Simulation of Meissner state and flux penetration in thin film superconductors in perpendicular field

Abstract

We present a comprehensive modeling framework to analyze the magnetic response of type-II superconductors in both the Meissner and mixed states, in the limit of thin-film geometries. Starting from the fluxoid quantization condition, we compute the magnetic susceptibility and its dependence on the penetration depth λ, highlighting the experimental resolution needed to detect small variations in λ. To describe the penetration of vortices in the mixed state, we implement a critical state model that imposes local current constraints, enabling simulation of magnetization curves in samples with and without weak links, such as grain boundaries. The flux penetration of the virgin magnetization curves of rectangular thin films exhibit quadratic dependency on the applied field, contrary to Brandt and Indenbom (1993 Phys. Rev. B 48 12893–906) cubic prediction owing to his simplification of the problem by assuming an infinitely long strip. Two complementary approaches-numerical minimization and flux front tracking yield consistent predictions for magnetization and allow extraction of both intra- and intergranular critical current densities. The simulated magnetic response, including subtle features in the derivative of magnetization with respect to the applied field, is in excellent agreement with experimental AC susceptibility measurements on single- and bicrystalline thin films.