Fe3O4 thick films as described by second order perturbed Heisenberg Hamiltonian

Modified second order perturbed Heisenberg Hamiltonian has been used to explain magnetic properties including magnetic easy axis orientation of Fe3O4 thick films up to 1000 spin layers. The variation of magnetic easy and hard directions with the number of spin layers and stress induced anisotropy was investigated. 3-D plot of energy versus angle and number of spin layers was plotted to find the values of number of spin layers corresponding to energy minima and maxima. By plotting the curve of energy versus angle at one selected value of number of layers, magnetic easy and hard directions were determined. Similarly 3-D plot of energy versus angle and stress induced anisotropy was plotted to find the values of stress induced anisotropy corresponding to energy minima and maxima. Then the curve of energy versus angle at one selected value of stress induced anisotropy was plotted to find the magnetic easy and hard directions. MATLAB software was employed to plot all the graphs.