A new scheme to calculate the exchange tensor and its application to diluted magnetic semiconductors

A new scheme to calculate the exchange tensor $\underline{\underline{J}}_{ij}$ 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-polarised 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 (DMS) system Ga$_{1-x}$Mn$_{x}$As. In the later case the results show that there is a noticeable anisotropy in the exchange coupling present, although not as pronounced as suggested in recent theoretical investigations.