Ultrasonic attenuation in chromium

Ultrasonic attenuation in chromium

Volume 37A, number 5 PHYSICS ULTRASONIC LETTERS ATTENUATION 20 December 1971 IN CHROMIUM A. M. S I M P S O N * Physics Department, Dalhousie U...

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Volume 37A, number 5

PHYSICS

ULTRASONIC

LETTERS

ATTENUATION

20 December 1971

IN

CHROMIUM

A. M. S I M P S O N * Physics Department, Dalhousie University, Halifax, Nova Scotia, Canada Received 9 November 1971

Measurements of the attenuation coefficient of ultrasonic shear waves have been made near the spin-flip transition of Cr. An explanation is advanced for the major features observed.

In a r e c e n t l e t t e r [1] m e a s u r e m e n t s of the u l t r a s o n i c a t t e n u a t i o n c o e f f i c i e n t in C r w e r e r e p o r t e d f o r both s h e a r and l o n g i t u d i n a l w a v e s w i t h the t e m p e r a t u r e v a r y i n g f r o m b e l o w the s p i n flip o r d e r - o r d e r t r a n s i t i o n n e a r 122 OK, T F , to a b o v e the N 6 e l p o i n t at 312 OK, T N. We h a v e m a d e s i m i l a r m e a s u r e m e n t s of the s h e a r w a v e coefficient under similar conditions, namely sound p r o p a g a t i o n a l o n g the [100] a x i s of a s i n g l e c r y s t a l of c h r o m i u m and p o l a r i z a t i o n a l o n g the [010] a x i s (± 2 °) but find q u a l i t a t i v e l y d i f f e r e n t results. T h e e x p e r i m e n t a l s y s t e m is the s a m e a s u s e d f o r m e a s u r e m e n t s of the l o n g i t u d i n a l c o e f f i c i e n t [2]. It p e r m i t s the s a m p l e to b e c o o l e d t h r o u g h T N w h i l e in the 50 kG f i e l d of a s u p e r c o n d u c t i n g s o l e n o i d s o a s to e s t a b l i s h a s i n g l e s p i n - d e n s i t y w a v e Q in the c h r o m i u m c r y s t a l [3]. T h e s a m p l e is a l s o the s a m e a s u s e d f o r the l o n g i t u d i n a l m e a s u r e m e n t s , b e i n g 0.815 c m l o n g and h a v i n g a r e s i s t a n c e r a t i o of 50. T h e t r a n s d u c e r s w e r e q u a r t z , Y - c u t , w i t h a f u n d a m e n t a l f r e q u e n c y of 10 MHz and w e r e b o n d e d to the c h r o m i u m w i t h A r a l d i t e e p o x y glue. In a l l the e x p e r i m e n t s one t r a n s d u c e r w a s u s e d a s both t r a n s m i t t e r and d e tector, a particular echo was selected, amplified, and r e c o r d e d on the Y a x i s of an X - Y r e c o r d e r . T h e X a x i s r e c o r d e d the t e m p e r a t u r e from a copperconstantan thermocouple. A fuller d e s c r i p t i o n of the e x p e r i m e n t a l m e t h o d is g i v e n

b e h a v i o u r of the d i f f e r e n t e c h o s , and s o the m e a s u r e m e n t s of the m a g n i t u d e of the s t r u c t u r e in the c u r v e s s h o u l d be r e g a r d e d a s only a p p r o x i m a t e . F i g . 1 s h o w s the r e l a t i v e a t t e n u a t i o n of a 49.7 MHz s o u n d w a v e a s a f u n c t i o n of t e m p e r a t u r e n e a r T F (a) w i t h no f i e l d c o o l i n g , and (b) a f t e r c o o l i n g t h r o u g h T N in a f i e l d of 46 kG a p p l i e d p a r a l l e l to [100]. T h e z e r o of a t t e n u a t i o n is a r b i t r a r i l y c h o s e n f o r c u r v e (b) and c u r v e (a) r e f e r r e d to the s a m e z e r o by c y c l i n g the t e m p e r a t u r e a b o v e T N and b a c k b e l o w T F w h i l e c o n t i n u o u s l y m o n i t o r i n g the s i g n a l . On w a r m i n g t h r o u g h T N the n o n - f i e l d c o o l e d s a m p l e e x h i b i t s a r a p i d d r o p in the a t t e n u a t i o n s i m i l a r to that r e p o r t e d in [1]. W h e n the f i e l d c o o l e d s a m p l e is w a r m e d t h r o u g h TN, h o w e v e r , t h e r e is only a s m a l l p e a k s u p e r i m p o s e d on a c o n t i n u o u s b a c k ground. T h e s a l i e n t f e a t u r e s of the r e s u l t s a r e thus, f o r the f i e l d c o o l e d s a m p l e a s m o o t h l y v a r y i n g b a c k g r o u n d a t t e n u a t i o n w i t h two s m a l l p e a k s s u p e r i m p o s e d at T F and TN, and f o r the n o n - f i e l d c o o l e d s a m p l e t h e r e i s a s t e p in the a t t e n u a t i o n at both T N and T F and an o s c i l l a t i o n

~4 i

in [2]. In a l l the m e a s u r e m e n t s the e n v e l o p e of the e c h o t r a i n d e p a r t e d f r o m the i d e a l e x p o n e n t i a l b e h a v i o u r by an a m o u n t that v a r i e d w i t h t e m p e r a t u r e . F o r that r e a s o n m e a s u r e m e n t s w e r e m a d e on s e v e r a l d i f f e r e n t e c h o s in the t r a i n . T h e r e s u l t s r e p o r t e d h e r e a r e an a v e r a g e of the * P r e s e n t address: Royal Society Mond Laboratory, F r e e School Lane, Cambridge.

O,

. T(°K)

Fig. 1. Relative attenuation of a 49.7 MHz ultrasonic shear wave as a function of temperature. Curve (a) : without field cooling; curve (b) : after field cooling through T N. 379

Volume 37A, number 5

PHYSICS L E T T E R S

n e a r T F. F o r T < T F t h e n o n - f i e l d c o o l e d a t t e n uation approaches the field cooled value. Similar b e h a v i o u r w a s o b s e r v e d w i t h a 30 M H z s i g n a l . The increased attenuation between T N and T F of t h e n o n - f i e l d c o o l e d s t a t e a b o v e t h e f i e l d c o o l e d c a s e i s r e m i n i s c e n t of t h e b e h a v i o u r of t h e l o n g i t u d i n a l c o e f f i c i e n t [2], a n d a s i m i l a r e x p l a nation may be advanced. Between T N and T F the non-field cooled Cr has three possible Q vectors i n e a c h of w h i c h t h e r e a r e t w o p o s s i b l e t r a n s v e r s e s p i n d i r e c t i o n s [4]. T h e r e a r e t h e n s i x t y p e s of d o m a i n w i t h a s m a l l m i s m a t c h of t h e l a t t i c e d i m e n s i o n s a t t h e d o m a i n b o u n d a r i e s [5]. T h e s o u n d w a v e c a n c a u s e m o v e m e n t s of t h e d o m a i n b o u n d a r i e s a n d l o s s of e n e r g y o c c u r s t h r o u g h a r e l a x a t i o n m e c h a n i s m . In t h e f i e l d c o o l e d s a m p l e t h e r e i s o n l y o n e Q v e c t o r a n d two p o s s i b l e d o m a i n t y p e s t h a t a r e s y m m e t r i c w i t h r e s p e c t to the sound propagation direction. The boundaries will not respond to the stress wave so readily

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20 December 1971

a n d s o w i l l not a b s o r b e n e r g y f r o m it. A t T F t h e s p i n p o l a r i z a t i o n c h a n g e s f r o m t r a n s v e r s e to longitudinal and is accompanied by sudden c h a n g e s i n t h e l a t t i c e d i m e n s i o n s [5], w h i c h again provide a mechanism for interaction with t h e s o u n d w a v e l e a d i n g to c h a n g e s i n a t t e n u a t i o n n e a r T F. B u t w h y t h e s e c h a n g e s s h o u l d t a k e t h e f o r m of a n o s c i l l a t i o n i s not c l e a r .

References [1] J. s. Imai and Y. Sawada, Phys. L e t t e r s 34A {1971) 333. [2] A.M. Simpson, M. Roth, M. H. J e r i c h o and J. O. S t r o m - O | s e n , Phys. Rev. B4 (1971) 3093. [3] R.A. Montalvo and J. A. Marcus, Phys. L e t t e r s 8 (1964) 151. [4] S. A. W e r n e r , A. A r r o t t and H. Kendrick, Phys. Rev. 155 (1967) 528. [5] M. O. Steinitz, L.H. Schwartz, J . A . Marcus, E. Fawcett and W. A. Reed, Phys. Rev. L e t t e r s 23 (1969) 979.