DIPOLE-EXCHANGE SURFACE WAVE DISPERSION AND LOSS FOR A METALLIZED FERRITE FILM

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DIPOLE-EXCHANGE SURFACE WAVE DISPERSION AND LOSS FOR A METALLIZED FERRITE FILM

T. Wolfram, R. de Wames

To cite this version:

T. Wolfram, R. de Wames. DIPOLE-EXCHANGE SURFACE WAVE DISPERSION AND LOSS

FOR A METALLIZED FERRITE FILM. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-1171-

C1-1173. �10.1051/jphyscol:19711419�. �jpa-00214461�

JOURNAL DE PHYSIQUE

Colloque C I , supplkment au no 2-3, Tome 32, Fe'vrier-Mars 1971, page C 1 -

¹

¹⁷¹

DIPOLE-EXCHANGE SURFACE WAVE DISPERSION AND LOSS FOR A METALLIZED FERRITE FILM

T. WOLFRAM and R. E. DE WAMES Science Center, North American Rockwell Corporation

Thousand Oaks, California, 91360

RBsum6.

-

Les courbes de dispersion pour un conducteur sur un film ferromagnetique sont calculCes, comprenant les effets de dipble, Cchange et de conductivite. Les pertes de conductivite dominent pour

f6

- ¹ tandis que les pertes d'echange sont grandes pour

afz 1,

f est la constante de propagation de l'onde de surface,

6

est la longueur de peau et

a

la constante $&change. La courbe de dispersion de l'onde de surface montre une varietC de forme qui depend des valeurs de

6, a

et la proportion

621~.

Les caractkres de la dispersion de l'onde de surface et des pertes sont r8sumCs.

Abstract.

-

The frequency versus wavenumber dispersion for a conductor on an insulating ferromagnetic film is calculated including dipolar, exchange and conductivity effects. Conductivity losses dominate for

f6

-

¹

while propa- gation losses are largest for

af2

> where f is the surface wave propagation constant,

6

the skin depth and

a

is the exchange constant. The surface wave dispersion curve exhibits a variety of shapes depending upon the values of

6

and

a

and ratio

@/a.

The general features of magnetic surface wave dispersion and loss are summarized.

Magnetostatic surface spin waves [I, 21 are impor- tant to magnetic device technology. Time delay, beam steering, filtering, and pulse compression devices have been designed utilizing the properties of the surface spin wave [3]. Layered magnetic on magnetic [4] and conductor on magnetic [5] film systems appear to offer desirable device characteristics. Recent studies have been made in order to determine the rather complex behavior of the surface wave spectrum when both dipolar and exchange interactions are considered [2].

We consider here some of the dispersive and loss characteristics of the conductor-on-magnetic system including both dipolar and exchange interactions.

Consider a metallized insulating ferromagnetic film which is infinite in the y-z plane and extends from x

⁼

0 to x

⁼

S. The non-magnetic conducting film with skin depth S extends from x

=

0 to x

=

- d.

In order to simplify the theory presented here, we approximate the conductor-magnetic system by two semi-infinite films (i. e., S

^-,

d

+

co) and discuss only surface waves propagating in the + y direction with propagation constant5 The theoretical results derived for this model apply to the finite thickness film system when f

%

1/S and d

5>

6. The behavior of the surface waves for f 5 1/S and d 5 6 have been discussed elsewhere [5].

Propagation effects and displacement currents may be neglected for most film systems of practical interest.

When dipolar and exchange interactions are included for the ferromagnetic film the magnetic potential

^I)

satisfies the dipole-exchange differential equation, [2],

where

8

is 52, - a V2, 52

=

0/(4 zyMo), 52,

=

H/4 nMo, H i s the applied field, Mo is the saturation magnetiza- tion and a is the exchange constant. The solutions of eq. (1) are admixtures of three waves whose relative amplitudes are determined by the boundary condi- tions [2].

In the conducting medium V x h

⁼

4 noE/c, and V x E

=

iohlc where o is the conductivity, c is the velocity and o is the angular frequency.

The tangential component of h and the normal component of b

⁼

h + 4 srm are continuous across the interface and in addition the normal derivative of m, amlax, is assumed to vanish. These conditions lead to the eigenvalue equation

:

where

E =

f

/g,

g 2

=

f - '2 i/d2, d2

=

c2/(2 ZOO), rc2

=

af ',

IC, =

a(r

-

rl),

- I C ~ =

a(r + rl), r

=

( a 2 +

^$)%,

r'

=

52, + af2 + $ and

Q,,, = Q, + af

4- IC:,3

.

The imaginary part of Q, determined from eq. (2), gives the surface wave losses. These losses stem from two quite different sources. The first is a conduction loss which arises from the penetration of the electric field E into the conductor. The second type, exchange loss, arises from the decay of the surface wave into the bulk continuum of spin waves.

For yttrium iron garnet a

z

2.6 x lo-'' cm2 so that

lc

is small for values off

i

lo5 cm-l. If a = 0 (no exchange interaction), then the solution of eq. (8) is 52

=

52, + ⁽¹ + &)-I. We note from the definition

E =

f / ( f 2

-

2i/d2)% that 52

+

52, + 1 as f + O and 52

-,

52, + 4 when f

-,

co. The latter result is identical to the surface wave frequency of an unmetallized magnetic film discussed by Damon and Eshbach [I], while the former result was obtained by Seshadri [6]

for the case in which the conductor has infinite conduc- tivity. The same limiting frequencies are approached

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711419

C 1

-

1172 T. WOLFRAM AND R. _E. DE WAMES

i f f + 0 is fixed and 6

+

0 (infinite conductivity) or

6

+

c o (vanishing conductivity). For finite and non- zero values o f f and 6,

E

is a complex number and conduction losses exist. For a given value of 6 the magnitude of the imaginary part of E, I Im

E

1, increases linearly with

x =

f6 for small

x.

For large values of

x,

I ^Im

^E

^I decreases as 1/x2. Thus the maximum conduc- tion losses occur for x - 1. The maximum value of I Im

E

I occurs for

x ⁼

(4/3)'14

=

1.07. The reason for the decrease in the conduction loss with increasing f is that the penetration of the surface wave electric field into the conductor decreases. For metals such as gold, silver, copper, and aluminium 6 - ^{cm for}

w

-- 109-1010 rad/s so that the maximum conduction losses occur for f - lo4 cm-I. Semiconductors may have much larger values of 6 and the maximum losses occur at smaller values off. The behavior of the surface wave dispersion is indicated schematically in figure 1 by the curve segments AB', AC', AD' and FE. The solid curves are 0, the real part of 52. The shading of the curves represents D,, the imaginary part of 52. The solutions derived here do not apply to films of finite thicknesses when f 5 11s. The behavior of the solu-

FIG. 1. - Schematic summary of behavior of the dispersion and linewidth of magnetic surface waves for a magnetic insu- lating film in contact with a conducting film. 52 is the surface wave angular frequency in units of 4 nyMo and f is the surface wave propagation constant. The bulk spin wave continuum which extends upward in 52 from the line (QZ,

+

^Of)1/2 is indicated by the crosshatching region. The solid lines are the real part of the surface wave frequency 5 2 ~ and the imaginary part is repre- sented by the shaded regions. The

- -

lines indicate the small f behavior which the film thickness is finite. The solid lines which end at the points A and F are the results for infinite film

thickness.

tions for f 5 1/S has been discussed elsewhere [5].

The results are shown schematically in figure 1 by the curve segments GB', CG', DG', GF' E and GE' E.

For f 5 lo5 cm-I we can obtain approximate solutions of eq. (2) by power series expansion in

K.

We find that

where

Consider YIG (yttrium iron garnet) with

in contact with a conducting film have 6 - ^cm.

Since 6 9

a%,

the effects of exchange will be important only for large values of

x.

Therefore, we may obtain a simple result for

o2

and

w 3

by evaluating these terms for

E

- ^{1 and D} - ^{52, + 3.} This procedure leads to the result that

The imaginary part of D must be negative since the fields vary as exp(-

iwt).

The results of eq. (5) apply for values off 5 lo5 cm-'. This type of behavior is shown schematically in figure 1 by the curve AD' D.

For small

x,

and

Im (1 + ^8)-I

⁼

-

i x .

When x

% K

the conductive losses dominate the exchange losses. For 6

=

cm and YIG with 4 nMO

=

1750 Oe and an applied field of lo3 Oe, eq. (8) yields

%

0.571 4 + 0.975 8 + .000 5 + ^{0.000 0}

⁼

^{1.547 7}

and 52,

=

- 0.218 7 - 0.000 0

=

- 0.218 7 for f

=

lo4 cm-l. When x is large, the Re (1 +

^{&)-I =}

3

and Im D

=

- i/(4

x2).

For f - ^{lo5 cm-}

and

where the first contribution to Im D is conductive loss and the second is exchange loss. For

the exchange koss is very large. Im D Re D and a well-defined surface state does not exist. The above results may be expressed in Oe by multiplying by 4nM0

=

1750 or in frequencies by multiplying by 2 yM,

=

4.90

x

10' Hz.

When

a%

- ^{6, then}

^m2

^and

^{w 3}

must be evaluated for

D

=

n, + (1 + and the regions of conductive

and exchange loss overlap. In such a case 52, does not

DIPOLE-EXCHANGE SURFACE WAVE DISPERSION AND LOSS FOR A METALLIZED C 1

- 1173 reach 52, + 4 before the exchange effects become large. effects of the conductor occur for f 5 1/S. The beha- This type of situation is illustrated by the curve vior of this type of system is illustrated by the segment AC' C. For the other extreme 6 - ^S

^{% a%}

^{curve GF' E.}

References DAMON (R. W.) and ESHBACH (J. R.),

J.

Phys. Chem.

Solids, 1960, 19, 308.

WOLFRAM (T.) and DE WAMES (R. E.). Solid State

~ o m m . , i970, 8, 191

;

~ h ~ s . ' ~ e t t e i s , 1969,

30A,

3 ; J. Appl. Phys., 1970, 41, 987

;

Phys. Rev., 1970,1,4358

;

Phys. Rev. Letters, 1970,24, 1489.

BRUNDLE (L. K.) and FREEDMAN

(N.

J.), Elect Letters, 1968, 4, 132

;

BONGIANNI (W.), COLLINS (J. H.), PIZZARELLO (F.) and WILSON (D. A.), IEEE

G-MTT Symposium Digest,

p.

376 (1969);

PIZZARELLO (F. A.), COLLINS (J. H.), and COER-

VER

(L. E.), J. Appl. Phys., 1970, 41, 1016.

141 WOLFRAM (T.), Appl. Phys. Comm. (in press).

[5] DE WAMES (R. E.) and WOLFRAM (T.), submitted to

J.

Appl. Phys.

161 SESHADRI (S. R.), Proc. of the IEEE, Letters, 1970,

58, 3.