An interaction matrix for the energy analysis of an n-layered magnetic thin-film system

Abstract

Normalized interaction factors have been developed for the analysis of the interaction energy and the magnetic as well as the electric properties of a multi-layered magnetic thin-film system. Mathematical expressions of these factors with respect to dimensions and separations of the films have been developed. Interaction factors and self-demagnetization energies of an n-layered magnetic thin-film system can be expressed by a matrix representation. For a magnetic thin-film system with k-dimensional magnetization, the interaction energy of the system can be described by k ( k ≤ 3) symmetric interaction matrices. Diagonal elements of the interaction matrices are zero because they represent the self-energy of the system. The off-diagonal elements of the interaction matrix are nonzero for a system which includes interactions. By using these interaction factors and finding a minimum energy configuration, the direction of magnetization in each film can be numerically determined. The numerical solutions to the electrical property of a coupled MR thin-film system using these interaction factors agree with previous experimental findings.