An analytic solution for magnetization distribution in multigrain ferromagnetic materials in an applied magnetic field

Abstract

The magnetic behavior of a material is governed by the variation in anisotropy direction from grain to grain as well as the changes in ferromagnetic parameters at grain boundaries and other defect regions. For example, transmission electron microscopy results show that chromium segregation occurs at the grand boundaries in CoCrTa films, which are used in hard disk drives. In this paper, we model the case of two adjacent semi-infinite grains with arbitrary crystalline orientations with respect to each other. A Gaussian distribution is used to model the change in magnetic properties at the interface, and boundary conditions are imposed on the direction of magnetization deep within the grains and at the interface. The effects due to the diffuse interface are included using perturbation theory. The sum of the exchange, anisotropy and Zeeman energies is minimized, and the resulting Euler equation is solved analytically. A profile of the magnetization orientation in an inhomogeneous medium in an applied field is obtained to show the extent of the effects of grain boundary segregation. These results can direct future large-scale computer calculations and media improvement.