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A new scheme to calculate the exchange tensor$\underline{\underline{J}}_{ij}$ describing in a phenomenological way theanisotropic exchange coupling of two moments in a magnetically ordered systemis presented. The ab-initio approach is based on spin-polarised relativisticmultiple-scattering theory within the framework of spin-density functionaltheory. The scheme is applied to ferromagnetic CrTe as well as the dilutedmagnetic semiconductor (DMS) system Ga$_{1-x}$Mn$_{x}$As. In the later case theresults show that there is a noticeable anisotropy in the exchange couplingpresent, although not as pronounced as suggested in recent theoreticalinvestigations.

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