Third Order Perturbed Heisenberg Hamiltonian of Thick Spinel Ferrite Films

TL;DR

This study uses a third order perturbed Heisenberg Hamiltonian to analyze the magnetic energy variations in thick spinel ferrite films, revealing new insights into their anisotropic energy behavior and differences from second order models.

Contribution

It introduces a third order perturbation approach to model the energy variation in thick spinel ferrite films, providing more detailed insights than previous second order models.

Findings

Energy variation shows abrupt changes with third order perturbation.

Maximum energy is higher than in second order models.

Energy behavior depends on stress-induced anisotropy values.

Abstract

The third order perturbed Heisenberg Hamiltonian was employed to investigate the spinel thick nickel ferrite films. The variation of energy up to N=10000 was studied. At N=75, the energy required to rotate from easy to hard direction is very small. For film with N=10000, the first major maximum and minimum can be observed at 202 and 317 degrees, respectively. This curve shows some abrupt changes after introducing third order perturbation. The maximum energy of this curve is higher than that of spinel thick ferrite films with second order perturbed Heisenberg Hamiltonian. At some values of stress induced anisotropy, the maximum energy is less than that of spinel thick ferrite films with second order perturbed Heisenberg Hamiltonian derived by us previously.