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The transition temperature of superconductors with paramagnetic impurities
Volume 21, n u m b e r 4
PHYSICS
LETTERS
w h e r e a s f o r 0 = 0 °, e s s e n t i a l l y a l l of t h e " s u r f a c e " i s p a r a l l e l . It i s t h e r e f o r e r e a s o n a b l e t h a t t h e q u a l i t a t i v e f e a t u r e s of t h e Ho(O) c u r v e s r e s e m b l e t h e c u r v e p r e d i c t e d by T i n k h a m f o r flat plates. H u r a u l t [10] h a s r e c e n t l y p r e d i c t e d t h a t " s u r face" superconductivity having a critical field HIv i n t h e r a n g e H c 2 < Hit < 1.69 H c 2 c a n n u c l e a t e at the interface between a superconductor and a n o r m a l m e t a l , p r o v i d e d t h e c o n d u c t i v i t y of t h e normal metal is less than the normal state cond u c t i v i t y of t h e s u p e r c o n d u c t o r . S u c h c o n d i t i o n s m a y e x i s t a t t h e g r a i n b o u n d a r i e s of t h e w i r e specimens reported here. The additional volume of s u c h s u p e r c o n d u c t i v i t y w o u l d h e l p t o a c c o u n t for the large transport currents which can be passed through these materials with H >Hc2 a n d 0 = 0 °, a n d w o u l d e x p l a i n s e v e r a l o t h e r effects which previously have been attributed [ e . g . 7] t o p o s s i b l e " f i l a m e n t a r y " s u p e r c o n d u c t i v i t y e x i s t i n g in t h e g r a i n b o u n d a r i e s . W e a r e g r a t e f u l to D r . D. F a i r b a n k s of t h e N a t i o n a l R e s e a r c h C o r p o r a t i o n a n d P r o f . R. R o s e
1 J u n e 1966
of t h e D e p a r t m e n t of M e t a l l u r g y a t M I T f o r p r o v i d i n g s a m p l e s . W e a l s o w i s h t o t h a n k L. N e u r i n g e r , B. S c h w a r t z , a n d Y. S h a p i r a f o r m a n y informative discussions.
References 1. P . S . S w a r t z and H . R . H a r t J r . , Phys. Rev. ]37 (1965) A818. 2. P . R . A r o n a n d H.C.Hitehcock, J.Appl. Phys. 33 (1962) 2242. 3. S . T . S e k u l a , R.W. Boom and C . J . B e r g e r o n , Appl. Phys. L e t t e r s 2 (1963) 102. 4. W . F . D r u y v e s t e y n and J . V o l g e r , Conf. on Phys. of type II superconductors, Cleveland, Ohiio, 1964. 5. D.Saint J a m e s and P . G . deGennes, Phys. L e t t e r s 7 (1964) 3O6. 6. L . J . N e u r i n g e r a n d Y . S h a p i r a , Phys. R e v . , to be published. 7. M . T a n e n b a u m and W.V. Wright, Superconductors. (Interscience, New York, 1962). 8. H.B.Shokovsky, K . M . R a l l s and R . M . R o s e , T r a n s . Metal. Soc. of AIME 233 (1965). 9. M.Tinkham, Phys. L e t t e r s 9 (1964)217; Phys. Rev. 129 (1963) 2413. 10. J . P . H u r a u l t , to be published.
* * * * *
THE
TRANSITION
TEMPERATURE PARAMAGNETIC
OF SUPERCONDUCTORS IMPURITIES*
WITH
J . E. C R O W a n d R . D . P A R K S * *
Department of Physics and Astronomy, University of Rochester Rochester, New York Received 30 April 1966
The dependence of the superconducting t r a n s i t i o n t e m p e r a t u r e on the concentration of Gd spins is r e p o r t e d for the La3_ x Gdx In s y s t e m . The r e s u l t s a r e c o m p a r e d with the predictions of the theory of Abrikosov and Gorkov and other e x p e r i m e n t a l attempts to verify the theory.
An i m p o r t a n t p r e d i c t i o n of t h e t h e o r y of A b r i k o s o v a n d G o r k o v of g a p l e s s s u p e r c o n d u c t i v i t y [1] i s t h e d e t a i l e d s h a p e of t h e T c v e r s u s n c u r v e of a s u p e r c o n d u c t o r c o n t a i n i n g p a r a m a g n e t i c i m p u r i t i e s ( s h o w n in fig. 1), w h e r e T c i s the superconducting transition temperature and n i s t h e c o n c e n t r a t i o n of p a r a m a g n e t i c i m p u r i t i e s . T h e e q u a t i o n of t h e c u r v e i s * Supported by the National Science Foundation. ** Alfred P.Sloan R e s e a r c h Fellow. 378
in T c / T c p = ~(½) - t~(½ + O . 1 4 0 n T c p / n c r T c )
(1)
w h e r e Tcp i s t h e t r a n s i t i o n t e m p e r a t u r e of t h e p u r e m a t e r i a l (n = 0), ~ i s t h e d i g a m m a f u n c t i o n a n d n c r i s t h e c o n c e n t r a t i o n of p a r a m a g n e t i c i m p u r i t i e s r e q u i r e d to d e p r e s s T c to z e r o . The most extensive experimental studies conc e r n i n g t h i s q u e s t i o n w e r e m a d e by M a t t h i a s e t a l . [2] a n d H e i n et a l . [3] w h o e x a m i n e d t h e d e p e n d e n c e of t h e s u p e r c o n d u c t i n g t r a n s i t i o n t e m p e r a t u r e of l a n t h a n u m on s m a l l a m o u n t s of
Volume 21, number4
PHYSICS L E T T E R S
1.0! V
.5
.2
o
.Z
.4
.6
.s
Lo
Lz
1.4
Fig. 1. T e / T o p versus n/her curves for the La3_xGc~In
and Lal_xGdx systems. The inset in the upper corner of the figure is a magnified display of the La3_xGctx In data in the vinicity of n/ncr = 0.85. dissolved gadolinium. R e a s o n a b l e a g r e e m e n t with the theory of Abrikosov and Gorkov was obtained in the l i m i t , n / n c r 4 0 , where the a s y m p totic f o r m of eq. (1) i s l i n e a r ; however, data for the m o r e c o n c e n t r a t e d a l l o y s departed from this theory and r e v e a l e d a n o m a l o u s behavior for c o n c e n t r a t i o n s in the vicinity of n c r (see fig. 1). One of the difficulties which may have plagued much of the work on the lanthanum s y s t e m i s the fact that l a n t h a n u m , when p r e p a r e d in c o n v e n tional ways, contains both fcc and hcp c r y s t a l p h a s e s at low t e m p e r a t u r e s [e.g. 4]. In o r d e r to escape this p r o b l e m and at the same time study the behavior of a new s y s t e m , we have m e a s u r e d the dependence of T c on the c o n c e n t r a t i o n of Gd ions (x) in La3_ x Gdxin , an i n t e r m e t a l l i c compound with the L12, Cu 3 Au type, cubic c r y s t a l s t r u c t u r e [5]. The s a m p l e s were p r e p a r e d by m e l t i n g the c o n s t i t u e n t s in a conventional a r c f u r n a c e . The b u t t o n - s h a p e d ingots w e r e t u r n e d over and r e m e l t e d many t i m e s to e n s u r e spatial homogeneity of the spin i m p u r i t y . X - r a y m e a s u r e m e n t s made at r o o m t e m p e r a t u r e s r e v e a l e d that the La3_ x GctxIn s a m p l e s were single phase. The lanthanum which was obtained from the Lunex Company contained l e s s than 0.05% r a r e e a r t h i m p u r i t i e s and l e s s than 0.01% t r a n s i t i o n m e t a l i m p u r i t i e s . The superconducting t r a n s i t i o n
1 June 1966
t e m p e r a t u r e of the r a p i d l y quenched, a r c m e l t e d La 3 In ingots was 9.0°K *. Annealing a La 3 In ingot (prepared in the a r c furnace) at 550oc for 36 h o u r s had no significant effect on the t r a n s i t i o n temperature. The T c v e r s u s n curve for the La3_ x GdxIn s y s t e m i s shown in fig. 1. We define Tc as the t e m p e r a t u r e at which the s a m p l e r e s i s t a n c e is one half its n o r m a l state value. The value of the c r i t i c a l c o n c e n t r a t i o n of spin i m p u r i t y , n c r which were used in plotting the data in fig. 1, were d e t e r m i n e d by n o r m a l i z i n g the e x p e r i m e n t a l data to the Abrikosov and Gorkov curve in the l i n e a r region (n ~ 0) and then calculating n c r from eq. (1). This gives for the La3_x GdxIn s y s t e m , n c r = 2.15 atomic p e r c e n t Gd, and for the L a l _ x Gd x s y s t e m , n c r = 0.82 atomic p e r c e n t Gd. The data for the La3_x Gdx In s y s t e m a r e in c o n s i d e r a b l y b e t t e r a g r e e m e n t with the theory Abrikosov and Gorkov than a r e the data for the L a l _ x Gd x s y s t e m . However, the La3_ x G d x I n s y s t e m exhibits a n o m a l o u s behavior at higher Gd c o n c e n t r a t i o n s which is qualitatively s i m i l a r to the a n o m a l o u s behavior of the La l_x Gdx sy stem. The f e a t u r e which is c o m m o n to both s y s t e m s i s the peaking of the T c v e r s u s n c u r v e at higher c o n c e n t r a t i o n s followed by a p l u m m e t i n g of T c towards zero with i n c r e a s i n g c o n c e n t r a t i o n . It is p o s s i b l e that this u n u s u a l behavior is an i n t r i n s i c p r o p e r t y of s u p e r c o n d u c t o r s with p a r a magnetic i m p u r i t i e s . Studies of other p a r a m a g netic, superconducting s y s t e m s may a n s w e r this question. It is a p l e a s u r e to thank W. B a s s e t t for his a s s i s t a n c e with X - r a y m e a s u r e m e n t s .
References 1. A.A.Abrikosov and L.P.Gorkov, Zh. Exp. i. Teor. Fiz. 39 (1960); Sov. Phys. JETP 12 (1961) 1243. 2. B.T.Matthias, H.Suhl and E.Corenzwit, Phys. Rev. Letters 1 (1958) 92. 3. R.A.Hein, R.L.Falge Jr.. B.T.Matthias and C. Corenzwit, Phys. Rev. Letters 2 (1959) 500. 4. D.K.Finnemore, D.L.Johnson, J.E.Ostenson, F.H.Spedding and B.J.Beaudry, Phys. Rev. 137 (1965) A550. 5. B.T. Matthias, V. B. Gompton and E. Corenzwit, J. Phys. Chem. Solids 19 (1961) 130. * This differs from the value, 10.4°K, reported in ref. 5.
* * * * *
379
PHYSICS
LETTERS
w h e r e a s f o r 0 = 0 °, e s s e n t i a l l y a l l of t h e " s u r f a c e " i s p a r a l l e l . It i s t h e r e f o r e r e a s o n a b l e t h a t t h e q u a l i t a t i v e f e a t u r e s of t h e Ho(O) c u r v e s r e s e m b l e t h e c u r v e p r e d i c t e d by T i n k h a m f o r flat plates. H u r a u l t [10] h a s r e c e n t l y p r e d i c t e d t h a t " s u r face" superconductivity having a critical field HIv i n t h e r a n g e H c 2 < Hit < 1.69 H c 2 c a n n u c l e a t e at the interface between a superconductor and a n o r m a l m e t a l , p r o v i d e d t h e c o n d u c t i v i t y of t h e normal metal is less than the normal state cond u c t i v i t y of t h e s u p e r c o n d u c t o r . S u c h c o n d i t i o n s m a y e x i s t a t t h e g r a i n b o u n d a r i e s of t h e w i r e specimens reported here. The additional volume of s u c h s u p e r c o n d u c t i v i t y w o u l d h e l p t o a c c o u n t for the large transport currents which can be passed through these materials with H >Hc2 a n d 0 = 0 °, a n d w o u l d e x p l a i n s e v e r a l o t h e r effects which previously have been attributed [ e . g . 7] t o p o s s i b l e " f i l a m e n t a r y " s u p e r c o n d u c t i v i t y e x i s t i n g in t h e g r a i n b o u n d a r i e s . W e a r e g r a t e f u l to D r . D. F a i r b a n k s of t h e N a t i o n a l R e s e a r c h C o r p o r a t i o n a n d P r o f . R. R o s e
1 J u n e 1966
of t h e D e p a r t m e n t of M e t a l l u r g y a t M I T f o r p r o v i d i n g s a m p l e s . W e a l s o w i s h t o t h a n k L. N e u r i n g e r , B. S c h w a r t z , a n d Y. S h a p i r a f o r m a n y informative discussions.
References 1. P . S . S w a r t z and H . R . H a r t J r . , Phys. Rev. ]37 (1965) A818. 2. P . R . A r o n a n d H.C.Hitehcock, J.Appl. Phys. 33 (1962) 2242. 3. S . T . S e k u l a , R.W. Boom and C . J . B e r g e r o n , Appl. Phys. L e t t e r s 2 (1963) 102. 4. W . F . D r u y v e s t e y n and J . V o l g e r , Conf. on Phys. of type II superconductors, Cleveland, Ohiio, 1964. 5. D.Saint J a m e s and P . G . deGennes, Phys. L e t t e r s 7 (1964) 3O6. 6. L . J . N e u r i n g e r a n d Y . S h a p i r a , Phys. R e v . , to be published. 7. M . T a n e n b a u m and W.V. Wright, Superconductors. (Interscience, New York, 1962). 8. H.B.Shokovsky, K . M . R a l l s and R . M . R o s e , T r a n s . Metal. Soc. of AIME 233 (1965). 9. M.Tinkham, Phys. L e t t e r s 9 (1964)217; Phys. Rev. 129 (1963) 2413. 10. J . P . H u r a u l t , to be published.
* * * * *
THE
TRANSITION
TEMPERATURE PARAMAGNETIC
OF SUPERCONDUCTORS IMPURITIES*
WITH
J . E. C R O W a n d R . D . P A R K S * *
Department of Physics and Astronomy, University of Rochester Rochester, New York Received 30 April 1966
The dependence of the superconducting t r a n s i t i o n t e m p e r a t u r e on the concentration of Gd spins is r e p o r t e d for the La3_ x Gdx In s y s t e m . The r e s u l t s a r e c o m p a r e d with the predictions of the theory of Abrikosov and Gorkov and other e x p e r i m e n t a l attempts to verify the theory.
An i m p o r t a n t p r e d i c t i o n of t h e t h e o r y of A b r i k o s o v a n d G o r k o v of g a p l e s s s u p e r c o n d u c t i v i t y [1] i s t h e d e t a i l e d s h a p e of t h e T c v e r s u s n c u r v e of a s u p e r c o n d u c t o r c o n t a i n i n g p a r a m a g n e t i c i m p u r i t i e s ( s h o w n in fig. 1), w h e r e T c i s the superconducting transition temperature and n i s t h e c o n c e n t r a t i o n of p a r a m a g n e t i c i m p u r i t i e s . T h e e q u a t i o n of t h e c u r v e i s * Supported by the National Science Foundation. ** Alfred P.Sloan R e s e a r c h Fellow. 378
in T c / T c p = ~(½) - t~(½ + O . 1 4 0 n T c p / n c r T c )
(1)
w h e r e Tcp i s t h e t r a n s i t i o n t e m p e r a t u r e of t h e p u r e m a t e r i a l (n = 0), ~ i s t h e d i g a m m a f u n c t i o n a n d n c r i s t h e c o n c e n t r a t i o n of p a r a m a g n e t i c i m p u r i t i e s r e q u i r e d to d e p r e s s T c to z e r o . The most extensive experimental studies conc e r n i n g t h i s q u e s t i o n w e r e m a d e by M a t t h i a s e t a l . [2] a n d H e i n et a l . [3] w h o e x a m i n e d t h e d e p e n d e n c e of t h e s u p e r c o n d u c t i n g t r a n s i t i o n t e m p e r a t u r e of l a n t h a n u m on s m a l l a m o u n t s of
Volume 21, number4
PHYSICS L E T T E R S
1.0! V
.5
.2
o
.Z
.4
.6
.s
Lo
Lz
1.4
Fig. 1. T e / T o p versus n/her curves for the La3_xGc~In
and Lal_xGdx systems. The inset in the upper corner of the figure is a magnified display of the La3_xGctx In data in the vinicity of n/ncr = 0.85. dissolved gadolinium. R e a s o n a b l e a g r e e m e n t with the theory of Abrikosov and Gorkov was obtained in the l i m i t , n / n c r 4 0 , where the a s y m p totic f o r m of eq. (1) i s l i n e a r ; however, data for the m o r e c o n c e n t r a t e d a l l o y s departed from this theory and r e v e a l e d a n o m a l o u s behavior for c o n c e n t r a t i o n s in the vicinity of n c r (see fig. 1). One of the difficulties which may have plagued much of the work on the lanthanum s y s t e m i s the fact that l a n t h a n u m , when p r e p a r e d in c o n v e n tional ways, contains both fcc and hcp c r y s t a l p h a s e s at low t e m p e r a t u r e s [e.g. 4]. In o r d e r to escape this p r o b l e m and at the same time study the behavior of a new s y s t e m , we have m e a s u r e d the dependence of T c on the c o n c e n t r a t i o n of Gd ions (x) in La3_ x Gdxin , an i n t e r m e t a l l i c compound with the L12, Cu 3 Au type, cubic c r y s t a l s t r u c t u r e [5]. The s a m p l e s were p r e p a r e d by m e l t i n g the c o n s t i t u e n t s in a conventional a r c f u r n a c e . The b u t t o n - s h a p e d ingots w e r e t u r n e d over and r e m e l t e d many t i m e s to e n s u r e spatial homogeneity of the spin i m p u r i t y . X - r a y m e a s u r e m e n t s made at r o o m t e m p e r a t u r e s r e v e a l e d that the La3_ x GctxIn s a m p l e s were single phase. The lanthanum which was obtained from the Lunex Company contained l e s s than 0.05% r a r e e a r t h i m p u r i t i e s and l e s s than 0.01% t r a n s i t i o n m e t a l i m p u r i t i e s . The superconducting t r a n s i t i o n
1 June 1966
t e m p e r a t u r e of the r a p i d l y quenched, a r c m e l t e d La 3 In ingots was 9.0°K *. Annealing a La 3 In ingot (prepared in the a r c furnace) at 550oc for 36 h o u r s had no significant effect on the t r a n s i t i o n temperature. The T c v e r s u s n curve for the La3_ x GdxIn s y s t e m i s shown in fig. 1. We define Tc as the t e m p e r a t u r e at which the s a m p l e r e s i s t a n c e is one half its n o r m a l state value. The value of the c r i t i c a l c o n c e n t r a t i o n of spin i m p u r i t y , n c r which were used in plotting the data in fig. 1, were d e t e r m i n e d by n o r m a l i z i n g the e x p e r i m e n t a l data to the Abrikosov and Gorkov curve in the l i n e a r region (n ~ 0) and then calculating n c r from eq. (1). This gives for the La3_x GdxIn s y s t e m , n c r = 2.15 atomic p e r c e n t Gd, and for the L a l _ x Gd x s y s t e m , n c r = 0.82 atomic p e r c e n t Gd. The data for the La3_x Gdx In s y s t e m a r e in c o n s i d e r a b l y b e t t e r a g r e e m e n t with the theory Abrikosov and Gorkov than a r e the data for the L a l _ x Gd x s y s t e m . However, the La3_ x G d x I n s y s t e m exhibits a n o m a l o u s behavior at higher Gd c o n c e n t r a t i o n s which is qualitatively s i m i l a r to the a n o m a l o u s behavior of the La l_x Gdx sy stem. The f e a t u r e which is c o m m o n to both s y s t e m s i s the peaking of the T c v e r s u s n c u r v e at higher c o n c e n t r a t i o n s followed by a p l u m m e t i n g of T c towards zero with i n c r e a s i n g c o n c e n t r a t i o n . It is p o s s i b l e that this u n u s u a l behavior is an i n t r i n s i c p r o p e r t y of s u p e r c o n d u c t o r s with p a r a magnetic i m p u r i t i e s . Studies of other p a r a m a g netic, superconducting s y s t e m s may a n s w e r this question. It is a p l e a s u r e to thank W. B a s s e t t for his a s s i s t a n c e with X - r a y m e a s u r e m e n t s .
References 1. A.A.Abrikosov and L.P.Gorkov, Zh. Exp. i. Teor. Fiz. 39 (1960); Sov. Phys. JETP 12 (1961) 1243. 2. B.T.Matthias, H.Suhl and E.Corenzwit, Phys. Rev. Letters 1 (1958) 92. 3. R.A.Hein, R.L.Falge Jr.. B.T.Matthias and C. Corenzwit, Phys. Rev. Letters 2 (1959) 500. 4. D.K.Finnemore, D.L.Johnson, J.E.Ostenson, F.H.Spedding and B.J.Beaudry, Phys. Rev. 137 (1965) A550. 5. B.T. Matthias, V. B. Gompton and E. Corenzwit, J. Phys. Chem. Solids 19 (1961) 130. * This differs from the value, 10.4°K, reported in ref. 5.
* * * * *
379