Second order perturbed Heisenberg Hamiltonian of Fe&lt;sub&gt;3&lt;/sub&gt;O&lt;sub&gt;4&lt;/sub&gt; ultra-thin films

P Samarasekara

doi:10.4038/cjs.v47i3.7529

Abstract

Due to the wide range of applications, theoretical models of Fe3O4 films are found to be important. Ultra thin Fe3O4 films with ferrite structure have been theoretically investigated using second order perturbed modified Heisenberg Hamiltonian. Matrices for ultra thin films with two and three spin layers are presented in this manuscript. Total magnetic energy was expressed in terms of spin exchange interaction, magnetic dipole interaction, second order magnetic anisotropy and stress induced magnetic anisotropy. Magnetic properties were observed for films with two spin layers and variant second order magnetic anisotropy. For the film with three spin layers, second order anisotropy constant was fixed to avoid tedious derivations. Magnetic easy axis rotates toward the in plane direction as the number of spin layers is increased from two to three because the stress induced anisotropy energy dominates at higher number of spin layers. According to some other experimental data, the magnetic easy axis of thin films rotates toward the in plane direction as the thickness is increased.

Highlights

Magnetite (Fe3O4) and maghemite (γ-Fe2O3) are the most popular natural oxides
Because magnetic moments of Fe3+ in tetrahedral and octahedral sites cancel each other, the net magnetic moment of Fe3O4 is completely due to the magnetic moments of four Fe2+ ions
Magnetic easy direction and magnetic hard direction were determined for films with two and three spin layers by plotting 3-D graphs of energy versus stress induced anisotropy and angle, and graphs of energy versus angle

Summary

Introduction

Magnetite (Fe3O4) and maghemite (γ-Fe2O3) are the most popular natural oxides. Fe3O4 finds potential applications in magnetic storage, industrial catalysts, water purification and drug delivery. Ferrite ultra-thin and thick films have been investigated using second order perturbed Heisenberg Hamiltonian by us (Samarasekara et al, 2009). The anisotropy energy term and the last term have been explained in our previous report for oriented spinel For m=2, 3, ----, N-1 ferrite (Samarasekara et al, 2009). D (2) 1 and were taken as the anisotropy constants of first and second spin layers of the Fe3O4 film, respectively.

Results

Conclusion