Magnetostatic Contribution to Perpendicular Magnetic Anisotropy Constant of Inhomogeneous Films

Abstract

Real magnetic films have an inhomogeneous distribution of magnetization. The typical case of magnetic inhomogeneity is a film consisting of two mixed magnetic phases with the different magnetizations M₁, M₂. This phase mixture can appear, for instance, at annealing (aging) of alloys - metastable solid solutions, in particular Co_xCu_1-x, Co_xAg_1-x. That is why the questions arise: what kinds of the inhomogeneities lead really to uniaxial (perpendicular) induced anisotropy formation due to magnetostatic coupling and what will be the dependence of this anisotropy constant on microscopical geometric characteristics of these inhomogeneities. The problem was firstly considered for the film with throughout columnar periodic structure in [1] (the ferromagnetic columns were embedded in nonmagnetic matrix). Then the analysis was generalized on arbitrary columnar structures in [2], suggesting that the film thickness L is many times larger than the structure period in the film plane. Calculation of magnetostatic coupling is especially actual for the granular films and multilayer films because this coupling effects not only on magnetic anisotropy but also on giant magnetoresistance (GMR) in these structures. Magnetic anisotropy determines the magnetization dependence on magnetic field H and therefore the GMR value dependence on H.