  Magnetic energy of simple cubic structured ferromagnetic films with 10 to 50
spin layers was determined using third order perturbed Heisenberg Hamiltonian.
By plotting 3-D plot of energy versus angle and stress induced anisotropy, the
values of stress induced anisotropy corresponding to energy minimums and
maximums were determined. By plotting the graphs of energy versus angle at
these different stress induced anisotropy values, the easy and hard directions
were determined. Magnetic easy and hard directions are related to energy
minimums and maximums of the curve. Similar graphs were plotted for spin
exchange interaction to determine the easy and hard directions. Graphs of
energy versus angle were plotted by keeping all the magnetic energy parameters
at constant values for each number of spin layers to determine the variation of
magnetic easy directions, hard direction and corresponding energies with the
number of spin layers. The magnetic easy axis gradually rotates from out of
plane to in plane direction as the number of spin layers is increased. In
addition, the magnetic anisotropy energy increases with the number of spin
layers.
