Physica C 196 (1992) 17-26 North-Holland PHYSICA Bean-Livingston surface barrier and magnetic properties of granular superconductors K.I. Kugel and A.L. Rakhmanov Institute for High Temperatures, 127412 Moscow,Russia Received 3 January 1992 The magnetic flux penetration into a granular superconductor is studied, accounting for the Bean-Livingston surface barrier (BLSB). It is shown that the magnetic flux distribution is strongly affected by the BLSB in the case of large, closely packed granules. In particular, the intergranular magneticfield Ho appears to be much higher than the external field Hwhen H<Hs=2H_,2/ lg (where l s is the characteristic granular size and 2 is the London penetration depth ). The effects related to the difference between H and Ho are discussed in the framework of a simplified model of a granular superconductor. The magnetic flux distribution is studied in the regular system of isotropic and anisotropic granules. The form of the Ho(H) curve is calculated for both increasing and decreasing field H. It is shown that the existence of the BLSBresults in the strong hysteresis of the Ho(H) curve. The relation between these effects and the form of the magnetic field dependence of critical current in ceramic superconductors is discussed. I. Introduction In high-Tc superconducting ceramics the magnetic field Ito in intergranular regions may appreciably differ from the external field H owing to magnetic flux expulsion from superconducting granules. This effect results in peculiarities of the field dependences of critical current j~(H), I-V characteristic, mag- netic susceptibility and some other properties of granular superconductors. Such phenomena are ev- idently of importance in weak fields H<H~, where Hc~ is the lower critical field for the granules. How- ever, there are two effects which lead to the broad- ening of the field range where the above-mentioned peculiarities may be appreciable. The first one is in- tragranular pinning. The influence of pinning on the magnetic flux distribution and on critical current j~ versus H curves in granular superconductors was considered, for example, in ref. [ 1 ]. The second ef- fect is the Bean-Livingston surface barrier (BLSB) [ 2 ] which impedes the penetration of flux lines into a superconductor owing to repulsive interaction be- tween the surface and an entering vortex. It was shown [3 ] that the existence of the BLSB leads to the sufficient difference between Ho and H in the granular system in the external field range extending up to several Hc, where Hc is the thermodynamic critical field for the granule. In the present paper the effect of the BLSB on flux penetration and on the jc(H) dependence for the granular system is discussed. The superconducting ceramics may be presented schematically as a system of granules with average size Is separated by narrow normal layers with char- acteristic thickness li. Usually, it is supposed that the normal layers are weak links. The magnetic flux pen- etrates the sample at H> hcl, where hot is the lower critical field of the intergranular weak links network. The local magnetic induction B may be defined as the value of magnetic flux intensity averaged over a sufficiently large volume. The local value of the in- tergranular field Ho may be much higher than B ow- ing to the flux expulsion from the granules. At H>> hcl the simple estimates give for the ratio Ho/B in a vol- ume element AV:Ho/B~ AV/AVef, where AVef is the part of A Vincluding the volume of the normal layers A Vi and the effective volume of the granules occu- pied by the magnetic flux. Obviously, the ratio Ho/ B has the highest value for the system of sufficiently large closely packed granules li <<2 <<l s , ( 1 ) 0921-4534/92/$05.00 © 1992 Elsevier Science Publishers B.V. All fights reserved.