Anisotropic exchange coupling in diluted magnetic semiconductors:<i>Ab initio</i>spin-density functional theory

Abstract

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 ${\text{Ga}}_{1\ensuremath{-}x}{\text{Mn}}_{x}\text{As}$. 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.