Third order perturbed Heisenberg Hamiltonian of sc ferromagnetic films with fifty spin layers

TL;DR

This study analyzes the magnetic energy and anisotropy directions of simple cubic ferromagnetic films with 10 to 50 layers using third order perturbed Heisenberg Hamiltonian, revealing how easy axes and anisotropy energies evolve with layer number.

Contribution

It applies third order perturbation theory to model magnetic energies in ferromagnetic films with varying layers, providing new insights into anisotropy direction shifts and energy variations.

Findings

Magnetic easy axis shifts from out-of-plane to in-plane as layers increase.

Magnetic anisotropy energy grows with the number of spin layers.

Easy and hard directions are identified through energy extremum plots.

Abstract

Magnetic energy of simple cubic structured ferromagnetic films with 10 to 50 spin layers was determined using third order perturbed Heisenberg Hamiltonian. By plotting 3-D plot of energy versus angle and stress induced anisotropy, the values of stress induced anisotropy corresponding to energy minimums and maximums were determined. By plotting the graphs of energy versus angle at these different stress induced anisotropy values, the easy and hard directions were determined. Magnetic easy and hard directions are related to energy minimums and maximums of the curve. Similar graphs were plotted for spin exchange interaction to determine the easy and hard directions. Graphs of energy versus angle were plotted by keeping all the magnetic energy parameters at constant values for each number of spin layers to determine the variation of magnetic easy directions, hard direction and corresponding energies with the number of spin layers. The magnetic easy axis gradually rotates from out of plane to in plane direction as the number of spin layers is increased. In addition, the magnetic anisotropy energy increases with the number of spin layers.