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Magnetic susceptibility of dilute AuV alloys
Volume 34A, number 3
MAGNETIC
PHYSICS LETTERS
SUSCEPTIBILITY J. E. V A N D A M
OF
DILUTE
22 February 1971
Au-V
ALLOYS*
and P. C. M. G U B B E N S
Karnerlingh Onnes Laboratoriurn, Leiden, The Netherlands Received 1 January 1971
The low-temperature behaviour of the susceptibility of dilute Au-V alloys has been studied. It is shown that AX ~ 1 - A(T/TK)2 with a TK of about 250 K.
F r o m v a r i o u s e x p e r i m e n t s on Au-V a l l o y s one can conclude that this s y s t e m b e h a v e s like a Kondo alloy with 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 T K of about 300 K [1]. T h e r e f o r e it s e e m s to be a suitable s y s t e m to study the p r o p e r t i e s of a Kondo alloy at t e m p e r a t u r e s f a r below T K. Since the t h e o r e t i c a l p r e d i c t i o n s f o r the b e h a v i o u r f a r be l ow T K (e.g., T < 0.1 T K) give d i f f e r e n t r e -
sults, it is hoped that by careful measurements one can get an idea which theory is most probably correct. Recently it has been shown that experimental evidence on several Kondo systems supports theories which predict a simple power-law behaviour for T << T K [2]. Since this evidence is restricted to resistivity and specific-heat data it seemed worthwhile to study the magnetic susceptibility of A u - V alloys. Previous results for the susceptibility of Au-V alloys have been obtained, e.g., by K u m e [3] and Creveling and Luo [4]. Kume [3] a n a l y s e d his data by a fit of A× (A× = Xalloy - XDure ) to a C u r i e - W e i s s law and obtained ge'ff = 3.0 ~B and T K = 290 K, i d e n t i fying T K with an a p p a r e n t C u r i e - W e i s s t e m p e r a t u r e . H o w e v e r , l a r g e d e v i a t i o n s f r o m this fit o c c u r . C r e v e l i n g and Luo [4] have fitted t h e i r
results to the expression x ( T ) =X o + C/(T+O)
(1)
c o n s i d e r i n g Xo, C and O to be adjustable p a r a m e t e r s of the fit. The v a r i a t i o n of t h e s e p a r a m e t e r s with c o n c e n t r a t i o n could be explained by a mode l in which the m a g n e t i c " s t a t e " of the Va t o m s depends on t h e i r mutual d i s t a n c e . The p r e s e n t r e s u l t s on a n u m b e r of Au-V a l l o y s * This work is part of the research program of the "Stichting FOM" and has been supported by "ZWO" and "TNO".
(0.15, 0.30, 0.50, 1.0, 2.0, 10 at % V) w e r e obtained by the F a r a d a y method using an a u t o m a t i c e l e c t r o b a l a n c e (Cahn, type RG) in the t e m p e r a t u r e r a n g e f r o m 2-300 K [5]. The a l l o y s w e r e prepared from very pure starting materials (Au:6N+, V:4N). The data have b e e n a n a l y s e d in d i f f e r e n t ways. F i r s t l y a fit was made by c o m p u t e r to f o r m u l a (1). With the e x c e p t i o n of the two m o s t dilute a l l o y s it a p p e a r e d that the f i t s w e r e p o o r , with d e v i a t i o n s of 10%. When f i t s w e r e t r i e d in l i m i t e d t e m p e r a t u r e r a n g e s (e.g., f r o m 2-80 K or f r o m 100-300 K) e x c e l l e n t r e s u l t s could be obtained with d e v i a t i o n s l e s s than 1%, which is equal to the e x p e r i m e n t a l a c c u r a c y . H o w e v e r , the p a r a m e t e r s f o r e a c h t e m p e r a t u r e r an g e a r e v e r y diff e r e n t (for the s a m e alloy). This might indicate the p r e s e n c e of V - a t o m s in d i f f e r e n t m a g n e t i c " s t a t e s " , with d i f f e r e n t TK'S , as s u g g e s t e d in r e f . [6]. F o r the 0.15 at % alloy, in which i n t e r i m p u r i t y i n t e r a c t i o n s can be n e g l e c t e d , the fit to f o r m u l a (1) gave the following v a l u e s of the p a r a m e t e r s : O = 315 K, ~ = 3.6 ~ and Xo = - 28.5 x 10 -t~ e m u / m o l . This value of ~o is eq u al to our p u r e Au value. It should be noted that the e f f e c t i v e m o m e n t is a l m o s t equal to that of a V2+ ion (3.8/~B). Secondly, we have plotted AX v e r s u s T 2 (fig. 1). As can be s e e n in the f i g u r e the data can be r e p r e s e n t e d r e a s o n a b l y by AX ~ (1 - A T 2) up to about 60 K f o r the 0.15 at % alloy and to about 40 K f o r the 0.30 at % alloy. F r o m the slope of the plot in fig. 1 we have d e r i v e d a v al u e of T K of about 250 K f o r the 0.15 at % alloy, using the e x p r e s s i o n d e r i v e d by Klein [7] and T K ~ 200 K f o r the 0.30 at % alloy. The d e c r e a s e of T K with i n c r e a s i n g c o n c e n t r a t i o n might indicate a conc e n t r a t i o n effect as o b s e r v e d by Star and B o e r s t o e l in the r e s i s t i v i t y and the s p e c i f i c heat [8]. The v a l u e s of T K given above a r e in good a g r e e 185
PHYSICS
Volume 34A, number 3 [
i
r
p
i
LETTERS
Au V
15
°
0"15
at
%
0.30 at %
The a u t h o r s a c k n o w l e d g e s t i m u l a t i n g d i s c u s s i o n s with d r s . W. M. S t a r and thank C. W. M. D e s s e n s and M i s s M. F. P i k a r t f o r a s s i s t a n c e d u r i n g the m e a s u r e m e n t s .
'° I
~0
T2 ~ 1 0 0 0
2000
3000
40100
50100 K~2
Fig. 1. The susceptibility of two dilute Au-V alloys plotted versus T2. The susceptibility of pure Au has been subtracted. m e n t w i t h t h o s e d e r i v e d f r o m the s l o p e of the r e s i s t i v i t y (of the s a m e a l l o y s ) v e r s u s T 2 [9]. In v i e w of the r e c e n t s u s c e p t i b i l i t y d a t a on A1-Mn [10], a s y s t e m w h i c h r e s e m b l e s A u - V , we a p p l i e d a l s o f o r m u l a (5) of r e f . [11]. T h i s r e s u l t e d in a v a l u e of T K of about 300 K, which is s l i g h t l y h i g h e r t h a n the v a l u e in t a b l e 1 of r e f . [11]. F i n a l l y , we c h e c k e d the p o s s i b i l i t y of a T -1/2t e m p e r a t u r e d e p e n d e n c e r e c e n t l y s u g g e s t e d to be v a l i d f o r A u - V a l l o y s by E d e l s t e i n [12]. If t h i s w e r e t r u e TAX would be p r o p o r t i o n a l to T 1/2. H o w e v e r , t h i s is not the c a s e ; in f a c t , &X a p p r o a c h e s a c o n s t a n t v a l u e at T = 0. T a k i n g into a c c o u n t the e v i d e n c e p r e s e n t e d in r e f s . [2,9] we w o u l d l i k e to c o n c l u d e that the p o s s i b i l i t y of a * * * * *
186
1971
T 2 - d e p e n d e n c e of A× a d d s to a u n i f i e d p i c t u r e , w h i c h a p p e a r s to e m e r g e f o r Kondo a l l o y s . A d e t a i l e d a n a l y s i s and a d i s c u s s i o n of the c o n c e n t r a t i o n d e p e n d e n c e and the i n f l u e n c e of h e a t t r e a t m e n t w i l l be d i s c u s s e d in a f u t u r e p a p e r [5].
I
10-5¢mu/m°l
22 February
References [1] A. J. Heeger, Solid State Physics, Vol. 23 (1969) p. 283; J. E. van Dam and G. J. van den Berg, Phys. Slat. Sol. A3 (1970) 11. [2] W. M. Star, B. M. Boerstoel and C. van Baarle, J. Appl. Phys. 41 (1970) 1152. [3] K. Kume, J. Phys. Soc. Japan 23 (1967) 1226. [4] L. Creveling and H. L. Luo, Phys. Rev. 176 (1968) 614. [5] J. E. van Dam et al., to be published. [6] J. Souletie and R. Tournier, to be published. [7] A.P. Klein, Phys. Rev. 172 (1968) 520. [8] W. M. Star and B. M. Boerstoel, Phys. Letters 29A (1969) 26; B. M. Boerstoel and W. M. Star, Phys. Letters 29A (1969) 97. [9] W. M. Star, private communication. [10] F. T. Hedgcock and P. T. Li, Phys. Rev. B2 (1970) 1342. [11] B. Caroli, P. L e d e r e r and D. Saint-James, Phys. Rev. Letters 23 (1969) 700. [12] A. S. Edelstain, Solid State Commun. 8 (1970) 1849.
MAGNETIC
PHYSICS LETTERS
SUSCEPTIBILITY J. E. V A N D A M
OF
DILUTE
22 February 1971
Au-V
ALLOYS*
and P. C. M. G U B B E N S
Karnerlingh Onnes Laboratoriurn, Leiden, The Netherlands Received 1 January 1971
The low-temperature behaviour of the susceptibility of dilute Au-V alloys has been studied. It is shown that AX ~ 1 - A(T/TK)2 with a TK of about 250 K.
F r o m v a r i o u s e x p e r i m e n t s on Au-V a l l o y s one can conclude that this s y s t e m b e h a v e s like a Kondo alloy with 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 T K of about 300 K [1]. T h e r e f o r e it s e e m s to be a suitable s y s t e m to study the p r o p e r t i e s of a Kondo alloy at t e m p e r a t u r e s f a r below T K. Since the t h e o r e t i c a l p r e d i c t i o n s f o r the b e h a v i o u r f a r be l ow T K (e.g., T < 0.1 T K) give d i f f e r e n t r e -
sults, it is hoped that by careful measurements one can get an idea which theory is most probably correct. Recently it has been shown that experimental evidence on several Kondo systems supports theories which predict a simple power-law behaviour for T << T K [2]. Since this evidence is restricted to resistivity and specific-heat data it seemed worthwhile to study the magnetic susceptibility of A u - V alloys. Previous results for the susceptibility of Au-V alloys have been obtained, e.g., by K u m e [3] and Creveling and Luo [4]. Kume [3] a n a l y s e d his data by a fit of A× (A× = Xalloy - XDure ) to a C u r i e - W e i s s law and obtained ge'ff = 3.0 ~B and T K = 290 K, i d e n t i fying T K with an a p p a r e n t C u r i e - W e i s s t e m p e r a t u r e . H o w e v e r , l a r g e d e v i a t i o n s f r o m this fit o c c u r . C r e v e l i n g and Luo [4] have fitted t h e i r
results to the expression x ( T ) =X o + C/(T+O)
(1)
c o n s i d e r i n g Xo, C and O to be adjustable p a r a m e t e r s of the fit. The v a r i a t i o n of t h e s e p a r a m e t e r s with c o n c e n t r a t i o n could be explained by a mode l in which the m a g n e t i c " s t a t e " of the Va t o m s depends on t h e i r mutual d i s t a n c e . The p r e s e n t r e s u l t s on a n u m b e r of Au-V a l l o y s * This work is part of the research program of the "Stichting FOM" and has been supported by "ZWO" and "TNO".
(0.15, 0.30, 0.50, 1.0, 2.0, 10 at % V) w e r e obtained by the F a r a d a y method using an a u t o m a t i c e l e c t r o b a l a n c e (Cahn, type RG) in the t e m p e r a t u r e r a n g e f r o m 2-300 K [5]. The a l l o y s w e r e prepared from very pure starting materials (Au:6N+, V:4N). The data have b e e n a n a l y s e d in d i f f e r e n t ways. F i r s t l y a fit was made by c o m p u t e r to f o r m u l a (1). With the e x c e p t i o n of the two m o s t dilute a l l o y s it a p p e a r e d that the f i t s w e r e p o o r , with d e v i a t i o n s of 10%. When f i t s w e r e t r i e d in l i m i t e d t e m p e r a t u r e r a n g e s (e.g., f r o m 2-80 K or f r o m 100-300 K) e x c e l l e n t r e s u l t s could be obtained with d e v i a t i o n s l e s s than 1%, which is equal to the e x p e r i m e n t a l a c c u r a c y . H o w e v e r , the p a r a m e t e r s f o r e a c h t e m p e r a t u r e r an g e a r e v e r y diff e r e n t (for the s a m e alloy). This might indicate the p r e s e n c e of V - a t o m s in d i f f e r e n t m a g n e t i c " s t a t e s " , with d i f f e r e n t TK'S , as s u g g e s t e d in r e f . [6]. F o r the 0.15 at % alloy, in which i n t e r i m p u r i t y i n t e r a c t i o n s can be n e g l e c t e d , the fit to f o r m u l a (1) gave the following v a l u e s of the p a r a m e t e r s : O = 315 K, ~ = 3.6 ~ and Xo = - 28.5 x 10 -t~ e m u / m o l . This value of ~o is eq u al to our p u r e Au value. It should be noted that the e f f e c t i v e m o m e n t is a l m o s t equal to that of a V2+ ion (3.8/~B). Secondly, we have plotted AX v e r s u s T 2 (fig. 1). As can be s e e n in the f i g u r e the data can be r e p r e s e n t e d r e a s o n a b l y by AX ~ (1 - A T 2) up to about 60 K f o r the 0.15 at % alloy and to about 40 K f o r the 0.30 at % alloy. F r o m the slope of the plot in fig. 1 we have d e r i v e d a v al u e of T K of about 250 K f o r the 0.15 at % alloy, using the e x p r e s s i o n d e r i v e d by Klein [7] and T K ~ 200 K f o r the 0.30 at % alloy. The d e c r e a s e of T K with i n c r e a s i n g c o n c e n t r a t i o n might indicate a conc e n t r a t i o n effect as o b s e r v e d by Star and B o e r s t o e l in the r e s i s t i v i t y and the s p e c i f i c heat [8]. The v a l u e s of T K given above a r e in good a g r e e 185
PHYSICS
Volume 34A, number 3 [
i
r
p
i
LETTERS
Au V
15
°
0"15
at
%
0.30 at %
The a u t h o r s a c k n o w l e d g e s t i m u l a t i n g d i s c u s s i o n s with d r s . W. M. S t a r and thank C. W. M. D e s s e n s and M i s s M. F. P i k a r t f o r a s s i s t a n c e d u r i n g the m e a s u r e m e n t s .
'° I
~0
T2 ~ 1 0 0 0
2000
3000
40100
50100 K~2
Fig. 1. The susceptibility of two dilute Au-V alloys plotted versus T2. The susceptibility of pure Au has been subtracted. m e n t w i t h t h o s e d e r i v e d f r o m the s l o p e of the r e s i s t i v i t y (of the s a m e a l l o y s ) v e r s u s T 2 [9]. In v i e w of the r e c e n t s u s c e p t i b i l i t y d a t a on A1-Mn [10], a s y s t e m w h i c h r e s e m b l e s A u - V , we a p p l i e d a l s o f o r m u l a (5) of r e f . [11]. T h i s r e s u l t e d in a v a l u e of T K of about 300 K, which is s l i g h t l y h i g h e r t h a n the v a l u e in t a b l e 1 of r e f . [11]. F i n a l l y , we c h e c k e d the p o s s i b i l i t y of a T -1/2t e m p e r a t u r e d e p e n d e n c e r e c e n t l y s u g g e s t e d to be v a l i d f o r A u - V a l l o y s by E d e l s t e i n [12]. If t h i s w e r e t r u e TAX would be p r o p o r t i o n a l to T 1/2. H o w e v e r , t h i s is not the c a s e ; in f a c t , &X a p p r o a c h e s a c o n s t a n t v a l u e at T = 0. T a k i n g into a c c o u n t the e v i d e n c e p r e s e n t e d in r e f s . [2,9] we w o u l d l i k e to c o n c l u d e that the p o s s i b i l i t y of a * * * * *
186
1971
T 2 - d e p e n d e n c e of A× a d d s to a u n i f i e d p i c t u r e , w h i c h a p p e a r s to e m e r g e f o r Kondo a l l o y s . A d e t a i l e d a n a l y s i s and a d i s c u s s i o n of the c o n c e n t r a t i o n d e p e n d e n c e and the i n f l u e n c e of h e a t t r e a t m e n t w i l l be d i s c u s s e d in a f u t u r e p a p e r [5].
I
10-5¢mu/m°l
22 February
References [1] A. J. Heeger, Solid State Physics, Vol. 23 (1969) p. 283; J. E. van Dam and G. J. van den Berg, Phys. Slat. Sol. A3 (1970) 11. [2] W. M. Star, B. M. Boerstoel and C. van Baarle, J. Appl. Phys. 41 (1970) 1152. [3] K. Kume, J. Phys. Soc. Japan 23 (1967) 1226. [4] L. Creveling and H. L. Luo, Phys. Rev. 176 (1968) 614. [5] J. E. van Dam et al., to be published. [6] J. Souletie and R. Tournier, to be published. [7] A.P. Klein, Phys. Rev. 172 (1968) 520. [8] W. M. Star and B. M. Boerstoel, Phys. Letters 29A (1969) 26; B. M. Boerstoel and W. M. Star, Phys. Letters 29A (1969) 97. [9] W. M. Star, private communication. [10] F. T. Hedgcock and P. T. Li, Phys. Rev. B2 (1970) 1342. [11] B. Caroli, P. L e d e r e r and D. Saint-James, Phys. Rev. Letters 23 (1969) 700. [12] A. S. Edelstain, Solid State Commun. 8 (1970) 1849.