Super-transferred hyperfine fields in the rare earth orthochromites and orthoferrites

Super-transferred hyperfine fields in the rare earth orthochromites and orthoferrites

VoLume 37A, number 3 PHYSICS LETTERS 22 November 1971 SUPER-TRANSFERRED HYPERFINE FIELDS IN THE RARE EARTH ORTHOCHROMITES AND ORTHOFERRITES M. A. ...

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VoLume 37A, number 3

PHYSICS

LETTERS

22 November 1971

SUPER-TRANSFERRED HYPERFINE FIELDS IN THE RARE EARTH ORTHOCHROMITES AND ORTHOFERRITES M. A. B U T L E R , M. EIBSCH£ITZ and L. G. VAN U I T E R T

Bell Telephone Laboratories, Inc., Murray Hill, New Jersy 07974, USA Received 24 September 1971

The variation of hyperfine field with exchange parameter J in the r a r e earth orthochromites and orthoferrites is shown to arise from changes in the superfransferred hyperfine field.

N u c l e a r m a g n e t i c r e s o n a n c e has b e e n u s e d to e x a m i n e the 5 3 C r h y p e r f i n e f i e l d in s e v e r a l of the c a n t e d a n t i f e r r o m a g n e t i c o r t h o c h r o m i t e s R C r O 3 w h e r e R is a r a r e e a r t h (RE) ion o r Y. A s y s t e m a t i c v a r i a t i o n of the h y p e r f i n e f i e l d with R E ion w a s o b s e r v e d r e m i n i s c e n t of the v a r i a t i o n found in the o r t h o f e r r i t e s R F e O 3 [1]. T h r e e e f f e c t s m a y c a u s e v a r i a t i o n s of the h y p e r f i n e f i e l d in s u c h a s e r i e s of c o m p o u n d s . 1) D i s t o r t i o n of the l a t t i c e m a y c h a n g e the o v e r l a p of the 3d w a v e f u n c t i o n s with the o x y g e n p and s o r b i t a l s and t h e r e b y c h a n g e the a m o u n t of c o v a l e n c y . It has b e e n shown that i n c r e a s i n g c o v a l e n c y r e s u l t s in a d e c r e a s i n g c o r e p o l a r i z a tion h y p e r f i n e f i e l d [2]. 2) C h a n g e s in c o v a l e n c y w o u l d a l s o e f f e c t any o r b i t a l c o m p o n e n t to the h y p e r f i n e f i e l d that is p r e s e n t . S i n c e i n c r e a s i n g c o v a l e n c y d e c r e a s e s the magnitude of the o r b i t a l g - s h i f t [2], it f o l l o w s that the magnitude of the o r b i t a l h y p e r f i n e f i e l d a l s o d e c r e a s e s . 3) V a r i a t i o n s in the o v e r l a p of the C r 3d and the o x y g e n p and s o r b i t a l s w o u l d a l s o c h a n g e the s u p e r t r a n s f e r r e d h y p e r f i n e f i e l d (STHF) [3]. T h i s is t h e f i e l d at one 5 3 C r n u c l e u s g e n e r a t e d by the e l e c t r o n i c s p i n on a n e i g h b o r i n g Cr site. Such e f f e c t s a r i s e f r o m t r a n s f e r of s p i n p o l a r i z a t i o n t h r o u g h the i n t e r v e n i n g o x y g e n o r b i t a l s . T h i s means increasing covalency-wavefunction overl a p - i n c r e a s e s the magnitude of the S T H F . S i n c e t h e s e t h r e e e f f e c t s all d e p e n d on the a m o u n t of c o v a l e n c y , it s e e m s a p p r o p r i a t e to e x a m i n e the h y p e r f i n e f i e l d as a f u n c t i o n of s o m e p a r a m e t e r c l o s e l y r e l a t e d to c o v a l e n c y . T h e e x c h a n g e i n t e g r a l is a f u n c t i o n of the f o u r t h p o w e r of the o v e r l a p b e t w e e n the t r a n s i t i o n m e t a l 3d and o x y g e n p w a v e f u n c t i o n s , J ~ I(M3+(3d) l O 2- (p)) ! 4, t h e r e f o r e we h a v e t a k e n the a v e r a g e e x c h a n g e d e t e r m i n e d f r o m the Nfiel t e m p e r a t u r e by the m e t h o d of R u s h b r o o k and Wood [4] a s t h i s p a r a m -

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Fig. 1. The hyperfine field per spin at 4.2 K as a function of the average exchange interaction J . The solid line is the slope predicted for RCrO 3 from the RFeO 3 data and the simple model discussed in the text. The e r r o r bar is characteristic of all RFeO 3 data. The e r r o r on the RCrO 3 data are smaller than the points. The RCrO 3 data point at J = 52.5 K are from ref. [5]. eter. The resulting hyperfine field data as a f u n c t i o n of J a r e d i s p l a y e d in fig. 1. T h e c o n t r i b u t i o n of the a b o v e t h r e e e f f e c t s to the t o t a l h y p e r f i n e f i e l d p e r spin m a y be d e s c r i b e d by: A t o t a l = A f r e e ion - a ](M3+(3d)l O2-(p))21 • b I
(1)

0 2- (P)I 21 <°2- (p) l M3+(s)>12~Aorb,

w h e r e the f i r s t t e r m is the v a l u e of the h y p e r f i n e f i e l d with no o r b i t a l f i e l d o r c o v a l e n c y e f f e c t s . T h e s e c o n d t e r m r e p r e s e n t s the r e d u c t i o n of the h y p e r f i n e f i e l d due to c o v a l e n c y and the t h i r d t e r m the S T H F e f f e c t s . A o r b is j u s t the o r b i t a l 199

Volume 37A, number 3

PHYSICS

c o n t r i b u t i o n to the h y p e r f i n e field. T h e o v e r l a p of the v a r i o u s w a v e f u n c t i o n s in eq. (1) a r e the m a j o r t e r m s c o n t r i b u t i n g and t h e r e f o r e t h e y a r e only r e p r e s e n t a t i v e of the i n t e r a c t i o n s . It is app a r e n t that the S T H F t e r m d e p e n d s on the o v e r l a p of different wavefunctions than the exchange integral. However, it is a reasonable approximation over a limited range of J t o assume AA (STHF)~ J as is observed for the RFeO3 data. As Fe 3+ has negligible orbital hyperfine field and as covalency would result in a negative slope, the positive slope to the RFeO3 data must be attributed to STHF effects. The sign of this slope a g r e e s with e x p e c t a t i o n s [3]. In c o n t r a s t with the F e ~+ ion which has a 3d5(6S) e l e c t r o n i c c o n f i g u r a t i o n , the C r 3+ ion has 3d3(4F) e l e c t r o n i c c o n f i g u r a t i o n w h i c h is s p l i t by the c u b i c c o m p o n e n t of the c r y s t a l f i e l d l e a v i n g an 4A2g s t a t e l o w e s t . T h u s for Cr 3+ t h e r e e x i s t s a s m a l l o r b i t a l f i e l d e s t i m a t e d f r o m g - s h i f t m e a s u r e m e n t s [6] as -7 kOe/spin. This negative orbital field implies a negative slope to the data. The less than half filled 3d shell for the Cr 3+ ion results in the STHF having opposite sign than for the Fe 3+ ion [3]. T h e r e f o r e all t h r e e m e c h n i s m s w h i c h can v a r y the h y p e r f i n e f i e l d r e q u i r e a n e g a t i v e s l o p e for the R C r O 3 data. It has b e e n p o i n t e d out that for a g i v e n t y p e of l i g a n d and c o o r d i n a t i o n , the c o r e p o l a r i z a t i o n h y p e r f i n e f i e l d is i n s e n s i t i v e to l a t t i c e p a r a m e t e r [7]. I g n o r i n g o r b i t a l e f f e c t s we m a y then a r g u e that both s e t s of d a t a r e f l e c t only S T H F e f f e c t s . Owen and T a y l o r [8] h a v e c a l c u l a t e d the S T H F at n e i g h b o r i n g 27A1 s i t e s to C r 3+ and F e 3+ i m p u r i -

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22 November 1971

t i e s in LaA10 3 and find S T H F ( F e ) / S T H F ( C r ) = = -3.4. To a f i r s t a p p r o x i m a t i o n t h i s r a t i o should be i n d e p e n d e n t of s t r u c t u r a l d e t a i l s and t h e r e f o r e should a p p r o x i m a t e the r a t i o of the s l o p e s for the d a t a in fig. 1. The s o l i d l i n e in fig. 1 is the s l o p e p r e d i c t e d for R C r O 3 u s i n g this r a t i o and the s l o p e of the R F e O 3 data. C o n s i d e r i n g the p o s s i b l e i n a d e q u a c y of J a s a m e a s u r e of c o v a l e n c y , the a g r e e m e n t is quite good. I n c l u s i o n of o r b i t a l e f f e c t s would only m a k e the p r e d i c t e d s l o p e s t e e p e r and a g r e e m e n t w o r s e . We t h e r e f o r e c o n c l u d e that one can a c c o u n t f o r the v a r i a t i o n of h y p e r f i n e f i e l d in the s e r i e s of c o m p o u n d s R C r O 3 and R F e O 3 s o l e l y on the b a s i s of S T H F e f f e c t s .

References [1] M.Eibschtltz, S.Shtrikman and D . T r e v e s , Phys. Rev. 156 (1967) 562. [2] W. Low, Paramagnetic Resonance in Solids (Academis P r e s s , New York, 1960) 109, [3] N.L.Huang, "R.Orbach, E.Simanek, J.Owen and D . R . T a y l o r , Phys. Rev. 156 (1967) 383 and reference contained therein. [4] G.S.Rushbrook and P.J.Wood, Mol. Phys. 6 (1963) 409. [5] D.T.Edmonds and D . R . T a y l o r . Proc. Phys. Soc. 91 (1967) 356. [6] D.Kiro, W.Low and A.Zusman, Paramag~etic Resonance (Academic Press, New York. 1963) Vol. 1, p. 44. [7] P . R . L o c h e r and S.Geschwind, Phys. Rev. 139 (] 965) A991. [8] J.Owen and D . R . T a y l o r , J. Appl. Phys. 39 (1968) 791.