Five Layered FCC Ferromagnetic Films as Described by Modified Second Order Perturbed Heisenberg Hamiltonian

For the first time, the 2^nd order perturbed Heisenberg Hamiltonian with all the seven magnetic energy parameters was solved for fcc structured ferromagnetic films with five layers. Previously, the 2^nd order perturbed Heisenberg Hamiltonian was solved for four layered ferromagnetic films under some special assumptions by us. However, the exact solution of 2^nd order perturbed Heisenberg Hamiltonian without any special assumption is formulated in this manuscript. The magnetic easy and hard directions were determined using the angles corresponding to the energy minimum and maximum in the 3-D and 2-D plots. The shape of the 3-D plots doesn’t change with the number of layers except the position of spikes. However, the magnetic easy direction varies with the number of layers. Most of the theoretical data obtained by our model agree with the experimental data of ferromagnetic thin films.