Variation of magnetic easy direction of bcc structured ferromagnetic films up to thirty spin layers

Abstract

Third order Heisenberg Hamiltonian was employed to determine the effect of number of spin layers on magnetic easy direction. 3-D graph of energy versus stress induced anisotropy and angle was plotted to find magnetic easy and hard directions. First values of stress induced anisotropy corresponding to minima and maxima of this 3-D plot were determined. Then the graph of energy versus angle was plotted at each of these stress induced anisotropy values in order to determine magnetic easy and hard directions. The same approach was applied to find the easy and hard directions for different values of spin exchange anisotropy. Magnetic easy direction gradually rotates from out of plane to in plane direction of the film, as the number of spin layers is increased from 10 to 30. The magnetic anisotropy energy (energy difference between magnetic easy and hard directions) gradually increases as the number of layers is increased. However, the angle between easy and hard directions doesn’t change considerably in this range of thickness. Our theoretical data agree with experimental data obtained by some other researchers. Easy axis oriented magnetic thin films are useful in magnetic memory devices due to the higher magnetic anisotropy and higher energy density.

Keywords

• heisenberg hamiltonian, third order perturbation, magnetic easy axis, spin layers