Abstract:
The solution of fourth order perturbed Heisenberg Hamiltonian of bcc structured
ferromagnetic ultra-thin films with three spin layers with all seven magnetic energy
parameters were investigated. All the magnetic energy parameters such as spin
exchange interaction, magnetic dipole interaction, second order and fourth order
magnetic anisotropy constants, in plane and out plane applied magnetic fields,
demagnetization factor and stress induced anisotropy were included in the fourth
order perturbed Heisenberg Hamiltonian. 3D plot of total magnetic energy versus
angle and stress induced anisotropy were plotted for different values of second
order magnetic anisotropy constants. All other magnetic energy parameters were
fixed at constant values. All the peaks are closely packed in the graphs plotted
using fourth order perturbed Heisenberg Hamiltonian compared to peaks in the
graphs plotted using second and third order perturbed Heisenberg Hamiltonian.
The order of magnetic energy was changed when the values of second order
anisotropy constants of three spin layers are varied. The magnetic energy is higher,
when the values of second order magnetic anisotropy constant in the top spin layer
is less than those of the bottom and middle spin layers. The order of magnetic
energy is lower, when the values of second order magnetic anisotropy constant in
the middle spin layer is less than those of the top and bottom spin layers. In
addition, the angle between consecutive magnetic easy and hard direction is nearly
90 degrees for all the cases.
