  We compute the magnetocrystalline anisotropy energy within two-dimensional
Rashba models. For a ferromagnetic free-electron Rashba model, the magnetic
anisotropy is exactly zero regardless of the strength of the Rashba coupling,
unless only the lowest band is occupied. For this latter case, the model
predicts in-plane anisotropy. For a more realistic Rashba model with finite
band width, the magnetic anisotropy evolves from in-plane to perpendicular and
back to in-plane as bands are progressively filled. This evolution agrees with
first-principles calculations on the interfacial anisotropy, suggesting that
the Rashba model captures energetics leading to anisotropy originating from the
interface provided that the model takes account of the finite Brillouin zone.
The results show that the electron density modulation by doping or an external
voltage is more important for voltage-controlled magnetic anisotropy than the
modulation of the Rashba parameter.
