Anisotropic exchange coupling in diluted magnetic semiconductors:Ab initiospin-density functional theory

A different scheme to calculate the exchange tensor ${\underset{͇}{J}}_{ij}$ describing in a phenomenological way the anisotropic exchange coupling of two moments in a magnetically ordered system is presented. The ab initio approach is based on spin-polarized relativistic multiple-scattering theory within the framework of spin-density functional theory. The scheme is applied to ferromagnetic CrTe as well as the diluted magnetic semiconductor system ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$. In the latter case the results show that there is a noticeable anisotropy in the exchange coupling present, although not as pronounced as those suggested in recent theoretical investigations.