Third order perturbed energy of fcc ferromagnetic thin films as described by Heisenberg Hamiltonian

Abstract

Magnetic energy of fcc structured ferromagnetic thin films was investigated using third order perturbed Heisenberg Hamiltonian with seven magnetic energy parameters by a MATLAB computer program for the first time. Spin exchange interaction, magnetic dipole interaction, second order anisotropy, fourth order anisotropy, applied field, demagnetization factor and stress induced anisotropy were taken into account. Ultra-thin films with three layers (N=3) were considered. Several magnetic easy and hard directions were found in all the 3-D plots. According to some graphs, the angle between easy and hard directions was 90 degrees. Previously, the third order perturbed Heisenberg Hamiltonian with spin exchange interaction, second order magnetic anisotropy and stress induced anisotropy terms only was solved manually for ferromagnetic films with two and three layers by us. Due to the unavailability of the experimental values of these seven magnetic parameters, some reasonable values were used for this simulation.

Keywords

• heisenberg hamiltonian, perturbation, thin films, ferromagnetic