Abstract
Magnetic energy of fcc structured ferromagnetic thin films was investigated using third order perturbed Heisenberg Hamiltonian with seven magnetic energy parameters by a MATLAB computer program for the first time. Spin exchange interaction, magnetic dipole interaction, second order anisotropy, fourth order anisotropy, applied field, demagnetization factor and stress induced anisotropy were taken into account. Ultra-thin films with three layers (N=3) were considered. Several magnetic easy and hard directions were found in all the 3-D plots. According to some graphs, the angle between easy and hard directions was 90 degrees. Previously, the third order perturbed Heisenberg Hamiltonian with spin exchange interaction, second order magnetic anisotropy and stress induced anisotropy terms only was solved manually for ferromagnetic films with two and three layers by us. Due to the unavailability of the experimental values of these seven magnetic parameters, some reasonable values were used for this simulation.
Highlights
The Heisenberg Hamiltonian up to 2nd order perturbation with few magnetic energy parameters has been solved by some other researchers
All the graphs are given for fcc structured ferromagnetic film with three layers (N=3)
The angle between easy and hard directions is 90 degrees according to Figures 2 and 4
Summary
The Heisenberg Hamiltonian up to 2nd order perturbation with few magnetic energy parameters has been solved by some other researchers. Ferromagnetic thin films have been studied using the Heisenberg Hamiltonian with spin exchange interaction, magnetic dipole interaction, applied magnetic field, second and fourth order magnetic anisotropy terms (Hucht and Usadel, 1997; Hucht and Usadel, 1999; Usadel and Hucht, 2002). Electric and magnetic properties of multiferroic thin films have been theoretically explained by modified Heisenberg and transverse Ising model using Green’s function technique (Kovachev and Wesselinowa, 2009). Easy and hard direction can be found using this 3-D plot.
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