Electric current and magnetization distributions’ self-organization features in a magnetoresistive film nanoelement under the influence of an external magnetic field

Abstract

The new generalized Laplace’s equation for an electric potential is presented, which in the general case, is nonlinear for media with resistance anisotropy caused by the anisotropic magnetoresistance (AMR) effect and determined by the orientation of the magnetization vector relative to the current density vector at an arbitrary point of the sample. The solution to this equation is obtained for an anisotropic medium with a non-uniform distribution of current density and magnetization in the case of an oblique-shaped plate of nanoscale thickness. In addition, the analytical solution was obtained for the current density distribution in such a medium using conformal mapping, which confirms the numerical solution in the case of an isotropic conductor. An analysis of the results showed that the presence of the AMR effect leads to a significant change in the current density distribution in the sample compared to the isotropic case, which is expressed in the deviation of the current density vector in perpendicular to the magnetization vector direction in the plate. It has been established that the presence of an external magnetic field in the film plane, which leads to the emergence of an inhomogeneous magnetization distribution, entails self-organization of the electric current distribution. The graphs of the plate resistance as a function of applied magnetic field demonstrate asymmetry for the cases of the direct and reverse directions of the external magnetic field, which cannot be obtained within the framework of simplified models of current flow in media with the AMR effect.