Tight binding study of single ion magnetic anisotropy of $\rm{Mn^{2+}}$ in Ga(Mn)As

Bulk uni-axial magnetic anisotropy of Ga(Mn)As observed in experiments has not been well understood as much as cubic magnetic anisotropy in the same material. We propose that the uni-axial anisotropy arises due to the coupling of local lattice distortions around $\rm{Mn^{2+}}$ impurity ion to its spin state through spin-orbit coupling of holes bound to the impurity ion. We model the coupling using nearest-neighbor tight-binding and many-body perturbation theory. The model includes intra-atomic Coulomb interaction inside $\rm{Mn^{2+}}$ ion, spin-orbit interaction of holes at the $\Gamma$ point, $p-d$ hopping interaction between $\rm{Mn^{2+}}$ ion $d$ orbitals and As ion $p$ orbitals, and strain due to local lattice distortions. We observe breaking of tetrahedral symmetry around the $\rm{Mn^{2+}}$ ion when the system is paramagnetic. We explore the effect of this broken symmetry in stabilizing certain magnetization directions through spin-orbit coupling in the ferromagnetic regime.