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EFFECTS OF RANDOM DILUTION OF SPIN-WAVE
RESPONSE IN FERROMAGNETIC BI-LAYER
COMPOUNDS
R. Tahir-Kheli
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C6, supplement au
no
8, Tome 39, aoitf 1978, page
C6-751
EFFECTS OF RANDOM DILUTION OF SPIN-WAVE RESPONSE IN FERROMAGNETIC BI-LAYER COMPOUNDS
R.A. Tahir-Kheli
Department
ofPhysics, Temp Ze U n i v e r s i t y Phi Zade Zphia, Pennsy Zvania
19122,
U.S. A.Rdsum6.- La "rdponse" d e s d o u b l e s couches magndtiques s o u s forme d ' o n d e s d e s p i n c o n s i s t e e n deux f o n c t i o n s d e l t a d e p o i d s &gaJ.,l7une s i t u B e a u n i v e a u d e s ondes d e s p i n e t l ' a u t r e d d p l a c d e d ' u n e L n e r g i e p r o p o r t i o n e l l e a u c o u p l a g e e n t r e deux couches a t o m i q u e s . L1inhomog6n6itB d e d i l u t i o n provo- que u n d l a r g i s s e m e n t d e s f o n c t i o n s d e l t a . C e t B l a r g i s s e m e n t a f f e c t e i n d g a l e m e n t l e s p o i d s e t l e s l a r g e u r s d e s deux maxima. A g r a n d e d i l u t i o n , s e u l e l a "rLponse" d e s mono-couches s u r v i t
B
g r a n d e l o n g u e u r d'onde e t l a r d c i p r o q u e e s t v a l i d e pour l e s p e t i t e s l o n g u e u r s d ' o n d e . Ces c u r i e u x e f f e t s p o u r r a i e n t 8 t r e o b s e r v 6 s p a r d i f f r a c t i o n d e s n e u t r o n s .A b s t r a c t . - Simple spin-wave r e s p o n s e o f m a g n e t i c b i - l a y e r s c o n s i s t s of two d e l t a f u n c t i o n s of e q u a l weight--one c e n t r e d a t t h e spin-wave e n e r g y f o r mono-layers and t h e o t h e r d i s p l a c e d from i t by a n e n e r g y p r o p o r t i o n a l t o t h e i n t e r l a y e r c o u p l i n g . P r e s e n c e o f random d i l u t i o n c a u s e s w i d e n i n g o f t h e d e l t a f u n c t i o n s . A l s o , i t a f f e c t s t h e w e i g h t s and w i d t h s of t h e two peaks d i f f e r e n t l y . I n d e e d , f o r l a r g e d i l u t i o n , o n l y t h e monolayer r e s p o n s e s u r v i v e s f o r l o n g wave-lengths w h i l e t h e c o n v e r s e i s
t r u e f o r s h o r t wave-lengths. T h i s c u r i o u s e f f e c t s h o u l d b e o b s e r v a b l e i n n e u t r o n s c a t t e r i n g e x p e r i - ments.
INTRODUCTION.- During t h e l a s t decade, experimen- t a l i s t s have b e e n a b l e t o make c h e m i c a l compounds whose m a g n e t i c b e h a v i o u r c l o s e l y r e s e m b l e s t h a t of monolayers. These a r e t h e s o c a l l e d two dimensio- n a l s y s t e m s , o f which t h e r e a r e now numerous exam- p l e s i n t h e l i t e r a t u r e . I n p a r t i c u l a r , t h e magnetic b e h a v i o u r o f t h e compounds o f t h e s e r i e s A2 M
BQ
,
where A
z
K o r Rb and B:
F o r C1 a r e non-magnetic c a t i o n s and M i s a 3d m e t a l (magnetic) i o n , h a s b e e n found t o c o r r e s p o n d e x c e l l e n t l y t o t h a t of ma- g n e t i c monolayers. R e c e n t l y , i t a p p e a r s t h a t compounds w i t h ma- g i i e t i c b i - l a y e r s have b e e n s y n t h e s i z e d . I n p a r t i - c u l a r / ] / , t h e s e r i e s As(Mn)2F7, A E Rb, K, c o n t a i n s m a g n e t i c b i - l a y e r s which a r e d o u b l e s h e e t s belon- g i n g t o t h e s i m p l e c u b i c l a t t i c e s y s t e m formed a s A MnF 3 .
Systems of d o u b l e s h e e t s a r e m u t u a l l y s e - p a r a t e d by two non-magnetic s h e e t s formed a s AF,which k e e p them m a g n e t i c a l l y i s o l a t e d . Our i n t e r e s t h e r e i s i n a n a l y z i n g t h e e f f e c t s o f m a g n e t i c d i l u t i o n o n t h e b e h a v i o u r o f s i m p l e s p i n - w a v e r e s p o n s e i n s u c h s y s t e m s . F o r s i m p l i c i t y , we c o n s i d e r o n l y t h e c a s e c f f e r r o m a g n e t i c ground s t a t e . Moreover, we employ a c o h e r e n t p o t e n t i a l a p p r o x i m a t i o n / 2 / (CPA) p r o c e d u r e which s h o u l d g i v e q u a l i t a t i v e l y r e a s o n a b l e r e s u l t s .
FORMULATION AND RESULTS.- We c o n s i d e r t h e Heisen-
=
-IILS~
-
JE
U> xi x j ; v 51 ,
( l )i
V;, jThe non-random Zeeman f i e l d i s k e p t h e r e o n l y a s a f o r m a l d e v i c e f o r i n s u r i n g t h e adequacy of t h e sim- p l e , random phase a p p r o x i m a t i o n (RPA) t y p e of s p i n - wave p i c t u r e . Randomness i s i n t r o d u c e d t h r o u g h t h e p r e s e n c e o f m a g n e t i c o c c u p a t i o n o p e r a t o r s , X
i '
(which a r e u n i t y i f t h e s i t e i i s o c c u p i e d by a ma-
g n e t i c atom b u t a r e z e r o o t h e r w i s e and t h e random bond v a r i a b l e
aV
whichi s
e i t h e r u n i t y o r z e r oi j '
a c c o r d i n g a s t h e exchange bond between n e i g h b o u r i n g s i t e s i and j a l o n g t h e d i r e c t i o n V i s c o n n e c t e d o r n o t .
W i t h i n a s i m p l e / 2 / CPA, we need o n l y two co- v h e r e n t exchange i n t e e r a l s J ( E ) ; v E I I and F o r t h e c o h e r e n t medium, t h e p l a n a r G r e e n ' s f u n c t i o n is where II
ak
= E- P -
21 I J ( ~ ) ( 1-
yk) ( 3 ) Here z 1 1 i s t h e i t r a p l a n a r c o o r d i n a t i o n number, andyk
= C e i"'ll / z " (xIl
a r e t h e n e a r e s t4,
n e i g h b o u r v e c t o r s ) .
The CPA r e l a t i o n s (2) which i n t u r n d e t e r - mine t h e unknown JYE) f o r any g i v e n E, c a n b e ge- n e r a t e d by e x t e n d i n g t h e d i s c u s s i o n of r e f e r e n c e
1 2 1 .
We f i n d [MU;. xix .-J\;~) ( i j xi l w ( c > v - 0 , v=
11 ,l ( 4 ) Cc) 1 -[payj x i x j - ~ ( , , ( i j U A ( V ) where M i s t w i c e t h e RPA m a g n e t i z a t i o n , i . e . M=2S a t T=O, W(c) i s t h e w e i g h t i n g f a c t o r f o r a g i v e n c o n f i g u r a t i o n {c) andWe have computed the spin-wave r e s p o n s e , i . e .
-
Imrk(w+ie), f o r a case w i t h magnetic s i t e d i l u - t i o n f o r a q u a d r a t i c b i - l a y e r system. I n f i g u r e s 1-+
and 2 we show t h e response f o r K = n ( n / 4 , n / 4 ) f o r n = 1 , 2, 3, 4 f o r 5
X
and 25X
d i l u t i o n (Note t h a t i n t h e p r e s e n t approximation, magnetic p e r c o l a t i o n c o n c e n t r a t i o n f o r such a b i - l a y e r system i s 40 X). I n f i g u r e 1 , w i t h 95 Z magnetic i o n s , t h e changes i n the behaviour of t h e response a r e a l r e a - dy becoming c l e a r . For r e l a t i v e l y long wavelength( c u r v e l ) , t h e mono-layer response i s r e l a t i v e l y u n a f f e c t e d whereas t h e second peak, which, a s i t were, n o t i c e s t h e presence of t h e second l a y e r i s
-+
c o n s i d e r a b l y reduced. On t h e o t h e r hand, f o r K a t the zone boundary t h e peak which a r i s e s due t o t h e presence of t h e second l a y e r assumes prominence. A t t h i s wave-vector, t h e system f u l l y s e n s e s t h e presence of t h e second l a y e r .
F i g . 1 : Spin-wave response f o r a magnetic b i - l a y e r c o n s i s t i n g of two neighbouring q u a d r a t i c magnetic l a t t i c e s with
5 X
d i l u t i o n . The t o t a l a r e a under any curve, n, isnx,
where X i s t h e magnetic concen- t r a t i o n (which i s e q u a l t o 0.95 f o r t h e p r e s e n t c a s e ) . The v a r i o u s curves a r e l a b e l l e d by n which i n d i c 3 t e s t h e r e l e v a n t wave-vector through t h e r e l a - t i o n K P n ( n / 4 , n / 4 ) .l u t i o n a s i s s e e n i n f i g u r e 2 which r e f e r s t o t h e c a s e of 75 Z magnetic c o n c e n t r a t i o n .
F i g . 2 : Same a s I e x c e p t X = 0.75 f o r t h i s f i g u r e .
Neutron s c a t t e r i n g experiments on magnetic b i - l a y e r systems, w i t h a p p r o p r i a t e non-magnetic d i -
l u t i o n , would b e of g r e a t i n t e r e s t f o r they w i l l b e s e n s i t i v e t o t h e e f f e c t s suggested by t h e p r e s e n t r a t h e r q u a l i t a t i v e t r e a t m e n t .
ACKNOWLEDGEMENT.- We a r e indebted t o P r o f e s s o r H. Amar f o r h i s i n t e r e s t and encouragement.
References
/ l / Navarro,R., S m i t , J . J . , Crama,W.J. and 1jd0,D.J. W., Physica
83B
( 1 976) 97/ 2 / Tahir-Kheli,R.A., Phys. Rev.
