Contribution of surface currents to magnetic hysteresis in the mixed state of a type II superconductor

Volume 20, number 6

PHYSICS LETTERS

4. N.V.Zavaritskii, (a) J. Exptl. Theoret. Phys. (USSR) 45 (1963) 1839; Transl. Soviet Physics JETP 18 (1964) 1260. (b) J. Exptl. Theoret. Phys. (USSR) 48 (1965) 837; Transl. Soviet Physics JETP 21 (1965) 557. 5. H.Suhl, B.T.Matthias and L.R. Walker, Phys. Rev. Letters 3 (1959) 552. 6. I.K.Ianson, V.M.Svistunov and I.M.Dmitrenko, Zuhr. Eksp. i Theoret. Fiz. 47 (1964) 2091.

Chynoweth f o r c o n t r i b u t i n g in s e v e r a l s t i m u l a t i n g d i s c u s s i o n s . We p a r t i c u l a r l y want to thank J . M . Rowell fo r m u c h a d v i c e and n u m e r o u s s u g g e s tions.

References 1. Y.Goldstein, Rev. Mod. Phys. 36 (1964) 213; R. W. Cohen, C.D. Cody and Y.Goldstein, RCA Review 25 (1964) 433. 2. B.N.Taylor and E.Burstein, Phys. Rev. Letters 10 (1963) 14. 3. E.S.Greiner and H.Mason Jr., J. Appl. Phys. 35 (1964) 3058.

*

*

1April 1966

*

*

*

CONTRIBUTION OF SURFACE CURRENTS THE MIXED STATE OF A TYPE

TO MAGNETIC HYSTERESIS II SUPERCONDUCTOR*

IN

L. J. BARNES and H. J . FINK Atornics International, A Division of North American Aviation, Inc., Canoga Park, California Received 26 February 1966

Evidence is presented which indicates that in the mixed state of well annealed low K type II superconducting Pb-T1 cylinders in axial fields the d.c. magnetic hysteresis results from induced critical surface currents.

We p r e s e n t m a g n e t i z a t i o n data obtained on w e l l - a n n e a l e d , p o l y c r y s t a l l i n e , and low K Pb-T1 alloy c y l i n d e r s in ax ia l f i e l d s . T h e r e s u l t s i n d i cate that in our s p e c i m e n s the m i x e d s t a t e m a g n e t i c h y s t e r e s i s has, in l a r g e p a r t , a s u r f a c e origin . S w a r t z and H a r t [1] have d e m o n s t r a t e d that e x t e r n a l l y i n t r o d u c e d t r a n s p o r t c u r r e n t s in annealed Pb - 5% T1 s t r i p s in the m i x e d s t a t e a r e at l e a s t p a r t i a l l y confined to the s u r f a c e , and a s one supporting m e c h a n i s m they s u g g e s t e d the s u p e r c o n d u c t i n g s u r f a c e sheath. It is r e a s o n a b l e to expect that s i m i l a r c u r r e n t s can be induced on the s u r f a c e of a c y l i n d e r in an axial field. B a r n e s , Fink and P a r k [2] h a v e s u g g e s t e d on t h e o r e t i c a l grounds that the s u r f a c e sheath e x i s t in the m i x e d s t a t e and can i n f l u e n c e the m a g n e t i z a t i o n c h a r a c t e r i s t i c s of type ]I s u p e r c o n d u c t o r s by supporting induced c r i t i c a l c u r r e n t s that can p a r t i a l l y shield * Based on work sponsored by the Research for Metallurgy and Materials Programs Division of Research, US Atomic Energy Commission, under Contract No. AT-(ll-1)-GEN-8.

the i n t e r i o r of a s p e c i m e n . A . c . s u s c e p t i b i l i t y m e a s u r e m e n t s h a v e a l s o been i n t e r p r e t e d [3] on the b a s i s of sh i el d i n g c u r r e n t s . Our m a g n e t i zation r e s u l t s , obtained u s i n g the s t a n d a r d b a l l i s t i c t ech n i q u e at T = 4.2°K, c o n f i r m that induced s u r f a c e c u r r e n t s a r e l a r g e l y r e s p o n s i b l e for the m i x e d s t a t e d.c. m a g n e t i c h y s t e r e s i s in w e l l - a n n e a l e d low K Pb-T1 a l l o y s . V a r i o u s f e a t u r e s of our r e s u l t s a r e given in fig. 1. Fig. l(a) shows that m i n o r h y s t e r e s i s loops, a c r o s s the e n t i r e span of the m i x e d state, a r e exactly bounded by the m a j o r m a g n e t i z a t i o n c u r v e s f o r i n c r e a s i n g and d e c r e a s i n g f i e l d s . T r a v e r s e s between the m a j o r m a g n e t i z a t i o n c u r v e s a r e c h a r a t e r i s t i c of p e r f e c t shielding [4w (dM/dH) = -1]. F u r t h e r , m a g n e t i z a t i o n data M(H) taken when the s p e c i m e n was cooled through i t s t r a n s i t i o n t e m p e r a t u r e T c in a f i el d H c o i n c i d e with the f i el d d e c r e a s i n g m a g n e t i z a t i o n c u r v e in the m i x e d state. T h e s e o b s e r v a t i o n s su g g est that the m a g n e t i c h y s t e r e s i s r e s u l t s f r o m the shielding of c r i t i c a l c u r r e n t s J c induced on the s u r f a c e of the c y l i n d e r s . T h e m a g n e t i c flux e x p e l l e d f r o m 583

Volume 20, number 6

(o)

PHYSICS LETTERS

j ~ /

/

/

2

/

'

I

.,is. ~" \ . ,

I ~ MINORHYSTERESISLOOPS] I

Pb + 6% T l

"

J

coOt.EO ~, FIE~

4

,,D 0 o -I

I

I

i

i

I

I

I

I

I

I

I

i

i

r

,

,

,

i

I

l

I

Z

_o

i

~

,

F-

(b) F-

~

,Ol. '

,

,

,

6 ~

2o

Hc~

4

H(G)

.

O,

i

-I

2

400

600

800

IOOO

12

H(G)

Fig. 1. (a) Magnetization curve showing minor hysteresis loops and points obtained when specimen was cooled in a field. (b) Magnetization curves of a specimen whose surface was chemically polished and Cr plated. % T1 given in (a) and (b) are nominal values. (c) Magnetization due to shielding currents near Hc2 as discussed in text. the s p e c i m e n , when it i s cooled in a field, can a l s o induce the c r i t i c a l s u r f a c e c u r r e n t s [4]. E v i d e n c e that the shielding c u r r e n t s a r e c o n fined to the s u r f a c e of the s p e c i m e n s i s given by the fact that n o r m a l m e t a l s e l e c t r o p l a t e d on the s p e c i m e n s r e d u c e the m i x e d s ta te h y s t e r e s i s , p r o b a b l y due to the p r o x i m i t y effect [5]. Cu plating the s p e c i m e n s m o t i c e a b l y r e d u c e s the m i x e d and sheath state h y s t e r e s i s . In c o n t r a s t , Cr (antif e r r o m a g n e t i c ) and Ni ( f e r r o m a g n e t i c ) p l a t i n g s have a much m o r e d r a s t i c effect: all e v i d e n c e of the sheath s t at e d i s a p p e a r s f o r H > Hc2 [6], and the m i x e d state h y s t e r e s i s i s c o n s i d e r a b l y r e d u c e d as is shown f o r C r plating in fig. l(b). M i n o r h y s t e r e s i s loops obtained on the Ni and C r plated s p e c i m e n s exhibit the s a m e c h a r a c t e r i s t i c s a s t h o s e o b s e r v e d on unplated s p e c i m e n s indicating that the n o r m a l m e t a l l a y e r s r e d u c e but do not e l i m i n a t e the s u r f a c e c u r r e n t s except n e a r Hc2. The m o r e d r a s t i c e f f e c t s of the Ni and C r l a y e r s a r e probably due to t h e i r m a g n e t i c p r o p e r t i e s [7]. C h e m i c a l p o l i s h in g of the s p e c i m e n s , whose s u r f a c e s had been untouched s i n c e annealing, 584

1April 1966

a l w a y s led to i n c r e a s e d m a g n e t i c h y s t e r e s i s in both the m i x e d and sheath state [6] p r e s u m a b l y due to the i m p r o v e d p h y s i c a l state of the s u r f a c e . Etching off the n o r m a l m e t a l l a y e r s i n c r e a s e d the h y s t e r e s i s of the p r e v i o u s tmplated l e v e l and r e p l a t i n g again r e d u c e d it. The r e p e a t e d polishing and plating had l i t t l e effect upon the amount of t r a p p e d flux at H = 0 (See fig. l(b)) probably b e c a u s e this is p r i m a r i l y a bulk effect and the s u r f a c e s w e r e of good quality. It is c l e a r that the h y s t e r e s i s r e s u l t s in l a r g e p a r t f r o m shielding c u r r e n t s induced on the s p e c i m en s u r f a c e s . Any s i g n i f i c a n t i r r e v e r s i b l e flux m o v e m e n t within the bulk of the s p e c i m e n s would lead to d i f f e r e n t h y s t e r e s t i c b e h a v i o r such as that o b s e r v e d in " h a r d " type II s u p e r c o n d u c t o r s [8]. the p r o p o s a l that the s u r f a c e sheath ex i st at H ~/Hc2 [6]. Th e h y s t e r e s i s n e a r Hc2 , h o w e v e r , i n d i c a t e s that the sheath p r o b a b l y does not support all of the c u r r e n t J c . One can d e t e r m i n e f r o m the data p r e s e n t e d in fig. l(b) the m a g n e t i z a t i o n component 47rMs r e s u l t i n g f r o m the s u r f a c e c u r r e n t s , as a function of the a v e r a g e i n t e r n a l f i el d H, a s s u m i n g the h y s t e r e s i s r e s u l t s solely f r o m t h e s e c u r r e n t s . N e a r H c 2 this as a v al i d a s s u m p t i o n as ev i d en ced by the c o m p l e t e r e m o v a l of the h y s t e r e s i s by the C r plating. V a l u e s Of 47rMs(H) a r e shown in fig. l(c). 47TMs and thus a l s o J c a r e seen to e x hibit a b r e a k at H c2 [1]. T h i s b e h a v i o r su g g est that a n o t h e r contribution to Jc( H ) ex i st below Hc2 o t h er than that of the s u r f a c e sheath. Conceivably t h i s added contribution below Hc2 could be a d e f e c t s t a b i l i z e d c u r r e n t n e a r the s u r f a c e . A m o r e d e t a i l e d t h e o r e t i c a l a n a l y s i s of s u r f a c e s u p e r conductivity in the m i x e d state is r e q u i r e d to characterize these surface currents.

References 1. P.S.Swartz and H.R.Hart Jr., Phys. Rev. 137 (1965) A818. 2. H.J.Fink, Phys. Rev. Letters 14 (1965) 853; J . G . P a r k , Phys. Rev. Letters 15 (1965)352; H . J . F i n k and L . J . Barnes, Phys. Rev. Letters 15 (1965) 792. 3. J . G . P a r k , Rev. Mod. Phys. 36 (1964) 87; M. Strongin, D.G. Sehweitzer, A. Paskin and P. P. Craig, Phys. Rev. 136 (1964) A926; A. Paskin, M.Strongin, D.G. 8chweitzer and B. Bertram, Phys. Letters 19 (1965) 277. 4. H.J. Fink, Phys. Letters 19 (1965) 364. 5. P.G.DeGermes, Rev. Mod. Phys. 36 (1963) 225. 6. L . J . B a r n e s and H.J. Fink, to be published. 7. J . J . Hauser, H.C. Theuerer and N. R. Werthamer, Phys. Letters 18 (1965) 222. 8. M.A.R.LeBlanc, Phys. Letters 9 (1964) 9.