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Deviations from the Curie-Weiss law in the magnetic susceptibility of dilute magnetic alloys
Volume 30A, number 9
PH Y S I C S L E T T E R S
29 December 1969
pected linear correlation between melting points and t h e e n e r g i e s of F - c e n t r e a b s o r p t i o n .
s e n t i n g RbC1 (715, 1.98), R b B r (682, 1.72) and K B r (723, 2.06), a s • U a s t h e t r i a n g l e s r e f e r r i n g to CsC1 (646, 2."~), C s B r (636, 1.83) and C s I (621, 1.58), a r e r o o m t e m p e r a t u r e v a l u e s . D a t a f o r t h e a l k a l i n e e a r t h f l u o r i d e s h a v e not b e e n i n c l u d e d in t h e f i g u r e f o r , a l t h o u g h the r e l e v a n t e n e r g i e s f o r C a F 2 (1360, 3.30), S r F 2 ( ? , 2.77) and B a F 2 (1280, 2.05) a r e known, n e i t h e r of t h e two v a l u e s g i v e n in t h e l i t e r a t u r e f o r t h e m e l t i n g p o i n t of S r F 2 (1190 and 1450oc) a p p e a r e d to b e a c c e p t a b l e in t h e l i g h t of the e x -
Reference s
1. T. Geszti, Phys. Letters 29A (1969) 425. 2. B.S. Gourary and F . J . Adrian, Phys. Rev. 105 (1957) 1180. 3. H. S. Bennett and A. B. Liddiard, Phys. Letters 18 (1965) 253. 4. P. Feltham, Phys. Stat. Sol. 20 (1967) 675. 5. R. Bessent and P. Feltham, Phys. Stat. Sol. 25 (1968) KI07.
DEVIATIONS FROM THE CURIE-WEISS LAW IN THE MAGNETIC SUSCEPTIBILITY OF DILUTE MAGNETIC ALLOYS
$
E. E. B A R T O N * and H. C L A U S University of Illinois, Urbana, Illinois 61801, USA
Received 29 November 1969
The magnetic susceptibility of dilute magnetic alloys of Mn in Rh and Fe in a Nb-Mo solid solution deviates from the Curie-Weiss law. The following temperature dependence is observed: A X = C / ( T +TK) + + ot log (TK/T), with (~ --- 0 for T > TKO.
In d i l u t e m a g n e t i c a l l o y s with K o n d o - t y p e b e h a v i o r , t h e C u r i e - W e i s s l a w , in the a b s e n c e of g e n e r a l t h e o r e t i c a l c a l c u l a t i o n s , is a c o n v e n i e n t interpolation formula for the magnetic susceptib i l i t y [1-4]. H o w e v e r , it i s known that t h e r e a r e systematic deviations from the Curie-Weiss l a w [4-6]. In t h i s l e t t e r we r e p o r t s u s c e p t i b i l i t y d a t a on two d i f f e r e n t d i l u t e a l l o y - s y s t e m s , R h - M n and ( M n 0 . T N b 0 . 3 ) - F e , w h e r e t h e s e d e v i a t i o n s c a n b e r e p r e s e n t e d in a s i m p l e a n a l y t i cal form. F i g . l a s h o w s t h e s y s t e m a t i c d e v i a t i o n s of t h e R h_h-Mn d a t a f r o m the c o m m o n l y u s e d C u r i e Weiss equation: X- Xs- ~
: C / ( T + T K)
(1)
w h e r e X i s t h e s u s c e p t i b i l i t y of the a l l o y , Xs that of t h e s o l v e n t . Xo a l l o w s f o r c h a n g e s in the t e m p e r a t u r e i n d e p e n d e n t s u s c e p t i b i l i t y . C is t h e C u r i e - c o n s t a n t (C = N p 2 / 3 k ) and T K i s a c h a r a c Supported by grants from the National Science Foundation and from the US Army R e s e a r c h Office. Durham, USA. * F o r m e r l y at the University of Illinois, now with the Union Carbide Company. Greenville, South Carolina, USA.
502
0.5
~.84%
Mn
.4~
J
Rh(1-x}Mnx
0.2 i
o ~r
;~O.1 <3
.22%Mn
i
b
0 I
I
I
t
Itlll
'
. . . . . .
J
I
I
I
IIIII
I
I
l
.
.
'
'
'
II
0051
.
.
.
.
.
LogT Fig. 1. Deviation of the experimental data from the Curie-Weiss law, AX-Xc.w" -= (X-Xs) ~ - [Xc~ C/(T ~TK) ] versus log T. The parameters of eq. (1) are determined by least squares analysis of the data in the temperature range T L < T < 300OK, where for part a, T L = 4OK, for p a r t b , T L - 20OK.
Volume 30A, number9
PHYSICS LETTERS
Table 1 Least squares fit parameters of eq. (1) and eq. (2) for the Rhl_xMnx and (Mo0.7Nb0.3)l_xFe x alloys: is the increase in the temperature independent susceptibility per mol of solute, p is the effective moment per solute atom in Bohr magneton.~ calculated from the Curie-constant, is a characteristic temperature (Kondo temperature), is the coefficient of the logarithmic term in eq. (2) per tool of solute.
Xo/X
C = Np2//3k. TK
x, at. fract.
104 Xo/X,
of solute
(emu/mol)
p,
Ol/x TK,
104
(x/x,
( ~ B ) (OK) (emu/mol)
Eq. (i) 0.0022 Mn
18
2.27
14.5
0.0045 Mn
17
2.23
14.6
0.0084 Mn
15
2.10
14.2
0.0071 Fe
14
1.25 1.3"
4.2 4*
0.0022 Mn
14
2.39
18.1
20
0.0045 Mn
12
2.40
20.1
28
0.0084 Mn
11
2.30
21.1
28
1.51
14.2
65
9.4
X-Xs-X°= C/(T+ TK)+{ (xl°g(TK/T)'O
, T> TK) (2)
Th e p a r a m e t e r s of eq. (2) a r e given in table 1. T h e M n - c o n c e n t r a t i o n of the Rh - Mn a l l o y s is known to an a c c u r a c y of only 5 to 10%. T h e r e f o r e , the p a r a m e t e r s in table 1 can be c o n s i d e r e d to be c o n c e n t r a t i o n independent. Since the two i n v e s t i g a t e d al l o y s y s t e m s a r e e l e c t r o n i c a l l y v e r y d i f f e r e n t , it is q u i t e p o s s i b l e that eq. (2) i s of g e n e r a l v a l i d i t y f o r dilute m a g n e t i c a l l o y s of 3d s o l u t e s in 4d and 5d t r a n s i t i o n m e t a l s . A s o m e w h a t s i m i l a r b e h a v i o r has been r e p o r t e d f o r dilute t e r n a r y a l l o y s of F e in Rh l _ x P d [5, 6], although the situation t h e r e is m o r e c o m p l i c a t e d b e c a u s e of p o l a r i z a t i o n e f f e c t s in the e x c h a n g e enhanced so l v en t s u s c e p t i b i l i t y . T h e r e a r e a l s o d e v i a t i o n s f r o m the C u r i e - W e i s s law in a l l o y s of 3d s o l u t e s in n o n - t r a n s i t i o n m e t a l s [4], but it i s not yet c l e a r w h e t h e r o r not t h e s e d e v i a t i o n s can be d e s c r i b e d by eq. (2).
x
Eq. (2)
0.0071 Fe
29 December 1969
* Ref. 7. t e r i s t i c t e m p e r a t u r e (Kondo t e m p e r a t u r e ) . The p a r a m e t e r s of eq. (1) w e r e d e t e r m i n e d by l e a s t s q u a r e s a n a l y s i s and they a r e shown in table 1. As can be s e e n in fig. l a , the d e v i a t i o n s of the data f r o m eq. (1) a r e significant. T h e s a m e is o b s e r v e d f o r the M__o0.7Nb0.3)-Fe a l lo y of ta b l e 1. If one u s e s only data above T > 20OK in d e t e r m i n i n g the p a r a m e t e r s of eq. (1) (table 1), no s y s t e m a t i c d ev i at i o n r e m a i n s in this t e m p e r a t u r e r a n g e (T > 20OK) but the data of l o w e r t e m p e r a t u r e s d e v i a t e l o g a r i t h m i c a l l y (fig. lb). Since f o r both alloy s y s t e m s this d e v ia ti o n is l i n e a r in l og T and s t a r t s j u s t below TK, the data can be r e p r e s e n t e d in the following way:
We would like to thank P r o f e s s o r P. A. B e c k f o r many s t i m u l a t i n g and helpful d i s c u s s i o n s and f o r his continuous i n t e r e s t in this work.
References 1. D.J. Scalapino, Phys. Rev. Letters 16 (1966) 937. 2. D.R. Hamann, Phys. Rev. Letters 17 (1966) 145. 3. H. Ishii and K. Yosida, Prog. Theoret. Phys. (Kyoto) 38 (1967) 61. 4. M. Daybell and W. A. Steyert, Rev. Mod. Phys. 40 (1968) 380. 5. H. Nagasawa, Phys. Letters 25A (1967) 475. 6. H. Nagasawa, J. Phys. Soc. Japan 25 (1968) 691. 7. A.M. Clogston, B. T. Matthias, M. Peter, H.J. Williams, E. Corenzwit and R. C. Sherwood, Phys. Rev. 125 (1962) 541.
503
PH Y S I C S L E T T E R S
29 December 1969
pected linear correlation between melting points and t h e e n e r g i e s of F - c e n t r e a b s o r p t i o n .
s e n t i n g RbC1 (715, 1.98), R b B r (682, 1.72) and K B r (723, 2.06), a s • U a s t h e t r i a n g l e s r e f e r r i n g to CsC1 (646, 2."~), C s B r (636, 1.83) and C s I (621, 1.58), a r e r o o m t e m p e r a t u r e v a l u e s . D a t a f o r t h e a l k a l i n e e a r t h f l u o r i d e s h a v e not b e e n i n c l u d e d in t h e f i g u r e f o r , a l t h o u g h the r e l e v a n t e n e r g i e s f o r C a F 2 (1360, 3.30), S r F 2 ( ? , 2.77) and B a F 2 (1280, 2.05) a r e known, n e i t h e r of t h e two v a l u e s g i v e n in t h e l i t e r a t u r e f o r t h e m e l t i n g p o i n t of S r F 2 (1190 and 1450oc) a p p e a r e d to b e a c c e p t a b l e in t h e l i g h t of the e x -
Reference s
1. T. Geszti, Phys. Letters 29A (1969) 425. 2. B.S. Gourary and F . J . Adrian, Phys. Rev. 105 (1957) 1180. 3. H. S. Bennett and A. B. Liddiard, Phys. Letters 18 (1965) 253. 4. P. Feltham, Phys. Stat. Sol. 20 (1967) 675. 5. R. Bessent and P. Feltham, Phys. Stat. Sol. 25 (1968) KI07.
DEVIATIONS FROM THE CURIE-WEISS LAW IN THE MAGNETIC SUSCEPTIBILITY OF DILUTE MAGNETIC ALLOYS
$
E. E. B A R T O N * and H. C L A U S University of Illinois, Urbana, Illinois 61801, USA
Received 29 November 1969
The magnetic susceptibility of dilute magnetic alloys of Mn in Rh and Fe in a Nb-Mo solid solution deviates from the Curie-Weiss law. The following temperature dependence is observed: A X = C / ( T +TK) + + ot log (TK/T), with (~ --- 0 for T > TKO.
In d i l u t e m a g n e t i c a l l o y s with K o n d o - t y p e b e h a v i o r , t h e C u r i e - W e i s s l a w , in the a b s e n c e of g e n e r a l t h e o r e t i c a l c a l c u l a t i o n s , is a c o n v e n i e n t interpolation formula for the magnetic susceptib i l i t y [1-4]. H o w e v e r , it i s known that t h e r e a r e systematic deviations from the Curie-Weiss l a w [4-6]. In t h i s l e t t e r we r e p o r t s u s c e p t i b i l i t y d a t a on two d i f f e r e n t d i l u t e a l l o y - s y s t e m s , R h - M n and ( M n 0 . T N b 0 . 3 ) - F e , w h e r e t h e s e d e v i a t i o n s c a n b e r e p r e s e n t e d in a s i m p l e a n a l y t i cal form. F i g . l a s h o w s t h e s y s t e m a t i c d e v i a t i o n s of t h e R h_h-Mn d a t a f r o m the c o m m o n l y u s e d C u r i e Weiss equation: X- Xs- ~
: C / ( T + T K)
(1)
w h e r e X i s t h e s u s c e p t i b i l i t y of the a l l o y , Xs that of t h e s o l v e n t . Xo a l l o w s f o r c h a n g e s in the t e m p e r a t u r e i n d e p e n d e n t s u s c e p t i b i l i t y . C is t h e C u r i e - c o n s t a n t (C = N p 2 / 3 k ) and T K i s a c h a r a c Supported by grants from the National Science Foundation and from the US Army R e s e a r c h Office. Durham, USA. * F o r m e r l y at the University of Illinois, now with the Union Carbide Company. Greenville, South Carolina, USA.
502
0.5
~.84%
Mn
.4~
J
Rh(1-x}Mnx
0.2 i
o ~r
;~O.1 <3
.22%Mn
i
b
0 I
I
I
t
Itlll
'
. . . . . .
J
I
I
I
IIIII
I
I
l
.
.
'
'
'
II
0051
.
.
.
.
.
LogT Fig. 1. Deviation of the experimental data from the Curie-Weiss law, AX-Xc.w" -= (X-Xs) ~ - [Xc~ C/(T ~TK) ] versus log T. The parameters of eq. (1) are determined by least squares analysis of the data in the temperature range T L < T < 300OK, where for part a, T L = 4OK, for p a r t b , T L - 20OK.
Volume 30A, number9
PHYSICS LETTERS
Table 1 Least squares fit parameters of eq. (1) and eq. (2) for the Rhl_xMnx and (Mo0.7Nb0.3)l_xFe x alloys: is the increase in the temperature independent susceptibility per mol of solute, p is the effective moment per solute atom in Bohr magneton.~ calculated from the Curie-constant, is a characteristic temperature (Kondo temperature), is the coefficient of the logarithmic term in eq. (2) per tool of solute.
Xo/X
C = Np2//3k. TK
x, at. fract.
104 Xo/X,
of solute
(emu/mol)
p,
Ol/x TK,
104
(x/x,
( ~ B ) (OK) (emu/mol)
Eq. (i) 0.0022 Mn
18
2.27
14.5
0.0045 Mn
17
2.23
14.6
0.0084 Mn
15
2.10
14.2
0.0071 Fe
14
1.25 1.3"
4.2 4*
0.0022 Mn
14
2.39
18.1
20
0.0045 Mn
12
2.40
20.1
28
0.0084 Mn
11
2.30
21.1
28
1.51
14.2
65
9.4
X-Xs-X°= C/(T+ TK)+{ (xl°g(TK/T)'O
, T> TK) (2)
Th e p a r a m e t e r s of eq. (2) a r e given in table 1. T h e M n - c o n c e n t r a t i o n of the Rh - Mn a l l o y s is known to an a c c u r a c y of only 5 to 10%. T h e r e f o r e , the p a r a m e t e r s in table 1 can be c o n s i d e r e d to be c o n c e n t r a t i o n independent. Since the two i n v e s t i g a t e d al l o y s y s t e m s a r e e l e c t r o n i c a l l y v e r y d i f f e r e n t , it is q u i t e p o s s i b l e that eq. (2) i s of g e n e r a l v a l i d i t y f o r dilute m a g n e t i c a l l o y s of 3d s o l u t e s in 4d and 5d t r a n s i t i o n m e t a l s . A s o m e w h a t s i m i l a r b e h a v i o r has been r e p o r t e d f o r dilute t e r n a r y a l l o y s of F e in Rh l _ x P d [5, 6], although the situation t h e r e is m o r e c o m p l i c a t e d b e c a u s e of p o l a r i z a t i o n e f f e c t s in the e x c h a n g e enhanced so l v en t s u s c e p t i b i l i t y . T h e r e a r e a l s o d e v i a t i o n s f r o m the C u r i e - W e i s s law in a l l o y s of 3d s o l u t e s in n o n - t r a n s i t i o n m e t a l s [4], but it i s not yet c l e a r w h e t h e r o r not t h e s e d e v i a t i o n s can be d e s c r i b e d by eq. (2).
x
Eq. (2)
0.0071 Fe
29 December 1969
* Ref. 7. t e r i s t i c t e m p e r a t u r e (Kondo t e m p e r a t u r e ) . The p a r a m e t e r s of eq. (1) w e r e d e t e r m i n e d by l e a s t s q u a r e s a n a l y s i s and they a r e shown in table 1. As can be s e e n in fig. l a , the d e v i a t i o n s of the data f r o m eq. (1) a r e significant. T h e s a m e is o b s e r v e d f o r the M__o0.7Nb0.3)-Fe a l lo y of ta b l e 1. If one u s e s only data above T > 20OK in d e t e r m i n i n g the p a r a m e t e r s of eq. (1) (table 1), no s y s t e m a t i c d ev i at i o n r e m a i n s in this t e m p e r a t u r e r a n g e (T > 20OK) but the data of l o w e r t e m p e r a t u r e s d e v i a t e l o g a r i t h m i c a l l y (fig. lb). Since f o r both alloy s y s t e m s this d e v ia ti o n is l i n e a r in l og T and s t a r t s j u s t below TK, the data can be r e p r e s e n t e d in the following way:
We would like to thank P r o f e s s o r P. A. B e c k f o r many s t i m u l a t i n g and helpful d i s c u s s i o n s and f o r his continuous i n t e r e s t in this work.
References 1. D.J. Scalapino, Phys. Rev. Letters 16 (1966) 937. 2. D.R. Hamann, Phys. Rev. Letters 17 (1966) 145. 3. H. Ishii and K. Yosida, Prog. Theoret. Phys. (Kyoto) 38 (1967) 61. 4. M. Daybell and W. A. Steyert, Rev. Mod. Phys. 40 (1968) 380. 5. H. Nagasawa, Phys. Letters 25A (1967) 475. 6. H. Nagasawa, J. Phys. Soc. Japan 25 (1968) 691. 7. A.M. Clogston, B. T. Matthias, M. Peter, H.J. Williams, E. Corenzwit and R. C. Sherwood, Phys. Rev. 125 (1962) 541.
503