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Physica B 194-196 (1994) 1807-1808 North-Holland

P o s s i b l e e v i d e n c e o f s u r f a c e s u p e r c o n d u c t i v i t y in the h i g h T c o x i d e s O. F. de Lima, R. Andrade Jr. and M. A. Avila Instituto de Fisica, UNICAMP 13081 Campinas, SP, Brazil

Good fits of magnetization data for a YBaCuO crystal near the transition onset, together with a predicted temperature dependence for the ratio H3/H2 give support to the possible occurrence of surface superconductivity in the high Tc oxides.

1. INTRODUCTION Surface superconductivity (SS) is known to occur in a thin surface layer of thickness slightly larger than ~(T) [1]. The surface nucleation field, Ho3, for H parallel to the sample surface, is ideally given by Ho3~ 1.7Ho2, Ho2 being the bulk nucleation field. Ho3(0)_>Ho2 and Ho3(0=x/2)=Ho2, where 0 is the angle between H and the surface. For a sample of arbitrary shape, the effects due to SS depends on: 1) The amount of plane surfaces and their angular distribution with respect to H; 2) The sample size, whose linear dimensions must be larger than g(T); 3) The ratio c~s/~N between the electrical conductivities of the superconductor sample in the normal state, and the surrounding material. SS is fully suppressed for t~N>~S, partially suppressed for CrN

shielding currents are induced 14]. The magnetization arising from this diamagnetic response can be written approximately as:

4xMs(H,t) _ ltc(t) (~L(t))~F(H) ,c(0 /-, ~2 =

where t=T/Tc3(0), Tos(0) is the surface nucleation temperature at H=0, X(t)=ko(1-t4) ~'2 is the magnetic penetration depth, Ho(t)=Ho0(1-t:) is the thermodynamic critical field, r~(t)=k(t)/~(t) is the GL factor, L is the average half-thickness of the sample perpendicular to H, and F(H/Ho2)= 2.56(H/Ho2)-2/3-1.80 is an interpolation formula valid for re(t)>3. Also: Ho2(t)=6o/27t~(t)2, where t~0=2.07x10 -7 Gem 2 is the flux quantum, and ~(t)=~o(1-t) 2'3 is the coherence length for the region [5] near the onset point To3(H). After some calculations 16] the effective surface magnetization, m~(H,t)zl~(t)/LlMs(H,t ) can be written ( Ho2

ms(H,t ) ~

(I+~y~43~ lAte(I-t) m I]B +

(1-t ),t-

(2)

with B ~ (4.33x10 4 ~b03)/(~0~,,07/2Hoo2 L 3/2) and An ~ -1.423 IHo2(0)/H] :~. m~(H',t)=0 implies H*zl.7Hc2, as expected [1]. Hoz(T) values can be determined at the point To2(H) where the linear extrapolation of the reversible region in the M vs. T curve crosses

0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved 0921-4526(93)1535-T

SSDI

(1)

1808

the normal state base line [7,8]. Using Abrikosov's expression for the equilibrium bull< magnetization [ 1] it can be shown that for K>> ! and near Tc2(H): M~(H, t2) = ( 1 + t~) [C (1 tz) + D H] -

(3)

0.2 0.0 -0.2 -0.4

(a)

-0.6

-0.8

with C ~ (8.02x10" ¢03)/(~0"- Ho02 k04 [3) and D ~ (5.04x10-4 qbo2)/(H¢o2 L04 [3). t~=T/To:(0) and ~(t2)={0(1-t2) -'/2, assuming the GL mean field regime for T

Due to the limited sensitivity of any measurement one can only refer to the surface and bulk nucleation fields, H3(t) and H2(t), given by: m~(H3,t)=-g and Mv(H2,t2)=-g, where -g is the minimum measurable signal. Using Eqs. 2 and 3 it can be shown that: H3 = 1.7 u2 [(1-0-~9 + ey(t)W(1 - no)

(4)

with f(t)=:(1-t9'/4/[(1 +t2)2(1-OS/:l, to=T3(0)/T2(0) and the fitting parameter E oc p,L3/2.

-1.0 -1.2

/ /

-1.4 -1.6

H//c

"

-1.880,

A4T

, , '8'2' ' ' '8'4' ' ' '8'6'''

'8'8'''

'9'0'''

'9'2' ' ' '9'4-'

T (K) 4

3

% ~Z

2

1 0.7

O.g

0.9

0

T/Ta(O) Fig. 1. (a) Fitting of Eqs. 2 and 3 (solid lines) to the Mvs.T data of a YBaCuO crystal [7]. (b)

Fitting of Eq. 4 for different granular samples. Fig. l(b) shows that Eq. 4 fits remarkably well to some data taken in our laboratory, regardless of being high or low T c [8]. We thank the support of FAPESP and CNPq. REFERENCES 1. D. Saint-James ct al., T y p e I1 Superconductivity (Pergamon, 1969). 2. J. P. Hurault, Phys. Letters 20 (1966) 587. 3. G.Deutscher et al., Phs. Rev. Lett. 59(1987) 1745. 4. H.J.Fink et al., Phys.Rev.Lett. 15 (1965) 792. 5. L.N.Bulaevskii et al.,Sov.Phys. JETP (1988) 1499. 6. O. t:. de Lima, Preprint (t992). 7. U.Welp et al., Phys.Rev.Lett. 62 (1989) 1908. 8. O.F.de Lima, Solid State Commun.,81(1992)411.