Computation of surface effects and its influence to critical magnetic field in materials

Abstract

This paper presents one kind of numerical method for investigating a problems related to the surface effects and surface characterization of materials. The aim of this paper is to show development of technique, which is sufficiently simple but effective to compute the surface critical effects of materials. We study such problems on the frame work of the Ginzburg–Landau equations. We choose nucleation field ( H c 3) and the formation of a superconducting state in isotropic type II superconductors situated in magnetic fields, whose magnitude between H c 2 and H c 3, as our physical case. Firstly we introduce the detailed variational approach which is close to the problem of finding the highest magnetic field for which the superconducting sheath states nucleates at the surface of the specimen. By considering the surface effect we can linearise the Ginzburg–Landau equation to get such kind of equation which is Schrödinger’s equation like. We then describe a method for choosing a suitable trial function, which represents the behavior of superconducting order parameter. With Raleigh–Ritz principle the Eigen value of ground state which is related with critical magnetic field H c 3 at which nucleation on the surface appears found computationally thus the methods used in this paper is useful in computational materials. The numerical relation of H c 2 is represented by h with ε that we have found, can be used to predict the nucleation field on specimen’s surface. Beside that by considering angular variation of external magnetic field we find the relation of H c 3 with H c 2 fulfill H c 3 = 1.7 H c 2 and we show that our results are in agreement with physical argument.