Magnetohydrodynamical-spin resonance in antiferromagnets

Volume 38A, number 5

PHYSICS

MAGNETOHYDRODYNAMICAL-SPIN

LETTERS

RESONANCE

28 February 1972

IN

ANTIFERROMAGNETS

I. A. AKHIEZER and E. M. CHUDNOVSKI Kharkov State University, Kharkov , USSR Received 18 January 1972

We consider coupled magnetohydrodynamical-spin waves in antiferromagnetic metals and semiconductors. For a certain value of the external magnetic field resonance coupling between these waves occurs in a broad frequency band. Ways of observing such a resonance are discussed.

We consider couple magnetohydrodynamical and s p i n w a v e s in a n t i f e r r o m a g n e t i c m e t a l s o r s e m i c o n d u c t o r s *. S i n c e m a g n e t o h y d r o d y n a m i c a l w a v e s and l o w - a c t i v a t i o n s p i n w a v e s h a v e l i n e a r dispersion laws, their phase velocities dependi n g on e x t e r n a l m a g n e t i c f i e l d H, c o u p l i n g b e tween these waves must have interesting pecul i a r i t i e s . V i z . , f o r a c e r t a i n v a l u e of H, p h a s e v e l o c i t i e s of the w a v e s c o i n c i d e , l e a d i n g to a r e s o n a n c e c o u p l i n g b e t w e e n the w a v e s o v e r a w i d e f r e q u e n c y r e g i o n ( c o n t r a r y to u s u a l e l e c t r o m a g n e t i c - s p i n r e s o n a n c e o c c u r r i n g f o r one d e f i n i t e v a l u e of f r e q u e n c y ) . T h e r e s o n a n c e v a l u e of m a g n e t i c f i e l d H r d e p e n d s on the p a rameters characterizing antiferromagnetising (N~el t e m p e r a t u r e , d e n s i t y of c h a r g e c a r r i e r s , e t c . ) and l i e s within 1 0 3 . 105 Oe. If H = H r , r e s o n a n c e c o u p l i n g of w a v e s m u s t o c c u r in the w h o l e f r e q u e n c y band f r o m 109 to 1012 s e c - 1 . F o r f r e q u e n c i e s of c o u p l e d w a v e s in t h i s r e g i o n w e obtain ¢o+=qva(l+&), &=(~xo)l/2sinO, (1) w h e r e v a is the A l f v ~ n v e l o c i t y , Xo the s t a t i c m a g n e t i c s u s c e p t i b i l i t y of the a n t i f e r r o m a g n e t i c m a t e r i a l , 0 the a n g l e b e t w e e n the w a v e v e c t o r q a n d the e x t e r n a l f i e l d / - / ( d i r e c t e d a l o n g the a n i sotropy axis). R e s o n a n c e c o u p l i n g of w a v e s m u s t m a n i f e s t i t s e l f in an e s s e n t i a l g r o w t h of the s u r f a c e i m p e d a n c e of a n t i f e r r o m a g n e t i s m . In the c a s e of the u s u a l e l e c t r o m a g n e t i c - s p i n r e s o n a n c e , an a l m o s t m o n o c h r o m a t i c w a v e is n e c e s s a r y f o r o b s e r v i n g s u c h a g r o w t h . In the c a s e of m a g n e t o h y d r o d y n a m i c a l - s p i n r e s o n a n c e the g r o w t h of the i m p e d a n c e m u s t o c c u r f o r w i d e w a v e packets. S c a t t e r i n g of s l o w n e u t r o n s in a n t i f e r r o m a g * Coupling between spin waves and Langmuir or helical waves has been considered e a r l i e r [1]. 360

n e t can a l s o be u s e d f o r o b s e r v i n g the r e s o n a n c e c o u p l i n g of w a v e s . F o r H f a r f r o m H r , s h a r p m a x i m a m u s t o c c u r in the a n g u l a r d i s t r i b u t i o n of s c a t t e r e d n e u t r o n s due to the e x c i t a t i o n o r a b s o r p t i o n of m a g n e t o h y d r o d y n a m i c a l w a v e s . F o r the c r o s s s e c t i o n of t h i s p r o c e s s (in the c a s e of n o n - p o l a r i z e d n e u t r o n s ) we obtain

dcr = (~ v n No) -1 fi-4(N w + 1)

(2) 2 F 2 ( q ) ¢o2 6(w2 _q2 v2) d 3 p , , × ~n w h e r e N w is the P l a n c k d i s t r i b u t i o n f u n c t i o n , ~n the m a g n e t i c m o m e n t of a n e u t r o n , F ( q ) the m a g n e t i c f o r m - f a c t o r , v n the v e l o c i t y of the i n c i d e n t n e u t r o n s , fiw and fiq the e n e r g y and m o m e n t u m t r a n s f e r r e d , N O the n u m b e r of a t o m s p e r unit v o l u m e . B e s i d e s t h e s e m a x i m a , t h e r e m u s t o c c u r a l s o w e a k e r m a x i m a due to the e x c i t a t i o n o r a b s o r p t i o n of s p i n w a v e s , t h e i r h e i g h t b e i n g p r o p o r t i o n a l to s m a l l p a r a m e t e r ×o" If H = H r , low m a x i m a o c c u r no m o r e , but e a c h of the high m a x i m a s p l i t s into two. T h e c r o s s s e c t i o n m a y b e o b t a i n e d f r o m eq. (2) by the s u b s t i t u t i o n

6(

2_q2v2 )

+

N o t i c e that if i n c i d e n t n e u t r o n s a r e p o l a r i z e d a l o n g / ' / , s c a t t e r i n g with e x c i t a t i o n o r a b s o r p tion of c o u p l e d m a g n e t o h y d r o d y n a m i c a l - s p i n w a v e s is a l w a y s a c c o m p a n i e d by s p i n - f l i p . F o r the o b s e r v a t i o n of m a g n e t o h y d r o d y n a m i c a l - s p i n r e s o n a n c e in a n t i f e r r o m a g n e t i c m e t a l s the t e m p e r a t u r e m u s t b e l o w e r than about 10°K s i n c e at h i g h e r t e m p e r a t u r e s m a g n e t o h y d r o d y n a m i c a l w a v e s a r e s t r o n g l y d a m p e d ( m a i n l y due to e l e c t r o n c o l l i s i o n s ) .

References [1] V. Bar'yakhtar, F.G. Rudashevski, M.A. Savchenko and C. N. Stepanov, Zh. Eksp. i Teor. Fiz. 51 (1966) 250.