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Low-temperature heat capacity of Ni0.62Rh0.38
Volume 37A, number 5
LOW-TEMPERATURE
PHYSICS
HEAT
LETTERS
20 December 1971
CAPACITY
OF
Ni0.62 Rh0.38
B. B. T R I P L E T T and N. E. PHILLIPS Inorganic Materials Research Division, Lawrence Berkeley Laboratory, and Department of Chemistry, University of California, Berkeley, Calif. 94720, USA
Received 8 November 1971
The magnetic field dependence of the anomalous heat capacity of Ni0.62 Rh0.38 at low temperatures is consistent with superparamagnetic behavior of ferromagnetic clusters, but not with spin fluctuation effects. Heat c a p a c i t y a n o m a l i e s have been o b s e r v e d f o r a n u m b e r of t r a n s i t i o n m e t a l a l l o y s at c o n c e n t r a t i o n s n e a r the c r i t i c a l c o n c e n t r a t i o n f o r the a p p e a r a n c e of o r d e r e d m a g n e t i c m o m e n t s . T h e s e a n o m a l i e s have u s u a l l y b e e n i n t e r p r e t e d a s a r i s i n g f r o m the s p l i t t i n g of the e n e r g y l e v e l s of s u p e r p a r a m a g n e t i c c l u s t e r s [1,2] by an a n i s o t r o p y field. F o r the N i - R h s y s t e m the a n o m a l o u s heat c a p a city above 1 K h a s b e e n shown [3] to have a t e m p e r a t u r e d e p e n d e n c e c o n s i s t e n t with t h e o r e t i c a l p r e d i c t i o n s [4] for s p i n fluctuation effects. H o w e v e r , it has a l s o b e e n s u g g e s t e d [5] that the N i - R h d a t a a r e equally c o n s i s t e n t with the heat c a p a c i t y e x p e c t e d for s u p e r p a r a m a g n e t i c c l u s t e r s . The m e a s u r e m e n t s r e p o r t e d h e r e w e r e u n d e r t a k e n to obtain heat c a p a c i t y d a t a for a N i - R h s a m p l e at l o w e r t e m p e r a t u r e s , and to study the d e p e n d e n c e of the a n o m a l o u s heat c a p a c i t y on m a g n e t i c f i e l d s to 38 kOe. The field d e p e n d e n c e was e x p e c t e d to p r o v i d e an a d d i t i o n a l b a s i s for d i s t i n g u i s h i n g b e t w e e n s u p e r p a r a m a g n e t i s m and s p i n fluctuations. A f i e l d of 30 kOe should i n c r e a s e the s p l i t t i n g of the e n e r g y l e v e l s of a c l u s t e r to 4 K and r e d u c e the below - 1 K h e a t c a p a c i t y of c l u s t e r s c o n s i d e r a b l y , but should have only a s m a l l effect on the a n o m a l o u s heat c a p a c i t y if it is a s s o c i a t e d with s p i n fluctuations. A Ni 0 62Rh0 38 s a m p l e was p r e p a r e d a s d e s c r i b e d in ref. [3], including the 3 - d a y a n n e a l at l l 0 0 ° C . The h e a t c a p a c i t y was m e a s u r e d b e t w e e n 0.05 and 4 K in z e r o field and b e t w e e n 0.1 and 0.6 K in 3 kOe. The h e a t c a p a c i t y was l a t e r m e a s u r e d b e t w e e n 0.3 and 2 5 K in 0, 9, 18 and 38 kOe, but in the m e a n t i m e the s a m p l e had b e e n a n n e a l e d for an a d d i t i o n a l 30 d a y s at l l 0 0 ° C . T h e a n n e a l i n c r e a s e d the heat c a p a c i t y by b e * Work supported in part by the U.S. Atomic Energy Commission.
tween 1 and 3% in the 0.3 to 4 K region. Fig. 1 shows the r e s u l t s e x c e p t that the z e r o field d a t a t a k e n b e f o r e the 30 day a n n e a l a r e o m i t t e d above 0.6 K for c l a r i t y . It is evident that the a n o m a l o u s c o n t r i b u t i o n to t h e heat c a p a c i t y is s t r o n g l y dependent on m a g n e t i c field. It has b e e n shown that a field equivalent to the spin fluctuation t e m p e r a t u r e Ts should b e r e q u i r e d to s u p p r e s s the h e a t c a p a c i t y c o n t r i b u t i o n a s s o c i a t e d with spin f l u c t u a t i o n s [4]. F o r Ni0.63Rh0.37 , Ts ~ 250 K has b e e n e s t i m a t e d [3], and Ts should b e s i m i l a r for Ni 0 62Rh 0 38 s i n c e the heat c a p a c i t i e s a r e s i m i l a r ' . The ()~served field d e p e n d e n c e is t h e r e f o r e an o r d e r of m a g n i t u d e g r e a t e r than would b e e x p e c t e d on the spin fluctuation model. The b e h a v i o r shown in fig. 1 i s , h o w e v e r , c o n s i s t e n t with that e x p e c t e d for s u p e r p a r a r n a g n e t i c c l u s t e r s . (A s i m i l a r f i e l d d e p e n d e n c e has been o b s e r v e d in the F e - V s y s t e m and i n t e r p r e t e d on the b a s i s of c l u s t e r s [6] .) In z e r o f i e l d the heat c a p a c i t y of the c l u s t e r s is e x p e c t e d to b e a p 20 19
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F i g . 1. The heat capacity of N i 0 , 6 2 R h 0 . 3 8 . 443
Volume 37A, number 5
PHYSICS LETTERS
p r o x i m a t e l y constant o v e r a l i m i t e d r a n g e of t e m p e r a t u r e , and to drop exponentially to z e r o be l ow a c h a r a c t e r i s t i c t e m p e r a t u r e that is d e t e r m i n e d by the a n i s o t r o p y field [1,2]. In the p r e s ence of an e x t e r n a l field l a r g e r than the a n i s o t r o p y field the c h a r a c t e r i s t i c t e m p e r a t u r e would be d e t e r m i n e d by the e x t e r n a l field, and, if the f r e e - e l e c t r o n g y r o m a g n e t i c r a t i o is a s s u m e d for the c l u s t e r s , should be of the o r d e r of 5 K in 38 kOe. Below 10K, the 38 kOe data a r e a p p r o x i m a t e l y fitted by the e x p r e s s i o n C = 13.3 T + 0.067 T 3 m J / m o l e K ,
the t e m p e r a t u r e dependence expected for c l u s t e r s on the b a s i s of g e n e r a l q u a l i t a t i v e cons i d e r a t i o n s [1,2] - a r e g i o n of a p p r o x i m a t e i n d e p e n d e n c e of t e m p e r a t u r e , and a s h a r p drop at l o w e r t e m p e r a t u r e s . T h e r e is a l s o s o m e i n d i c a tion of the expected drop at h i g h e r t e m p e r a t u r e s but this is o b s c u r e d by the i n c r e a s i n g l a t t i c e heat capacity. We wish to thank Dr. E. B u c h e r f o r supplying the s a m p l e and s u g g e s t i n g the m e a s u r e m e n t s .
(1)
which s u g g e s t s that the a n o m a l o u s heat capacity has b e e n l a r g e l y shifted to h i g h e r t e m p e r a t u r e s . (The T 3 t e r m and the s m a l l p o s i t i v e d e v i a t i o n s f r o m eq. (1) n e a r 2 K p r o b a b l y include s o m e heat capacity of m a g n e t i c origin. ) We conclude that the field d e p e n d e n c e of the a n o m a l o u s heat c a p a c i t y is c o n s i s t e n t with the s u p e r p a r a m a g n e t i s m m o d e l and not with the spin fluctuation model. If it is a s s u m e d that eq. (1) is an a p p r o x i m a tion to the sum of the l a t t i c e and e l e c t r o n i c heat c a p a c i t i e s , the l o w - t e m p e r a t u r e l o w - f i e l d m a g ne ti c heat c a p a c i t y can be found by s u b t r a c t i n g eq. (1) f r o m the e x p e r i m e n t a l data. T h e m a g n e t i c heat c a p a c i t y c a l c u l a t e d in this way shows
444
20 December 1971
References [1] K. SchrSder and C.H.Cheng, J. Appl. Phys. 31 (1960) 2154; K. SchrSder, J. Appl. Phys. 32 (1961) 880. [2] J.D. Livingston and C. P. Bean, J. Appl. Phys. 32 (1961) 1964. [3] E.Bucher, W.F.Brinkman, J . P . M a i t a and H.J.Williams, Phys. Rev. Letters 18 (1967) 1125. [4] W. F. Brinkman and S. Engelsberg, Phys. Rev. 169 (1968) 417. [5] A. Hahn and E.P.Wohlfarth, Helv. Phys. Acta 41 (1968) 857. [6] W. Proctor and R.G. Scurlock, Proc. Eleventh Intern. Conf. on Low temperature physics, St. Andrews, 1968, eds. J . F . A l l e n , D.M. Finlayson and D. M. McCall (University of St. Andrews Printing Department, 1968) p. 1320.
LOW-TEMPERATURE
PHYSICS
HEAT
LETTERS
20 December 1971
CAPACITY
OF
Ni0.62 Rh0.38
B. B. T R I P L E T T and N. E. PHILLIPS Inorganic Materials Research Division, Lawrence Berkeley Laboratory, and Department of Chemistry, University of California, Berkeley, Calif. 94720, USA
Received 8 November 1971
The magnetic field dependence of the anomalous heat capacity of Ni0.62 Rh0.38 at low temperatures is consistent with superparamagnetic behavior of ferromagnetic clusters, but not with spin fluctuation effects. Heat c a p a c i t y a n o m a l i e s have been o b s e r v e d f o r a n u m b e r of t r a n s i t i o n m e t a l a l l o y s at c o n c e n t r a t i o n s n e a r the c r i t i c a l c o n c e n t r a t i o n f o r the a p p e a r a n c e of o r d e r e d m a g n e t i c m o m e n t s . T h e s e a n o m a l i e s have u s u a l l y b e e n i n t e r p r e t e d a s a r i s i n g f r o m the s p l i t t i n g of the e n e r g y l e v e l s of s u p e r p a r a m a g n e t i c c l u s t e r s [1,2] by an a n i s o t r o p y field. F o r the N i - R h s y s t e m the a n o m a l o u s heat c a p a city above 1 K h a s b e e n shown [3] to have a t e m p e r a t u r e d e p e n d e n c e c o n s i s t e n t with t h e o r e t i c a l p r e d i c t i o n s [4] for s p i n fluctuation effects. H o w e v e r , it has a l s o b e e n s u g g e s t e d [5] that the N i - R h d a t a a r e equally c o n s i s t e n t with the heat c a p a c i t y e x p e c t e d for s u p e r p a r a m a g n e t i c c l u s t e r s . The m e a s u r e m e n t s r e p o r t e d h e r e w e r e u n d e r t a k e n to obtain heat c a p a c i t y d a t a for a N i - R h s a m p l e at l o w e r t e m p e r a t u r e s , and to study the d e p e n d e n c e of the a n o m a l o u s heat c a p a c i t y on m a g n e t i c f i e l d s to 38 kOe. The field d e p e n d e n c e was e x p e c t e d to p r o v i d e an a d d i t i o n a l b a s i s for d i s t i n g u i s h i n g b e t w e e n s u p e r p a r a m a g n e t i s m and s p i n fluctuations. A f i e l d of 30 kOe should i n c r e a s e the s p l i t t i n g of the e n e r g y l e v e l s of a c l u s t e r to 4 K and r e d u c e the below - 1 K h e a t c a p a c i t y of c l u s t e r s c o n s i d e r a b l y , but should have only a s m a l l effect on the a n o m a l o u s heat c a p a c i t y if it is a s s o c i a t e d with s p i n fluctuations. A Ni 0 62Rh0 38 s a m p l e was p r e p a r e d a s d e s c r i b e d in ref. [3], including the 3 - d a y a n n e a l at l l 0 0 ° C . The h e a t c a p a c i t y was m e a s u r e d b e t w e e n 0.05 and 4 K in z e r o field and b e t w e e n 0.1 and 0.6 K in 3 kOe. The h e a t c a p a c i t y was l a t e r m e a s u r e d b e t w e e n 0.3 and 2 5 K in 0, 9, 18 and 38 kOe, but in the m e a n t i m e the s a m p l e had b e e n a n n e a l e d for an a d d i t i o n a l 30 d a y s at l l 0 0 ° C . T h e a n n e a l i n c r e a s e d the heat c a p a c i t y by b e * Work supported in part by the U.S. Atomic Energy Commission.
tween 1 and 3% in the 0.3 to 4 K region. Fig. 1 shows the r e s u l t s e x c e p t that the z e r o field d a t a t a k e n b e f o r e the 30 day a n n e a l a r e o m i t t e d above 0.6 K for c l a r i t y . It is evident that the a n o m a l o u s c o n t r i b u t i o n to t h e heat c a p a c i t y is s t r o n g l y dependent on m a g n e t i c field. It has b e e n shown that a field equivalent to the spin fluctuation t e m p e r a t u r e Ts should b e r e q u i r e d to s u p p r e s s the h e a t c a p a c i t y c o n t r i b u t i o n a s s o c i a t e d with spin f l u c t u a t i o n s [4]. F o r Ni0.63Rh0.37 , Ts ~ 250 K has b e e n e s t i m a t e d [3], and Ts should b e s i m i l a r for Ni 0 62Rh 0 38 s i n c e the heat c a p a c i t i e s a r e s i m i l a r ' . The ()~served field d e p e n d e n c e is t h e r e f o r e an o r d e r of m a g n i t u d e g r e a t e r than would b e e x p e c t e d on the spin fluctuation model. The b e h a v i o r shown in fig. 1 i s , h o w e v e r , c o n s i s t e n t with that e x p e c t e d for s u p e r p a r a r n a g n e t i c c l u s t e r s . (A s i m i l a r f i e l d d e p e n d e n c e has been o b s e r v e d in the F e - V s y s t e m and i n t e r p r e t e d on the b a s i s of c l u s t e r s [6] .) In z e r o f i e l d the heat c a p a c i t y of the c l u s t e r s is e x p e c t e d to b e a p 20 19
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F i g . 1. The heat capacity of N i 0 , 6 2 R h 0 . 3 8 . 443
Volume 37A, number 5
PHYSICS LETTERS
p r o x i m a t e l y constant o v e r a l i m i t e d r a n g e of t e m p e r a t u r e , and to drop exponentially to z e r o be l ow a c h a r a c t e r i s t i c t e m p e r a t u r e that is d e t e r m i n e d by the a n i s o t r o p y field [1,2]. In the p r e s ence of an e x t e r n a l field l a r g e r than the a n i s o t r o p y field the c h a r a c t e r i s t i c t e m p e r a t u r e would be d e t e r m i n e d by the e x t e r n a l field, and, if the f r e e - e l e c t r o n g y r o m a g n e t i c r a t i o is a s s u m e d for the c l u s t e r s , should be of the o r d e r of 5 K in 38 kOe. Below 10K, the 38 kOe data a r e a p p r o x i m a t e l y fitted by the e x p r e s s i o n C = 13.3 T + 0.067 T 3 m J / m o l e K ,
the t e m p e r a t u r e dependence expected for c l u s t e r s on the b a s i s of g e n e r a l q u a l i t a t i v e cons i d e r a t i o n s [1,2] - a r e g i o n of a p p r o x i m a t e i n d e p e n d e n c e of t e m p e r a t u r e , and a s h a r p drop at l o w e r t e m p e r a t u r e s . T h e r e is a l s o s o m e i n d i c a tion of the expected drop at h i g h e r t e m p e r a t u r e s but this is o b s c u r e d by the i n c r e a s i n g l a t t i c e heat capacity. We wish to thank Dr. E. B u c h e r f o r supplying the s a m p l e and s u g g e s t i n g the m e a s u r e m e n t s .
(1)
which s u g g e s t s that the a n o m a l o u s heat capacity has b e e n l a r g e l y shifted to h i g h e r t e m p e r a t u r e s . (The T 3 t e r m and the s m a l l p o s i t i v e d e v i a t i o n s f r o m eq. (1) n e a r 2 K p r o b a b l y include s o m e heat capacity of m a g n e t i c origin. ) We conclude that the field d e p e n d e n c e of the a n o m a l o u s heat c a p a c i t y is c o n s i s t e n t with the s u p e r p a r a m a g n e t i s m m o d e l and not with the spin fluctuation model. If it is a s s u m e d that eq. (1) is an a p p r o x i m a tion to the sum of the l a t t i c e and e l e c t r o n i c heat c a p a c i t i e s , the l o w - t e m p e r a t u r e l o w - f i e l d m a g ne ti c heat c a p a c i t y can be found by s u b t r a c t i n g eq. (1) f r o m the e x p e r i m e n t a l data. T h e m a g n e t i c heat c a p a c i t y c a l c u l a t e d in this way shows
444
20 December 1971
References [1] K. SchrSder and C.H.Cheng, J. Appl. Phys. 31 (1960) 2154; K. SchrSder, J. Appl. Phys. 32 (1961) 880. [2] J.D. Livingston and C. P. Bean, J. Appl. Phys. 32 (1961) 1964. [3] E.Bucher, W.F.Brinkman, J . P . M a i t a and H.J.Williams, Phys. Rev. Letters 18 (1967) 1125. [4] W. F. Brinkman and S. Engelsberg, Phys. Rev. 169 (1968) 417. [5] A. Hahn and E.P.Wohlfarth, Helv. Phys. Acta 41 (1968) 857. [6] W. Proctor and R.G. Scurlock, Proc. Eleventh Intern. Conf. on Low temperature physics, St. Andrews, 1968, eds. J . F . A l l e n , D.M. Finlayson and D. M. McCall (University of St. Andrews Printing Department, 1968) p. 1320.