  Magnetic anisotropy controls the orientational stability and switching
properties of magnetic states, and therefore plays a central role in
spintronics. First-principles density-functional-theory calculations are able,
in most cases, to provide a satisfactory description of bulk and interface
contributions to the magnetic anisotropy of particular film/substrate
combinations. In this paper we focus on achieving a simplified understanding of
some trends in interfacial magnetic anisotropy based on a simple tight-binding
model for quasiparticle states in a heavy-metal/ferromagnetic-metal bilayer
film. We explain how to calculate the magnetic anisotropy energy of this model
from the quasiparticle spin-susceptibility, compare with more conventional
approaches using either a perturbative treatment of spin-orbit interactions or
a direct calculation of the dependence of the energy on the orientation of the
magnetization, and show that the magnetic anisotropy can be interpreted as a
competition between a Fermi-sea term favoring perpendicular anisotropy and a
Fermi-surface term favoring in-plane anisotropy. Based on this finding, we
conclude that perpendicular magnetic anisotropy should be expected in an
itinerant electron thin film when the spin magnetization density is larger than
the product of the band exchange splitting and the Fermi level
density-of-states of the magnetic state.
