EXPERIMENTAL OBSERVATION OF SURFACE AND INTERFACE MODES BY LIGHT SCATTERING

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EXPERIMENTAL OBSERVATION OF SURFACE AND INTERFACE MODES BY LIGHT SCATTERING

J. Sandercock

To cite this version:

J. Sandercock. EXPERIMENTAL OBSERVATION OF SURFACE AND INTERFACE MODES BY LIGHT SCATTERING. Journal de Physique Colloques, 1984, 45 (C5), pp.C5-27-C5-36.

�10.1051/jphyscol:1984503�. �jpa-00224111�

JOURNAL DE PHYSIQUE

Colloque C 5 , suppl6rnent a u n04, Tome 45, avril 1984 page C5-27

EXPERIMENTAL OBSERVATION OF SURFACE AND INTERFACE MODES BY L I G H T

SCATTERING

J . R . Sandercock

Laboratories BCA Ltd., Badenerstrasse 569, 8048 Zurich, Switzerland Resume - Un apersu est donn6 des expgriences r6centes par diffusion

-- de la lumiere sur des surfaces et des faces separatrices. I1 a pour but de comprendre la nature des modes phonons observes et les mecanismes par lesquels ils couplent a la lumi@re.

Abstract - A review is given of recent light scattering measurements at surfaces and interfaces with a view to understanding the nature of the observed phonon modes and the mechanisms by which they couple to light.

The study of surface and localised phonon modes in layered materials dates back to the investigations of Lord Rayleigh /1/ into the propagation of earthquakes. More recently the development of surface acoustic wave devices lead to a resurgence of interest in these excitations. Investigations have been made using ultrasonic techniques and recently atomic and electron scattering, but the most powerful technique presently available is that of inelastic light scattering. This latter technique became possible with the development of the high contrast tandem Fabry- Perot interferometer.

This paper summarises the properties of the different surface and localized phonon states and introduces the rather complex problem of deriving the cross-section for light scattered from such states. Results of scattering measurements from a variety of different substrates and substrate/film combinations are presented.

Finally, the analog problem of scattering from spin waves in magnetic substrates and films is briefly discussed.

THE LIGHT SCATTERING EXPERIMENT

For some years light scattering has been used as a tool to study phonons in bulk material. The interaction between the phonon and light was described by Brillouin /2/ in terms of the fluctuation in the dielectric constant produced by the strain associated with the phonon. Since the development of the laser, Brillouin scattering has ripened into a useful and diversified technique.

Figure 1 illustrates the technique, where for simplicity a backscattering arrange- ment is shown.

A transparent sample has been assumed with the scattering volyme contained within the bulk of the material. The incident light of wavevector k1 and frequency w1 is scattered by a phonon q,R into the state kS, wS such that

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984503

C5-28 JOURNAL DE PHYSIQUE

F i g . 1 - a ) E x p e r i m e n t a l set-up f o r b a c k s c a t t e r i n g w i t h a Fabry-Perot i n t e r - f e r o m e t e r

b ) Transmission o f monochromatic l i g h t b y scanning Fabry-Perot i n t e r - f e r o m e t e r .

PIN

FABRY-PEROT SPECTROMETER

The + s i g n r e f e r s t o a b s o r p t i o n o f t h e phonon, t h e - s i g n t o emission. ( R e s p e c t i v e l y t h e a n t i - S t o k e s and Stokes processes).

For b a c k s c a t t e r i n g i n a t r a n s p a r e n t medium o f r e f r a c t i v e i n d e x n we have q = 2nko (Lo i s t h e vacuum wavevector o f t h e l a s e r l g h t ) . The s c a t t e r e d l i g h t c o n t a i n s com- ponents a t t h e f r e q u e n c i e s w1 + R c o r r e s p o n d i n g t o a l l e x c i t a t i o n s p r e s e n t h a v i n g t h e above wavevector. A normal spectrum w i l l t h e r e f o r e show sharp peaks s h i f t e d b y f r e q u e n c i e s

n

b) 4 L, I-

TRANSDUCER

I ---

T h e s c a t t e r e d l i g h t i s analysed u s i n g a Fabry-Perot i n t e r f e r o m e t e r as i l l u s t r a t e d i n f i g . l b . W h i l e t h i s i n s t r u m e n t i s adequate f o r t h e o b s e r v a t i o n o f s c a t t e r i n g i n t r a n s p a r e n t m a t e r i a l s , i t i s q u i t e inadequate f o r s t u d y i n g e x c i t a t i o n s near s u r f a c e s p a r t i c u l a r l y i n opaque m a t e r i a l s . I n t h i s case t h e l i g h t s c a t t e r e d e l a s t i c a l l y f r o m s u r f a c e d e f e c t s swamps t h e much weaker B r i l l o u i n components. T h i s problem can be overcome b y t h e use o f t h e h i g h c o n t r a s t m u l t i p a s s i n t e r f e r o m e t e r / 3 / - however even then a d i f f i c u l t y remains, namely t h a t n e i g h b o u r i n g o r d e r s o f i n t e r f e r e n c e a r e n o t w i d e l y separated f r o m one another w i t h t h e r e s u l t t h a t B r i l l o u i n s p e c t r a measured i n n e i g h b o u r i n g o r d e r s o v e r l a p . T h i s i s p a r t i c u l a r l y troublesome f o r s p e c t r a c o n t a i n i n g many f e a t u r e s o r b r o a d f e a t u r e s - t y p i c a l o f t h e s p e c t r a t o be d e s c r i b e d f r o m s u r - f a c e s and i n t e r f a c e s . T h i s problem has r e c e n t l y been overcome w i t h t h e i n t r o d u c t i o n o f t h e tandem m u l t i p a s s i n t e r f e r o m e t e r /4, 5, 6/, an i n s t r u m e n t which combines h i g h r e s o l u t i o n , h i g h c o n t r a s t and a s t r o n g suppression o f n e i g h b o u r i n g i n t e r f e r e n c e o r d e r s . A novel scanning stage common t o b o t h i n t e r f e r o m e t e r s a u t o m a t i c a l l y ensures s y n c h r o n i s a t i o n and forms t h e b a s i s o f a compact and h i g h l y s t a b l e design.

I

T

An a l t e r n a t i v e scheme r e l y i n g p u r e l y on t h e e l e c t r o n i c c o u p l i n g o f two s e p a r a t e i n t e r f e r o m e t e r s / 7 / has a l s o been demonstrated.

I

A t y p i c a l spectrum t a k e n u s i n g t h e tandem i n t e r f e r o m e t e r i s shown i n F i g u r e 2. T h i s spectrum /6/ measured i n b a c k s c a t t e r i n g on t h e s u r f a c e o f Ge, shows t h e d e p o l a r i s e d l i g h t s c a t t e r e d f r o m t r a n s v e r s e phonons and demonstrates two i m p o r t a n t aspects o f l i g h t s c a t t e r i n g near s u r f a c e s .

a) The peaks a r e seen t o be c o n s i d e r a b l y broadened. T h i s broadening i s n o t r e l a t e d

FREQUENCY SHIFT

ern-'

F i g . 2 - D e p o l a r i z e d spectrum o f t r a n s v e r s e phonons i n Ge.

t o t h e phonon l i f e t i m e , b u t a r i s e s due t o t h e h i g h o p t i c a l a b s o r p t i o n /8/ which l i m i t s t h e p e n e t r a t i o n o f t h e l i g h t t o w i t h i n a few wavelengths f r o m t h e s u r f a c e . The wavevector c o n s e r v a t i o n c o n d i t i o n o f e q u a t i o n 1 o n l y a p p l i e s when a l l dimensions o f t h e s c a t t e r i n g volume a r e l a r g e compared t o t h e wavelengths i n v o l v e d . For h i g h o p t i c a l a b s o r p t i o n t h e e q u a l i t y i s o n l y approximate - a r a n g e o f phonon wavevectors A q - oC (where d i s t h e a b s o r p t i o n c o e f f i c i e n t ) c e n t r e d around q = - k1 a l l c o n t r i b u t e t o t h e s c a t t e r i n g a n d so g i v e r i s e t o t h e observed b r o a d e n i n g e f f e c t . b ) A l t h o u g h t h e l i n e w i d t h i s i n good agreement w i t h s i m p l e c a l c u l a t i o n s t h e marked asymmetry observed cannot be e x p l a i n e d i n terms o f o p t i c a l a b s o r p t i o n . It was shown b y P i n e and Dresselhaus /9/ ( i n an a l b e i t i n c o r r e c t c a l c u l a t i o n ) t h a t t h e asymmetry a r i s e s f r o m t h e c o h e r e n t r e f l e c t i o n o f t h e phonons a t t h e s u r f a c e .

The above two f a c t s , namely t h a t t h e presence o f t h e s u r f a c e (and i n t e r f a c e s ) r e - l a x e s t h e wavevector c o n s e r v a t i o n r e q u i r e m e n t and m o d i f i e s t h e phonon s t a t e s w i t h r e s p e c t t o t h e b u l k , a r e o f fundamental importance t o an u n d e r s t a n d i n g o f t h e l i g h t s c a t t e r i n g experiments.

We c o n s i d e r f i r s t t h e m o d i f i c a t i o n t o t h e phonon modes.

PHOFlON MODES I N TtlE PRESENCE OF SURFACES AND INTERFACES

The s o l u t i o n s o f t h e e q u a t i o n s o f m o t i o n f o r an e l a s t i c continuum a r e t h e w e l l known l o n g i t u d i n a l and t r a n s v e r s e a c o u s t i c e x c i t a t i o n s . I n t h e presence o f a surface, which i n t r o d u c e s a s t r e s s - f r e e d i s c o n t i n u i t y , new e x c i t a t i o n s appear, namely t h e Rayleigh, Lamb and Love modes.

A good f e e l i n g f o r t h e n a t u r e o f t h e s e modes can be o b t a i n e d f o l l o w i n g t h e e l o q u e n t t r e a t m e n t o f A u l d / l o / u s i n g t h e v e r y s i m p l e t r a n s v e r s e resonance t e c h n i q u e . I t i s c o n v e n i e n t t o f i r s t d e r i v e t h e modes o f a p l a t e . The r e s u l t s f o r t h e p l a t e may t h e n be c a r r i e d o v e r t o t h e case o f a s e m i - i n f i n i t e sample b y a l l o w i n g t h e p l a t e t h i c k - ness t o approach i n f i n i t y .

JOURNAL DE PHYSIQUE

MODES OF A PLATE

The symmetry o f t h e p r o b l e m w i t h r e s p e c t t o t h e p l a n e t h r o u g h t h e m i d d l e o f t h e p l a t e ( z = 0) r e q u i r e s t h a t t h e waves be e i t h e r symmetric o r a n t i s y m m e t r i c w i t h r e s p e c t t o t h i s p l a n e . We t h u s r e q u i r e a t l e a s t two p l a n e waves w i t h w a v e v e c t o r s

Z

/ .

b ) P a r t i a l wave p a t t e r n f o r mixed l o n g i t u d i n a l ( L ) and shear v e r t i c a l (SV) p r o p a g a t i o n L+SV -modes (LAMB WAVE) (Lamb waves)

(b)

k and k , where i s o b t a i n e d b y r e f l e c t i n g k on t h e symmetry p l a n e . The s i m p l e s t case i s t h a t o f shear h o r i z o n t a l waves ( F i g . 3 ) . I n t h i s case, t h e p o l a r i z a t i o n remains h o r i z o n t a l upon r e f l e c t i o n and o n l y two waves, k and k, a r e r e q u i r e d t o f u l f i l l t h e boundary c o n d i t i o n s (no f o r c e i n t h e z d i r e c t i o n ) . T h i s boundary con- d i t i o n r e q u i r e s t h a t t h e d i s p l a c e m e n t a m p l i t u d e v a n i s h e s a t z = + b/2, i.e.,

where t h e a n g l e 8 i s d e f i n e d i n F i g . 3. E q u a t i o n 2 has a c o n t i n u u m o f s o l u t i o n s w i t h a l o w e r c u t o f f f o r W = u t r / b .

The s i t u a t i o n i s more c o m p l i c a t e d whenever l o n g i t u d i n a l waves a r e i n v o l v e d upon r e f l e c t i o n on t h e p l a t e boundary; t h e s e waves a r e p a r t l y c o n v e r t e d i n t o shear -

v e r t i c a l waves (SV) and f o u r p l a n e waves ( L w i t h k l and fT1 and SV w i t h k t and k t ) a r e r e q u i r e d t o f u l f i l l t h e s e boundary c o n d i t i o n s l e a d i n g t o

and

t a n ( k z t b / 2 ) = - (kgt - ^k$,12

( a n t i s y m m e t r i c ) .

tan(kzlb/2) 4p2kztkZl

The mode f r e q u e n c i e s w a r e g i v e n by

There a r e t h r e e f r e q u e n c y regimes i m p l i c i t i n e q u a t i o n s 4 :

a) Ld/P > ^Ui. In this case, both k,l and kzt are real and the solutions are normal bulk modes.

b ) V 1 7 W / k > ^Ut. Here, kzt is real but kzl is purely imaginary.

The solutions represent bulk transverse modes combined with a longitudinal component which is strongly localised at the surface. These modes are referred to as Lamb waves.

c) W / P < ^{u t . In} this case, both transverse and longitudinal components are localised at the surfaces.

These modes are related to the Rayleigh surface mode of a semi-infinjte solid. In fact, the sum of the lowest order symmetric and antisymmetric solutions in the limit p b -+-is just the Rayleigh solution.

In the limit /3b - 0 0 , the discrete Lamb and shear horizontal (SH) solutions form continua in which the SH modes are indistinguishable from normal bulk modes. The Lamb modes, on the other hand, are bulk transverse modes with an additional longi- tudinal component localised at the surface.

The Rayleigh mode and the surface component of the Lamb mode are localised typically within one wavelength from the surface.

The first observation /11/ of these plate modes was reported for the rather trivial case of near-normal incidence scattering from thin films of collodion and from thin crystalline platelets. For this case /3-> 0 with the phonons propagating back- ward and forward across the plate. The Lamb solution separates into a Love wave

and a longitudinal wave with kZ1 = mTT/b. The restriction of the scattering volume in the z direction leads to a wavevector uncertainty Aq ^{~ l / b with the} result that typically 3 of the longitudinal modes could be observed.

A more complex example is in the spectrum of GaAs /12/ shown in figure 4. Here we see the bulk phonon peaks, absorption broadened as in the case of Ge discussed

FREQUENCY SHIFT GHz

Fig. 4 - Spectrum of GaAs showing scattering from both bulk (L,T) and surface modes.

above. In addition the Rayleigh surface phonon is clearly resolved together with a broad shoulder arising from scattering from tile continuum of Lamb waves. The

C5-32 JOURNAL DE PHYSIQUE

shoulder extends fro,n W = q " U t to W = q " U 1 as expected from the discussion on the nature of the Lamb wave.

A surprising feature of the spectrum however, is that the Rayleigh surface wave peak is more intense than the bulk phonon peak. Since the Rayleigh wave is localised within a wavelength from the surface, the interaction volume with the light is an order of magnitude smaller than for the bulk phonons. The origin of the strong Rayleigh wave scattering was explained by Mishra and Bray /13/ who pointed out that the phonons ripple the surface and that light may be directly scattered from these ripples. The total scattered intensity must be calculated therefore in terms of both, elastooptic and ripple scattering mechanisms allowing for the interference between the two. The calculations have been performed by several groups /12, 14-19/

and the theory found to be in excellent agreement with the measurements. Notice that the spectrum of figure 2 is depclarised, there being in this case no contribu- tion from the ripple mechanism.

Polycryst.

D

An important result of the calculation of the ripple scattering crossection is that in general higher reflectivity materials will scatter more strongly. In parti- cular, phonons in metals may be easily observed via this mechanism. In figure 5 are shown measurements on polycrystalline A1 /20/. The Rayleigh wave and the Lamb continuum are clearly resolved and the ihset shows the excellent agreement with

Fig. 5 - Spectrum of polycrystalline A1 showing Rayleigh wave an continuum of Lamb waves. Inset theoretical fit to data.

2

T m

cr

W t- v,

\

B v,

\ g' lo-

U

>

k In

z

theory / 1 4 j . Earlier measurements by Dil and Brody /21/ on liquid metals have also been satisfactorily explained in terms of the ripple mechanism /16, 22/.

A variety of measurements of thin films on substrates have been performed. The substrate, of course, modifies the properties of the plate modes. Before discussing these measurenznts we qualitatively summarise the properties of the modes of a supported plate.

W t-

z

-

v GHz

I I

-k%'

-

-

MODES OF A PLATE ON A HALF-SPACE

Assuming the lower surface of the plate to be the interface with the half-space, the reflection coefficient for phonons at the lower plate surface is now no longer unity.

This fact seriously complicates the analysis since the transmitted waves must be included. This section is restricted to a qualitative discussion of the modes with emphasis on their similarity to the modes of the unsupported plate.

I ^I

r

-

.

Love Modes. The s o l a t i o n s o f i n t e r e s t a r e t h o s e which a r e t r a p p e d w i t h i n t h e slab, c o r r e s p o n d i n g t o t o t a l i n t e r n a l r e f l e c t i o n w i t h o n l y an evanescent wave e x t e n d i n g i n t o t h e s u b s t r a t e . I t can be shown / l o / t h a t t r a p p i n g can o n l y o c c u r f o r t h e SH waves if LT( 7 U' where U{ i s t h e t r a n s v e r s e v e l o c i t y i n t h e s u b s t r a t e . The t r a n s v e r s e resonance c o n d i t i o n i s n o t as s i m p l e as ( 2 ) due t o t h e phase change o c c u r r i n g on r e f l e c t i o n a t t h e i n t e r f a c e . The modes a r e r e f e r r e d t o as Love waves.

G e n e r a l i s e d Lamb Waves. These s o l u t i o n s w i t h p o l a r i s a t i o n i n t h e xz p l a n e a l s o depend on t h e r e l a t i o n s h i p between U( and Ut .

a ) U[C< . I n t h i s case, o n l y one s o l u t i o n i s p o s s i b l e which i n t h e l i m i t p b ->O becomes t h e R a y l e i g h wave on t h e s u b s t r a t e .

b ) U; >> Ut

.

Under c e r t a i n c o n d i t i o n s f o r v{.* vt, t h e mode Mpl becomes a bound i n t e r f a c e mode known as t h e S t o n e l e y wave. The S t o n e l e y wave v e l o c i t y US must s a t i s f y t h e con- d i t i o n

where U; i s t h e R a y l e i g h wave v e l o c i t y on t h e b a r e s u b s t r a t e .

F o l l o w i n g a r e some examples of l i g h t s c a t t e r i n g f r o m s u p p o r t e d f i l m s . I n g e n e r a l a c a l c u l a t i o n o f t h e l i g h t s c a t t e r i n g c r o s s - s e c t i o n becomes c o m p l i c a t e d - i n t h e most g e n e r a l case o f a t r a n s p a r e n t f i l m on a t r a n s p a r e n t s u b s t r a t e t h e r e a r e c o n t r i - b u t i o n s t o t h e s c a t t e r i n g f r o m b o t h s u r f a c e and i n t e r f a c e r i p p l e s and f r o m t h e e l a s t o o p t i c e f f e c t i n b o t h f i l m and s u b s t r a t e . I n a d d i t i o n , l i m i t a t i o n s on t h e s c a t t e r i n g volume imposed b y f i l m t h i c k n e s s and/or o p t i c a l a b s o r p t i o n modulate t h e s c a t t e r i n g c r o s s - s e c t i o n as d i s c u s s e d above.

An example of t h e s i m p l e s t s i t u a t i o n i n which o n l y t h e s u r f a c e r i p p l e i s i m p o r t a n t i s shown i n f i g u r e 6 f o r s c a t t e r i n g f r o m a f i l m of A1 on S i . T h i s spectrum s h o u l d be compared w i t h t h a t o f p u r e A1 i n f i g u r e 5. N o t i c e t h a t t h e continuum o f Lamb waves observed i n f i g u r e 5 becomes d i s c r e t e modes f o r t h e t h i n f i l m . The con- t i n u o u s l i n e o f f i g u r e 6 i s t h e c a l c u l a t e d c r o s s - s e c t i o n /23/. Vacher and co- workers have r e p o r t e d measurements o f t h e R a y l e i g h wave o n l y on A1 f i l m s on d i f f e - r e n t s u b s t r a t e s /24/.

Measurements o f SiO2 on S i c o u l d be t h e o r e t i c a l l y e x p l a i n e d i n d e t a i l /25/ u s i n g t h e known e l a s t o o p t i c and e l a s t i c p r o p e r t i e s o f f i l m and s u b s t r a t e . On t h e o t h e r hand, i n t e r p r e t a t i o n o f s p e c t r a o f Au f i l m s on S i (see subsequent paper i n t h e s e p r o c e e d i n g s ) has y i e l d e d t h e p r e v i o u s l y unknown e l a s t o o p t i c c o n s t a n t s o f Au.

Of i n t e r e s t a r e measurements b y D i l and coworkers / 7 / on p o l y c a r b o n a t e f i l m s on g l a s s i n w h i c h Love waves were s u c c e s s f u l l y observed. Both t h e s e measurements and measurements on a Hg/glass sample which show a bound i n t e r f a c e mode s i m i l a r t o t h e S t o n e l e y mode a r e d e s c r i b e d i n t h e s e proceedings.

As expected f o r low r e f l e c t i v i t y m a t e r i a l s t h e s p e c t r a f r o m polycarbonate!glass samples a r e found t o be v e r y weak. Rowel1 and Stegeman have demonstrated t h a t p r i s m c o u p l i n g t e c h n i q u e s may be used t o c o u p l e t h e l i g h t more e f f e c t i v e l y and o b t a i n e d s t r o n g s p e c t r a o f R a y l e i g h and Sezawa modes i n o p t i c a l waveguide s t r u c t u r e s .

JOURNAL DE PHYSIQUE

FREQUENCY SHIFT GHz

Fig. 6 - Spectrum of thin film of A1 on Si showing discrete Sezawa (SW) and Lamb (LB) waves.

LIGHT SCATTERING FROM MAGNETIC MATERIALS

Spinwaves in magnetic materials modulate the dielectric constant of the medium (via the spin orbit interaction) and so can scatter light. Early measLwements on YIG demonstrated that the scattered intensity is comparable to that from phonons, and further that a lot of information relating to the magnetic system may be derived from the spectra. Several measurements on relatively transparent materials have been discussed in a short review by Borovik-Romanov and Kreines /26/.

Two differences between phonon spectra and spinwave spectra are of particular interest:

a) Even in the region of wavevectors accessible to light scattering (less than 1%

of the Brillouin zone) spinwaves show strong dispersion due to the exchange inter- action. Measurements as a function of wavevector thus yield useful information -

by comparison phonons show no dispersion in this range.

b ) The lack of time reversal symmetry between Stokes and anti-Stokes scattering events leads to marked asymmetry in the observed spectra.

The early measurements on relatively transparent materials showed only scattering from bulk spinwaves. More recently, measurements on opaque ferromagnets have been reported in which surface features have been observed. The surface spinwave, first described by Damon and Eshbach / 2 7 / has the strange property of non-reciprocal nro- pagation. More precisely on a surface with magnetisation in the plane of the surface a surface spinwave may only propagate from left to right across the field direction.

As a result in a light scattering measurement (which involves absorption of an exci- tation in one direction and emission in the opposite direction) the surface spin wave peak will be obcerved only in the Stokes or anti-Stokes spectrum depending on the field direction. This strange asymmetry was first observed by Grunberg and

Metawe /28/ i n EuO, S i m i l a r o b s e r v a t i o n s have been r e p o r t e d i n Fe and N i /29/.

F i g u r e 7 shows a spectrum f r o m Fe and demonstrates n o t o n l y t h e marked asymmetry b u t

F i g . 7 - Spectrum o f Fe showing s c a t t e r i n g f r o m b u l k and s u r f a c e spinwaves.

>

t m Z W F z

a l s o a s t r o n g broadening i n t h e b u l k spinwave peak a r i s i n g f r o m t h e h i g h o p t i c a l a b s o r p t i o n . Cottam /30/ has c a l c u l a t e d t h e s p e c t r a l l i n e shape f o r t h e b u l k modes as a f u n c t i o n o f o p t i c a l a b s o r p t i o n , exchange c o n s t a n t and degree o f p i n n i n g o f t h e s p i n s . Camley and M i l l s /31/ have performed a n u m e r i c a l c a l c u l a t i o n i n c l u d i n g s c a t t e r i n g f r o m t h e s u r f a c e spinwave and o b t a i n e x c e l l e n t agreement w i t h t h e e x p e r i - mental data.

There has r e c e n t l y been c o n s i d e r a b l e i n t e r e s t i n s c a t t e r i n g f r o m t h i n magnetic f i l m s b o t h t h e o r e t i c a l l y /32-34/ and e x p e r i m e n t a l l y /35, 36/. Due t o l a c k o f space t h e r e a d e r i s r e f e r r e d t o t h e l i t e r a t u r e .

60 40 20 0 -20 -40 -60

S 4

"

--

CONCLUSIONS

IRON T = 350K H = 2 . 6 k G

B r i l l o u i n s c a t t e r i n g has r i p e n e d i n t o a p o w e r f u l t o o l f o r t h e s t u d y o f s m a l l wave- v e c t o r e x c i t a t i o n s , b o t h phonons and spinwaves, a t s u r f a c e s and i n t e r f a c e s on m a t e r i a l s r a n g i n g f r o m t r a n s p a r e n t d i e l e c t r i c s t o h i g h l y opaque m e t a l s .

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