Third order perturbed modified Heisenberg Hamiltonian of fcc structured ferromagnetic films with seventy spin layers

TL;DR

This paper models the magnetic properties of fcc ferromagnetic films with up to seventy layers using a third order perturbed Heisenberg Hamiltonian, analyzing magnetic orientations and energies.

Contribution

It introduces a semi-classical third order perturbed Heisenberg Hamiltonian model that incorporates microscopic and macroscopic interactions for ferromagnetic films.

Findings

Magnetic easy axis varies discretely with layer number.

Model qualitatively agrees with experimental Fe and Ni film data.

Magnetic energies and anisotropies depend on layer thickness and external fields.

Abstract

Magnetic properties of fcc structured ferromagnetic films with the number of spin layers up to seventy was described using third order perturbed Heisenberg Hamiltonian. The variation of magnetic easy direction, magnetic energies in easy and hard directions, magnetic anisotropy energy and the angle between easy and hard directions was investigated by varying the number of spin layers. Spin exchange interaction, magnetic dipole interaction, second and fourth order magnetic anisotropies, in and out of plane applied magnetic fields, demagnetization factor and stress induced anisotropy were considered in the model. Because magnetic dipole interaction and demagnetization factor represent microscopic and macroscopic properties of the sample, respectively, both these terms were incorporated in our theoretical model. Although our model is a semi-classical model, some discrete variations of angle of easy axis were observed. Our theoretical data qualitatively agree with experimental data of Fe and Ni ferromagnetic films.