Intrinsic flux pinning in high Tc oxide superconductors

PhysieaC162-164 (1989) 241-242 No~h-HoNand

INRINSIC FLUX PINNING IN HIGH T

c

OXIDE SUPERCONDUCTORS

M. Tachiki and S. Takahashi Institute

for

Materials

Research,

Tohoku

University,

Katahira

In the high-T_ oxide superconductors with layered structures than the lattice constant. This fact suggests that the layer pinning centers for the flux lines whose axes are parallel to density estimated from this pinning mechanism is very high, current density in high-quality films and single crystals.

I. INTRODUCTION The current-carrying capacity of the high-Tc oxide superconductors has been increased by the the improvement of sample quality in thin films and single crystals. 1'2 This direction is opposite to that in conventional superconductors where local inhomogeneities such as impurities, defects, precipitates, and grain boundaries are introduced into the sample for pinning centers. In high-~ materials like the oxide superconductors, the interaction of the normal cores of the flux lines with the pinning centers dominates • . 3 for the flux plnnlng. Unfortunately the normal-core dimension in the oxides is extremely small, so that the conventional pinning centers will not be effective in the oxides. This fact may indicate that some unconventional pinning mechanism works in the oxides. In YBa2Cu307, the layers with CuO 2 planes are superconductive and the layers with CuO chains and BaO planes may be weakly superconductive. Therefore, when the flux lines are parallel to the CuO 2 planes, the flux lines tend to take the position at the weakly superconducting layers to make the loss of the superconducting condensation energy least. Consequently, the spatial modulation of the superconducting order parameter on the scale of the crystal unit cell may cause the strong flux pinning for the flux lines parallel to the CuO 2 planes. 4 In the following we estimate the strength of pinning force and the critical current density which comes from the present pinning mechanism. 2. FORMULATION Let us consider a single crystal of YBa2Cu 3 07 . The superconducting order parameter has a

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the coherence length is shorther structure itself works as strong the layers. The critical current and comparable to the critical

periodic spatial modulation with t h e l a t t ~ c e c o n stant a . This modulation may cause the modulac tion of the thermodynamical critical field expressed as Hc(Z)=Hc[l+6cos(2~Z/ac)]

,

(0<~
(i)

H and ~ being positive parameters. The z axis c is taken along the c axis. The maximum of Hc(Z) occurs at the CuO 2 planes. The order parameter in the presence of a flux line at x=0 and z=z 0 is approximately expressed as 1/2 • (r)=~0(z)tanh~k~abJf x ~ + ~[-~0)

,

(2)

where T0(z) is the order parameter in the Meissner state , and ~ab and ~c are the coherence lengths parallel and perpendicular to the ab planes, respectively. The increase in the free energy in the presence of the flux line is estimated by H2(z) 2

c

¥(r) ]

The elementary pinnig force f . which prevents pm the flux line from moving along the c axis is the muximum value of -(d/dz0)~(z 0) and given by f pM

= (H2/8~)2~a "[~ /~ ]'~ c c ab c M

(4)

The dimensionless quantity ~M in (4) is plotted as a function of ~c/ac in Fig.l. In the oxide superconductors, ~c ~t OK ando 77K are estimated to be 2A ~ 4A and 4A ~ 8A, respectively. The correspoding values of ~ /a at OK and 77K are cc 0.2 ~ 0.35 and 0.35 ~ 0.7, respectively. Therefore, the oxide superconductors take the values around the peak of ~M"

M. Tachiki and S. Takahashi / Intrinsic flux pinning in high T~ oxide superconductors

242

Critical

current density J

c

TABLE i and the p a r a m e t e r s

used

for

estimating

the

values

of

0K

~c=3~ a) ~ ab=16~a) Aab=1400~,b) Hc=I.0T a) ~c/ac=0.26, OM=0.24, Jc=2Xl08A/cs 2

77K

~ =6X, ~b=34~,

Aab=2600~,

H¢=0.3T,

$ /a =0.52, wM=0.12,

a) Reference 5, The pinning force density F . is obtained by pm summing the elementary pininng force of individual flux lines. Since the London penetration depth of the oxide superconductors is very large, the repulsive interaction between the flux lines caused by the current-current interaction is very weak compared to the present pinning interaction. In this circumstance, all the flux lines are pinned in the weakly superconductive layers. Thus F . is proportional pm to the product of the elementary pinning force f . and the density of the flux lines : F = pm ab . pM f .'(B/~n)'(I-B/B ~) where B is the magnetic Dm u cz ab flux density and Bc2 is the upper critical field parallel to the ab planes. The factor aD (I-B/Bc2) origxnates from the decrease in the condensation energy in the magnetic field. The critical current density is determined by the balance of the pinnig force density with the

J

c

.

J =2xl06A/cm 2 b)

Reference 6.

°41 a:o.8 77M

0.2

0

O.5

~c/(]c FIGURE i Parameter indicating the strength of the pinning force in Eq.(4).

Lorentz force: Jc=CFpM/B. 3. RESULTS AND DISCUSSIONS Using the values of nM for 6=0.6 in Fig.l, we estimate the critical current density J in the c magnetic field parallel to the ab planes in single crystals of YBa.CuoO ~. With use of the L ~ , • 5 • 5 experimental values ~ (0)=3A, ~ . (0)=16%, o 6 c 5 ao Aab(O) =1400A, and Hc(O)=iTesla, the critical current density at OK is estimated to be 2X10 S A/cm 2 for B<
single crystal of YBa2Cu307 . The present pinning mechanism also works in other superconducting oxides Bi-Sr-Ca-Cu-O and TI-Ba-Ca-Cu-O. In conclusion, the critical current density predicted by the present theory is very high and comparable to the experimental values of the critical current density in high-quality films and single crystals of the oxide superconduc tots. The strong flux pinning originates from the fact that the oxide superconductors with high Tc superconductivity have the layer structure and the extremely small coherence length. REFERENCES I. K.Watanabe 2. B.D.Biggs

et al.,Appl.Phys.Lett.54(1988)575 et al., Phys.Rev. B39(1989)7309.

3. A.M.Campbell 199(1972).

and J.M.Evetts,

4. M.Tachiki and S.Takahashi, Commun.70(1989)291.

Advan.Phys.21,

Solid State

5. U.Welp et al., Phys.Rev. Lett.63(1989)1908. 6. A.T.Fiory et al.,Phys.Rev.Lett.61(1988)1419.