easy magnetization axis
the domain structure
magnetostatic scalar potential
Analysis problems of domain structures in ferromagnets are studied by many authors over several decades, but they are relevant to the present for creation of a series of practical devices. The paper presents for the first time an efficient method for numerical simulation of domain walls (DW) using the scalar magneto-static potential by way of example of Neel and Bloch boundaries in the films of yttrium iron garnet. Our approach is used in the analysis of domain structures in single-axis films and can be extended to multi-axis films. The method allows one to solve the problems of analyzing the DW for domain structures of finite size. It allows one to use the experimental results that can be used as initial data on the shape and size of domains in calculations, while most studies on the DW approximation use an infinite sample, or impose restrictions on the shape of the DW.
When creating a model of the DW, the magneto-static energy, the energy of exchange interaction, and magnetic anisotropy energy is taken into account. The test sample of YIG film is represented as a system of magnetic dipoles and the interaction energy of magnetic dipoles that belong to the domains and boundaries is determined. When solving the one-dimensional optimization problem, by varying the thickness of the DW, the values of the DW thickness that correspond to the minimum energy density are determined. The paper presents the results of calculations of relative energy density and the thickness of the DW when the film thickness is varying over a wide range of values. The estimations of the applicability of the DW models according to Bloch and Neel are performed depending on the thickness of the YIG film.