Third order perturbed Heisenberg Hamiltonian of spinel ferrite ultra-thin films

Abstract

The classical Heisenberg Hamiltonian equation of spinel ferrite ultra-thin films will be solved for third order perturbation. When second order anisotropy constant do not vary within the film of N=2, the film behaves as an oriented film. But the film of N=3 does not behave as an oriented film even for invariant second order anisotropy. Also the second and third order perturbations become zero in perpendicular and in plane directions, indicating that films behave as oriented films. For N-2 film, nearest maximum and minimum can be observed at 45 0 and 135 0 , respectively. For N=3, the first nearest maximum and minimum are observed at 470 and 1370 , respectively. In both cases, the angle between easy and hard direction is 900 , and the energy at hard or easy directions does not vary with angle. The 3- D plot of total energy versus angle and stress induced anisotropy indicates some energy minimums. Fourth order anisotropy slightly destroys the smoothness of the energy curve with N=3.