Nuclear spin relaxation, hybridization, and low-temperature 4f spin fluctuations in intermediate-valent SmB6

~

Solid State Communications, Vol.40, pp.539-54]. Pergamon Press Ltd. 198]. Printed in Great Britain.

0038-1098/81/4 ] 0539-03502.00/0

N U C L E A R SPIN RELAXATION, H Y B R I D I Z A T I O N , A N D L O W - T E M P E R A T U R E 4f SPIN F L U C T U A T I O N S IN I N T E R M E D I A T E - V A L E N T SmB 6 O. Pe~a, M. Lysak,

and D. E. M a c L a u g h l i n

D e p a r t m e n t of Physics, U n i v e r s i t y of C a l i f o r n i a Riverside, C a l i f o r n i a 92521, U.S.A. and Z. Fisk D e p a r t m e n t of Physics, U n i v e r s i t y of California, La Jolla, C a l i f o r n i a 92037, U.S.A.

San Diego

(Received 14 J u l y 1981 by H. Suhl) liB s p i n - l a t t i c e r e l a x a t i o n m e a s u r e m e n t s have b e e n c a r r i e d out in SmB 6 samples w i t h large l o w - t e m p e r a t u r e r e s i s t i v i ties. A b o v e 15 K the r e l a x a t i o n is activated, w i t h approximately the same gap (%6 meV) as found p r e v i o u s l y in transport and o p t i c a l m e a s u r e m e n t s . 4f spin fluctuations app a r e n t l y d o m i n a t e the relaxation, so t h a t these results give s t r o n g e v i d e n c e for 4 f - c o n d u c t i o n b a n d h y b r i d i z a t i o n at the gap edge. An a n o m a l o u s peak in the r e l a x a t i o n rate was o b s e r v e d at ~5 K, w h i c h is t e D t a t i v e l y a t t r i b u t e d to fluctuations of " r e m a g n e t i z e d " Sm 3+ ions near Sm-site vacancies.

sults II has e n a b l e d us to clarify the role of defects, and in p a r t i c u l a r to v e r i f y the defect i n d e p e n d e n c e of the a c t i v a t e d b e h a v i o r (E~ = 5.6 ± 0.5 meV) p r e v i o u s l y o b s e r v e d a~ove 15 K. Below this t e m p e r a t u r e I/T 1 e x h i b i t s an anom a l o u s i n c r e a s e to a m a x i m u m at about 5 K. This feature was p ~ t i a l l y m a s k e d in p r e v i o u s m e a s u r e m e n t s ±± by defectinduced i n h o m o g e n e o u s relaxation, w h i c h seems to be less e v i d e n t in the p r e s e n t data. The f l u x - g r o w n s p e c i m e n was obt a i n e d in the f o r m of small single crystals. Four-probe resistance measurements y i e l d e d a r e s i d u a l r e s i s t a n c e ratio (RRR) p ~ R(4.2K)/R(300K) = 1.9 x 104 , w h i c h c o m p a r e s f a v o r a b l y to other specimens p r e p a r e d in this manner. 3 N M R s p e c t r a and l o n g i t u d i n a l r e l a x a t i o n functions w e r e o b s e r v e d using a p u l s e d s p i n - e c h o s ~ e c ~ [ o m e t e r and s t a n d a r d techniques, u, The large l o w - t e m p e rature r e s i s t i v i t y of the sample a l l o w e d r a d i o f r e q u e n c y field p e n e t r a t i o n into the a s - g r o w n c r y s t a l s b e l o w about 10 K; p o w d e r i n g of the sample, to p e r m i t N M R m e a s u r e m e n t s at h i g h e r temperatures, had no e f f e c t on the r e l a x a t i o n rate at 4.2 ~IB f i e l d - s w e p t s p e c t r a w e r e obt a i n e d b e t w e e n 1.5 and 900 K on specimens w i t h i 0 3 ~ p ~ 2 x 10 ~. The isotropic f r e q u e n c y shift K i a~d the quadrupole c o u p l i n g c o n s t a n t e~qQ w e r e found to be i n d e p e n d e n t of t e m p e r a t u r e and P

Highly-resistive intermediatev a l e n t (IV) r a r e - e a r t h c o m p o u n d s such as SmS u n d e r pressure, TmSe, and SmB& have r e c e n t l y b e e n the s u b j e c t s of c o n S i d e r a ble t h e o r e t i c a l and e x p e r i m e n t a l attention. 1 T h e s e m a t e r i a l s e x h i b i t large and p o o r l y - u n d e r s t o o d d e p a r t u r e s from the F e r m i - f l u i d b e h a v i o r z w h i c h characterizes IV compounds w i t h m e t a l l i c resistivities, In SmB6, for example, it is g e n e r a l l y a g r e e d t h a t a qap of 5 to 10 m e V d e s c r i b e s transport, 3 optical, 4-5 and t u n n e l i n g 5 properties. This gap has b e e n a s c r i b e d To 4 f ' c o n d u c t i o n b a n d h y b r i d i z a t i o n , v A n d e r s o n loca~ization, 7 and W i g n e r lattice formation; Q its p r e s e n c e m a k e s SmB 6 a s m a l l - g a p s e m i c o n ductor. Nuclear spin-lattice relaxation m e a s u r e m e n t s in m a g n e t i c systems y i e l d i n f o r m a t i o n on the s t r e n g t h and lowf r e q u e n c y f l u c t u a t i o n s p e c t r a of electronic spin excitations. ~ In m e t a l l i c IV s y s t e m s 4f spin f l u c t u a t i o n s are eff e c t i v e and s o m e t i m e s d o m i n a n t relaxation m e c h a n i s m s ; ~v this e f f e c t i v e n e s s w o u l d also be e x p e c t e d in the highlyr e s i s t i v e IV m a t e r i a l s . If r e l a x a t i o n is due to states at a gap edge, the rel a x a t i o n rate I/T 1 s h o u l d be activated: I/T 1 ~ e x p ( - E a / k B T ) , w h e r e E a is the ac . .v . a. t ~ o n energy. t~ We r e p o r t h e r e lIB N M R data obt a i n e d f r o m a h i g h l y resistive, h e n c e r e l a t i v e l y d e f e c t - f r e e SmB 6 specimen. C o m p a r i s o n of these and e a r l i e r N M R re539

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w i t h i n the above ranges: K i=-0.05 ± 0.01%, and e 2 q Q / h = 1 . 1 8 5 ± 0.010 MHz. The r e l a x a t i o n function AMz(t), w h i c h d e s c r i b e s the return of the l o n g i t u d i n a l n u c l e a r m a g n e t i z a t i o n to e q u i l i b r i u m following saturation, was o b s e r v e d for several SmB 6 samples as w e l l as for the isos t r u c t u r a l n o n m a g n e t i c c o m p o u n d LaB 6. In the ~ t t e r m e t a l l i c s y s t e m a v a i l a b l e data ~ are c o n s i s t e n t w i t h a K o r r i n g a law T I T ~ 103 s e c - K at 4.2, 77, and 300 K. The r e l a x a t i o n rates in SmB 6 are more than an o r d e r of m a g n i t u d e f a s t e r than in LaB 6 at all t e m p e r a t u r e s , so that the K o r r i n g a m e c h a n i s m appears to be n e g l i gible in SmB 6. B e l o w 15 K AMz(t) begins to exhibit a n o n e x D o n e n t i a l c h a r a c t e r which, b e c a u s e of its t e m p e r a t u r e dependence, is not likely to b e due to the quadr~o~ s p l i t t i n g of the lIB resonance ~ , ~ b u t r a t h e r to a spatial dist r i b u t i o n of r e l a x a t i o n rates in the sample due to defects. I 0 ' I I N e i t h e r the degree of n o n e x p o n e n t i a l i t y nor the long-time a s y m p t o t i c r e l a x a t i o n rate I/T 1 w e r e o b s e r v e d to be very d e p e n d e n t on R R R w i t h i n the range i n v e s t i g a t e d , a l t h o u g h some d e p e n d e n c e of I/T 1 on app lied m a g n e t i c field was seen in an imp e r f e c t s a m p l e (p = 1.4 x 103). Such field d e p e n d e n c e is a c h a r ~ t $ ~ i s t i c of d e f e c t - i n d u c e d relaxation. ~ ' ~ = The t e m p e r a t u r e , m a g n e t i c field, and sample d e p e n d e n c e of l/T] are s h o w n in Fig. i, w h e r e it can be ~een that, although data from the I o w - R R R s a m p l e are not a c c u r a t e at low t e m p e r a t u r e s , there is little s y s t e m a t i c d e p e n d e n c e of I/T 1 on RRR. The two s t r i k i n g features of these m e a s u r e m e n t s are the a c t i v a t e d beh a v i o r at high t e m p e r a t u r e s , and the anomaly at 5 K. The former c l e a r l y indicates that the Sm spin f l u c t u a t i o n s res p o n s i b l e for the r e l a x a t i o n are due to states at the edge of a gap in the excitation spectrum. The fact t h a t a p p r o x i m a t e l y the same gap e n e r g y c h a r a c t e r i z e s both 4f spin f l u c t u a t i o n s and the itinerant e l e c t r o n states r e s p o n s i b l e for transport properties 3 strongly supports a 4f-conduction band hybridization model for the o r i g i n of the gap. 6 It is hard to see how this result w o u l d o b t a i n for m o d e l s in w h i c h l o w - t e m p e r a t u r e conduction is p r e v e n t e d by defects. 7,8 The a n o m a l y in I/T 1 is m o s t c l e a r l y seen in the data for the p u r e s t s a m p l e (circles and d a s h e d curve of Fig. i). There is a s u g g e s t i o n of an a n o m a l y in the s p e c i f i c heat in this same t e m p e r a ture range. 8 Since most e x p l a n a t i o n s of the l o w - t e m p e r a t u r e t r a n s p o r t p r o p e r t i e s invoke r e s i d u a l disorder, ~-~ it is natural to compare our N M R results w i t h c o r r e s p o n d i n g data from the w e l l - c h a r a c t e r i z e d d i s o r d e r e d s e m i c o n d u c t o r Si:P. Here no I/T 1 anomaly was o b s e r v e d e i t h e r above or b e l o w the m e t a l - i n s u l a t o r trans i t i o n at ~3 x 1018 donors/cm3. 14 An i n c r e a s e in I/T 1 with d e c r e a s i n g t e m p e r a t u r e is o f t e n a s s o c i a t e d w i t h a d e c r e a s e in the rate of f l u c t u a t i o n s of

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FIG. i. Temperature dependence of the lib relaxation rate in SmB 6. Solid curve: hightemperature Arrhenlus law describing activated relaxation. Dashed curve: low-temperature anomaly, seen most clearly in the data for residual resistance ratio p = 1.9 × 104 . An upper bound on I/T 1 for LaB 6 at 77 K is also shown; at 4.2 K TI(LaB 6) ~ 250 sec. local fields at the nuclei. 9 If the f l u c t u a t i o n rate falls b e l o w the N M R p r e c e s s i o n frequency, the n u c l e a r relaxa t i o n rate passes t h r o u g h a m a x i m u m and d e v e l o p s a field d e p e n d e n c e at lower temperatures. This field d e p e n d e n c e is not o b s e r v e d in the p u r e s t s a m p l e (Fig. i), so that the m a x i m u m appears to b e due to a d e c r e a s e in f l u c t u a t i o n amplitude at low t e m p e r a t u r e s r a t h e r than an i n c r e a s e in f l u c t u a t i o n time. E v a l u a t i o n of m o d e l s for the anomaly is h a m p e r e d by lack of p r e c i s e d e f e c t c h a r a c t e r i z a t i o n in n e a r l y pure SmB=. One p i c t u r e 7 a t t r i b u t e s Sm 3~ f o r m a t i o n to the p r e s e n c e of n e i g h b o r i n g S m - s i t e vacancies. T h e s e or o t h e r p a r a m a g n e t S q centers m i g h t then r e l a x s u r r o u n d i n g ~ B nuclei, w i t h d i f f u s i o n of spin e n e r g y between nuclei 15 s m o o t h i n g out some of the i n h o m o g e n e i t y in T I. We have used spinecho decay m e a s u r e m e n t s to e s t i m a t e the s p i n T ~ i f f ~ s i o n c o n s t a n t D crudely at i0 -x" cm~/sec at 4.2 K. This y i e l d s a h o m o g e n e o u s T 1 only if the a v e r a g e distance b e t w e e n i m p u r i t i e s is less t h a n (DTI) I/2 % 2 0 ~ at 4.2 K, w h i c h corresponds to an i m p u r i t y c o n c e n t r a t i o n of the o r der of 10- J m o l e f r a c t i o n or greater. D e t e r m i n a t i o n of i m p u r i t y c o n c e n t r a t i o n s at this low level is difficult. Suscept i b i l i t y m e a s u r e m e n t s on our N M R samples have revealed low-temperature Curi@-Weiss "tails" which, if a t t r i b u t e d to S m 3+ spins as o u t l i n e d above, y i e l d i m p u r i t y c o n c e n t r a t i o n s of the o r d e r of 10 -~ m o l e fraction. This is larger than the c r u d e lower limit e s t a b l i s h e d above, so that

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defect-induced spins could cause the anomaly. The m a x i m u m in I/T 1 m i g h t b e e x p l a i n e d b y l o c a l s p i n o r d e r i n g d u e to i n t r a c l u s t e r e x c h a n g e , in w h i c h the t e m p e r a t u r e of t h e m a x i m u m w o u l d b e of the o r d e r of t h e e x c h a n g e c o n s t a n t a n d r o u g h l y i n d e p e n d e n t of c o n c e n t r a t i o n as observed. T h e i n s e n s i t i v i t y of t h e m a g n i t u d e of I/T 1 to c h a n g e s in R R R r e m a i n s puzzling. A n o t h e r c a n d i d a t e for t h e a n o m a l y ~ h i n d e r e d r o t a t i o n of b o r o n o c t a h e d r a . ° , ~ v E v e n t h o u g h t h e s e p h o n o n m o d e s , if f u l l y e x c i t e d , c o u l d g i v e t h e o b s e r v e d o r d e r of m a g n i t u d e of I/TI,9 s u c h r o t a t i o n w o u l d a l s o g i v e r i s e to t e m p e r a t u r e - d e p e n d e n t motional narrowing ~ the quadrupoles p l i t N M R s p e c t r u m . As T h i s is n o t observed. In a d d i t i o n t h e p h o n o n s p e c t r a of SmB 6 and LaB 6 s h o u l d b e s i m i l a r , 8 a n d t h e a n o m a l y is no t p r e s e n t in L.aB$ as n o t e d above. T h i s is n o t s u r p r ~ s l n g : t h e p h o n o n e n e r g i e s h a v e b e e n e s t i m a t e d 16 at %40 m e V >> k B T at 5 K.

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To c o n c l u d e , the a c t i v a t e d s p i n - l a t tice r e l a x a t i o n a b o v e 15 K in SmB 6 d e m o n s t r a t e s t h a t S m 4f s t a t e s are f o u n d at the e d g e of an e n e r g y gap, as is a l s o t r u e of c o n d u c t i o n s t a t e s w h i c h g o v e r n transport properties. This is a p o s i t i v e i n d i c a t i o n of the r o l e of h y b r i d i z a t i o n in t h e f o r m a t i o n of the gap. u The anomaly b e l o w 15 K is p r o b a b l y a s s o c i a t e d w i t h impurities which, however, have remarkab l y l i t t l e c o r r e l a t i o n w i t h the RRR. It is t e m p t i n g to s p e c u l a t e on the p o s s i b l e e x i s t e n c e of i n t r i n s i c r e l a x a t i o n m e c h a nisms, s u c ~ ^ a ~ o l o w - l y i n g n o n - h y b r i d i z i n g 4f s t a t e s , ± u , ± g a l t h o u g h w e k n o w of no t h e o r e t i c a l e x p e c t a t i o n or c o r r o b o r a t i n g e x p e r i m e n t a l e v i d e n c e for l o w - f r e q u e n c y f l u c t u a t i o n s a s s o c i a t e d w i t h such states. We are g r a t e f u l for d i s c u s s i o n s w i t h J. A a r t s , J. W. Allen, B. B a t l o g g , J. B. B o y c e , a n d T. K a s u y a . This r e s e a r c h was s p o n s o r e d in p a r t by the N a t i o n a l S c i e n c e F o u n d a t i o n u n d e r G r a n t s D M R - 7 8 1 0 3 0 1 and D M R - 7 6 2 1 1 7 8 , and by t h e U.C. R i v e r s i d e C o m m i t t e e on R e s e a r c h .

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See e.g. Proc. Int. Conf. on Valence Fluctuations in Solids, Santa Barbara, California, 1981 (to be published in Physica), and references therein.

2.

J. M. Lawrence, ibid.; also C. M. Varma, Revs. Mod. Phys. 48, 219 (1976).

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A. Menth, E. Buehler, and T. H. Geballe, Phys. Rev. Letters22, 295 (1969); J. C. Nickerson, R. M. White, K. N. Lee, R. Bachmann, T. H. Geballe, and G. W. Hull, Phys. Rev. B 3, 2030 (1971); J. W. Allen, B. Batlogg, and P. Wachter, Phys. Rev. B 20, 4807 (1979); T. Tanaka, R. Nishitani, C. Oshima, E. Bannai, and S. Kawai, J. Appl. Phys. 51, 3877 (1980).

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8.

T. Kasuya, K. Kojima, and Valence Instabilities and Band Phenomena, edited by (Plenum, New York, 1977),

M. Kasaya, in Related NarrowR. D. Parks p. 137.

T. Kasuya, K. Takegahara, T. Fujita, T. Tanaka and E. Bannai, J. Phys. (Paris) 40, C5-308 (1979).

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A. Abragam, Principles of Nuclear Magnetism (Clarendon, Oxford, 1961), chaps. 8 and 9.

i0. D. E. MacLaughlin, F. R. de Boer, J. Bijvoet, P. F. de Chatel, and W. C. M. Martens, J. Appl. Phys. 50, 2094 (1979); D. E. MacLaughlin, O. Pefla, and M. Lysak, Phys. Rev. B 23, 1039 (1981). II. O. Pe~a, D. E. MacLaughlin, M. Lysak and Z. Fisk, J. Appl. Phys. 52, 2152 (1981). 12. See also T. A. Kaplan and Mark Rubenstein, J. Appl. Phys. 52, 2168 (1981). 13. See e.g.A. Narath, Phys. Rev. 162, 320 (1967). 14. S. Kobayashi, Y. Fukagawa, S. Ikehata and W. Sasaki, J. Phys. Soc. Japan 45, 1276 (1978). 15. See e.g.P. Bernier and H. Alloul, J. Phys. F ~, 869 (1973). 16. G. Shell, H. Winter, and H. Superconductivity i_nnd__-and edited by H. Suhl and M. B. mic Press, New York, 1980),

Rietschel, in f-band Metals, Maple (Acadep. 465.

17. A. Abragam op. cit., chap. i0. 18. P. W. Anderson, in Ref. I.