim a“t

Fig3. Sam as Fib2 f a pp&#lon akmgtheqgdvey-;aia

surface resonances, which correspond8 to the applied magnetic field Imtud of th is we have measured the propagation 1088 and the transrmo - 8ion baudwiddl of the “tatic d a c e wave to see the a c t d propegation -c8. As “3 in the last sedan we wed a LaGaYIG as a

f e “ p e a ‘c maberia, the f h of which was grown on a “ q p 6 c ” t c G G G b y a a “ ‘onalliquidpha# epitaxial method. On the grown film was coated an

tbichr#rofthe * f i b I l W a s 3 ( k m .

“ d b y Vayiog thekngthddre mcdlic*onthc

n6aostriplinetnmsdooar waenaedtocJrcaeandtodve

~ w i t h a f i m p a s y . Tbtdots=- daak d tbe salibline giver, the (heoretica pedic(ianf”l(1) f a

almmir” layex by a vscmnn evaporation tdmiqoe. The

Tbe pmpgationla~ of the magndic surface wave was

surface of the ferrimagnetic layer. Here conventional

t h e I ” ‘c d a c e wave. Fig4 pesenhs the curve showing the variation of the measured surface wave

A~tbetweenthecalcolatedaadthe

The surface wave has a band pass transmission charadgisticin afrectoency range shown in Fip.2 and 3. We have measured the band pass characteristics for

oftbtmtrdfilm. hKg.5isplottcdcbe3dBhdwidthof

v* is fairly gpod

p” in the + y ~ with E#pect to tbe t h i h

[l] R.E.De Wamer and T. Wolfram, “Characteristics of magnetostatic surface waves for a metalized farite slab,” JAppLPVy.. vd.41. pp.5243-% 1970.

[2] G.A. Bennett and J.D.Adam, ”Identification OC surface wave “ m m a m g l b&edYIGsIab.” Elecarm Lett, v d 6 ,

[3] M.S.Sodha and N.C.Srivastava, Microwave Propgotion in

141 K.-H.schlereth and UTaclre, “The complex pqaption carhmtofdtilayex wav- an alpithm f a a p w x m a l amptex,” IEEJY J. Qua” Ekclron.. vd.26, pp.627&0, 1990.

[SI IAwai, KAhtsuka, and J.IteoOue. “Interaction of magnetic d a c e waves with drifting carries, ” I’.&dJ%ys., vd. 15, pp1m- 1304.1976

pp78pT99 1970.

F V * ,PlearmReae,NewYalr.l!Bl.