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MAGNETIZATION OF THE II KIND
SUPERCONDUCTORS IN THE RESISTIVE STATE
Yu. Krasnov, L. Matushkina, V. Shukhman
To cite this version:
JOURNAL DE PHYSIQUE
Colloque
C6, supplgment au no 8, Tome 39, aofit 1978, page C6-629
M A G N E T I Z A T I O N OF T H E I 1 K I N D SUPERCONDUCTORS I N THE R E S I S T I V E S T A T E Y.u. K. Krasnov, L.V. Matushkina and V.A. Shukhman
I n s t i t u t e
of
Physica, Georgian Academy of Sciences, Z'bilisai, USSR.Rbsum6.- On montre que l ' i n f l u e n c e du c o u r a n t de t r a n s p o r t s u r l a p e r m 6 a b i l i t b magngtique dynamique des supraconducteurs dans l ' b t a t mixte p e u t - t t r e observee dans une l a r g e g a m e de c o u r a n t s ii p a r t i r du c o u r a n t c r i t i q u e ; c e l a confirme l e s conceptions dtentra?nement p a r t i e l d e s t o u r b i l l o n s en prb- sence du c o u r a n t de t r a n s p o r t .
Abstract.- It h a s been shown t h a t t h e i n f l u e n c e of t r a n s p o r t c u r r e n t on dynamic magnetic permeabili- t y of a superconductor i n mixed s t a t e t a k e s p l a c e o v e r a l a r g e range of c u r r e n t s beginning from t h e c r i t i c a l c u r r e n t which confirms t h e concepts of p a r t i a l i n v o l v i n g of v o r t i c e s ( i n t o motion) i n t h e presence of t r a n s p o r t c u r r e n t .
The problem how t h e t r a n s p o r t c u r r e n t i n f l u - ences t h e magnetization of superconductor was qua- l i t a t i v e l y analyzed i n t h e l i m i t s of t h e c r i t i c a l s t a t e model / I / i n 121. It was shown i n /3/
-
151, t h a t t h e magnetization i n t h e f i e l d decreases a s t h e t r a n s p o r t c u r r e n t i s i n c r e a s e d and when t h i s c u r r e n t h a s reached i t s c r i t i c a l v a l u e I the magne- t i z a t i o n curve c o i n c i d e s w i t h t h e r e v e r s i b l e one. These r e s u l t s i n d i c a t e , t h a t i n t h e r e s i s t i v e s t a t e , when I > Ic, t h e magnetization curve w i l l a l s o be r e v e r s i b l e . The b a l l i s t i c method which was employed i n / 3 /-
151, i s s e n s i t i v e t o t h e v a l u e of t h e mean i n d u c a t i o n a t t h e given e x t e r n a l f i e l d . We r e p o r t h e r e t h e experimental r e s u l t s on t h e r a t e of change of t h e mean i n d i c a t i o n dB/dt i n t h e a l t e r n a t i v e ma- g n e t i c f i e l d .The f o i l s of In
-
2.5 at.% Bi were employed a s t h e specimens w i t h dimensions 10mm
x 0.77m
x140 p. The copper wire wind was s t u c k upon t h e s u r f a - c e of t h e specimen i n t h e l i m i t s of i t s width
.
(The diameter of t h e wire $=90 p ) . T h i s w i n d s e r v e d u s t h e s o u r c e o f s i g n a l , whichwasinducedby t h e a l t e r n a t i n g f i e l d h , s u p e r i m p o s e d o n t h e m a g n e t i c f i e l d H a n d paral- l e l t o i t . A t t h e frequency of a l t e r n a t i n g f i e l d of 9 kHz and i t s amplitude ho = 0.55 G t h e a p p a r a t u r e was capable t o measure t h e changes i n v o l t a g e % 0.05 pV, w h i l e t h e s i g n a l l e v e l i n t h e normal s t a t e was e q u a l t o 2.5 pV. A t T>
Tc t h e s i g n a l E~ c o r r e s - ponding t o t h e normal s t a t e , was f i x e d a s t h e cons- t a n t magnetic f i e l d H was switched o f f t h e s i g n a lE~ corresponding t o t h e meissner s t a t e , was f i x e d ; The s i g n a l E then was measured a s a f u n c t i o n of e i - t h e r magnetic f i e l d H a t t h e f i x e d v a l u e s of t r a n s -
p o r t c u r r e n t I, o r wiseversa a s a f u n c t i o n of I a t t h e f i x e d v a l u e s of H. Simultaneously, i n b o t h c a s e s t h e v o l t a g e along t h e specimenwas f i x e d . Then t h e v a l u e A = (E-EJ
/
( E -€&I was c o n s t r u c t e d a sn
a f u n c t i o n of b o t h m a g n e t i c ' f i e l d H and c u r r e n t I . It was e a s y t o s e e , t h a t
where <dB/dt>
-
i s t h e r a t e of change of t h e magne- t i c i n d u c t i o n , averaged upon t h e time, and f-
t h e o s c i l l a t i o n frequency of h. R e a l l y t h e t o t a l f l u x of magnetic i n d u c t i o n through t h e winding i s t h e sum of t h e f l u x $ connected w i t h v o r t i c e s and t h e f l u x (I: which i s connected w i t h t h e d i s t o r t i o n of magnetic f i e l d l i n e s i n t h e v i c i n i t y of t h e s p e c i - men s u r f a c e and which c r e a t e s t h e n o i s e s i g n a l E!.Considering $' = yH', where y i s c o n s t a n t connected w i t h geometry, and H ' i s t h e v a l u e of t h e f i e l d on
t h e s i d e durface of t h e specimen i n t h e c a s e t h e specimen were i n t h e m i s s n e r s t a t e and t h e homoge- neous e x t e r n a l f i e l d of H-B v a l u e were a p p l i e d t o i t , t h a t i s H' = (H-B)/(l-n) (n- t h e demagnetiza- t i o n f a c t o r ) . The n o i s e s i g n a l E' = y / c ( l - n ) x (< d h / d t >
-
<dB/dt>). Then =,E 4yhof/c(l-n), t h a t i s E' = ~ , ( l - l / h ~ f x < d ~ / d t > ) . A s E = E' +'Ic
x S x <dB/dt> ( S-
t h e a r e a of t h e measuring wind and E = S/C x <dH/dt>, we r e c e i v e ( 1 ) . The b a s i c experimental r e s u l t s a r e a s f o l l o w s 1) When I = 0, A(H) i n c r e a s e s immediately a f t e r t h e specimen t r a n s i t s i n t o r e s i s t i v e s t a t e and e q u a t e s 1 n e a r H (curve 1 f i g . 1 ) .c 2
2) The t r a n s p o r t c u r r e n t does n o t i n f l u e n c e
A
u n t i lI < Ic
3) When I > Ic a t any f i x e d magnetic f i e l d H A in-
c r e a s e s w i t h I and reaches i t s l i m i t i n g valueAo(H) c u r r e n t d e n s i t y ) . The measured v a l u e s A(ho) a t H = on t h e i n t e r v a l of
111,
% 5. corlst. and I = 0 a r e w e l l d i s c r i b e d by ( 2 ) , and i t*
4 ) The comparison of V-I c h a r a c t e r i s t i c s w i t h t h e A appears, t h a t when H = H,
A"- a. ( I ) behaviour shows, t h a t A r e a c h e s i t s l i m i t i n gvdlue Ao(H) a t t h e same c u r r e n t s , where t h e pronoun- ced n o n l i n e a r i t y of V-I c h a r a c t e r i s t i c s t e r m i n a t e s .
5) The c r i t i c a l c u r r e n t I, i n t h e presence of the a l t e r n a t i n g magnetic f i e l d h is l e s s than 1:
-
the v a l u e of the c r i t i c a l c u r r e n t i n t h e absence of h,*
and Ic reaches zero when H = H < H.
c 2
Thus, t h e i n f l u e n c e of t h e t r a n s p o r t c u r r e n t on t h e magnetization i s n o t terminated a t I = Ic, a s i t was observed i n /3/-151, b u t only s t a r t s a f t e r t h e r e s i s t i v e s t a t e occures.
'0
ro
20 30 40 50 60 70 60 Hebe)F i g . 1 :
The dependence A(H) a t I = 0 can be c a l c u l a t e d on t h e b a s i s of t h e c r i t i c a l s t a t e model. The i d e a of such a c a l c u l a t i o n i s i l l u s t r a t e d i n f i g u r e 2a, which r e p r e s e n t s t h e magnetic i n d u c t i o n p r o f i l e i n
t h e p l a t e of 2a width a t t h e i n s t a n t e n e o u s v a l u e of h ( s o l i d curve) Bo(H + ho) and Bo(H
-
ho) a r e v a l u e s of t h e magnetic i n d u c t i o n on the s u r f a c e , which correspond t o t h e amplitude v a l u e s of t h e a l t e r n a - t i n g f i e l d ( t h e i n d u c t i o n on t h e s u r f a c e corresponds t o i t s r e v e r s i b l e v a l u e B ) . <dB/dt> i s determined by t h e a r e a enclosed between d o t t e d l i n e s i n f i g u r e2a.
I n accordance with ( I ) , we r e c e i v e f o r the l i n e a r p r o f i l e
cho/8aajc x (dBo/dHI2, A- 6 a
(dBo/dH)
-
2ajca/cho, A->
a ( 2 ) where A-= c h o / 4 s j c x (dBo/dH) i s t h e p e n e t r a t i o ndepth of t h e a l t e r n a t i n g f i e l d ( j c
-
t h e c r i t i c a lFig. 2 :
This f a c t allows us t o suppose, t h a t t h e a l t e r n a t i n g f i e l d p e n e t r a t i n g i n t o A - l a y e r c r e a t e s t h e v o r t e x movement t h e t r a n s p o r t c u r r e n t I < I flows n o t i n t h e whole specimen c r o s s a t i o n , b u t i n t h e l a y e r of 2 ( a
-
A"), where v o r t i c e s remain pinned and t h u s , t h e c u r r e n t flow does n o t provide any d i s s i p a t i o n . From t h i s p o i n t of view t h e independence of A on I a t I < Ic i s q u i t e n a t u r a l because t h e s i t u a t i o n i n t h e A" l a y e r remains t h e same, a s i n t h e c a s e , when I = 0. But when I > I n o n d i s s i p a t i v e c u r r e n t flow i s impossible and t h e c u r r e n t i s r e d i s t r i b u t e d upon t h e whole specimen c r o s s s e c t i o n . According t o t h e c r i t i c a l s t a t e model a s soon a s I = I t h e magnetic i n d u c t i o n p r o f i l e behaves i n t h e manner r e p r e s e n t e d i n f i g u r e 2b and i t i s e a s y t o see t h a t f o r a l l I > Ic A = d ~ / d ~ : I n t h e o t h e r words, t h e v a l u e of A a t I = I should jump t o i t s r e v e r s i b l e v a l u e Ao(H).The r e s u l t s we have r e c e i v e d a r e i n c o n t r a d i c - t i o n w i t h t h i s conclusion ( s e e p. 3 ) . Our e x p l a n a t i o n of t h e f a c t i s t h a t even a t I > Ic t h e number of e f - f e c t i v e l y f r e e v o r t i c e s i s l e s s than t h e t o t a l vor- t e x number
i m
t h e specimen. This makes <dB/dt> de- c r e a s e i n comparison with t h e r e v e r s i b l e c a s e .References --
--
- ./ 1 / Bean C.P., Rev. Mod. Phys., 36 (1964), 31. --. / 2 / Livingston J.D., Schadler H.W., Progr. Mater.
S c i . , l?., (1964), 183.
/3/ Le Blanc M.A.R. Phys. Rev. L e t t . , 1 1 , (1963), 149.
/4/ Druyvesteyn W.F., Phys. L e t t . ,
