Thick ferromagnetic films and their anisotropies as described by second order perturbed Heisenberg Hamiltonian

TL;DR

This paper analyzes the anisotropy dependence of energy in thick ferromagnetic films using a second and fourth order perturbed Heisenberg Hamiltonian, revealing how anisotropy constants influence film orientation and energy variation.

Contribution

It introduces a detailed model for thick ferromagnetic films considering second and fourth order anisotropies using perturbation theory, providing insights into energy behavior and film orientation.

Findings

Energy varies periodically with anisotropy constants.

Maximum energy decreases with higher fourth order anisotropy.

Second order anisotropy results in larger energy than fourth order anisotropy.

Abstract

Second and fourth order anisotropy dependence of energy of thick simple cubic ferromagnetic films with 10000 layers is explained using Heisenberg Hamiltonian with second order perturbation in this manuscript. The second and fourth order anisotropy constants were assumed to be constants through out the film. When the fourth order anisotropy is given by fourth order anisotropy of 6, the sc(001) ferromagnetic thick films with 10000 layers can be easily oriented in 0.6 radians direction for the energy parameters given this report. Under the influence of the second order anisotropy given by second order anisotropy of 6.3, the easy direction of sc(001) film with 10000 layers is given by 0.66 radians. Although the energy varies periodically in all cases, the maximum energy considerably decreases with fourth order anisotropy constant. According to 3-D plots, energy under influence of second order anisotropy is larger than energy under influence of fourth order anisotropy.