A technique for relativistic spin-polarised calculations

Abstract. Band structure calculations for the magnetic rare earth metals are complicated by both the necessity of including relativistic effects, and the desire to keep spin as a good quantum number for describing the Russell-Saunders-like 4f-shell and the exchange polarisa-tion of the conduction electrons. We present a technique for the reduction of the Dirac equation which initially omits the spin-orbit interaction (thus keeping spin as a good quantum number), but retains all other relativistic kinematic effects such as mass-velocity, Darwin, and higher order terms. The technique is easily adopted using existing non-relativistic band structure programs. Coupled first-order differential equations are solved which do not involve derivatives of the potential. The spin-orbit interaction can be included as a perturba-tion once the ‘relativistic ’ spin-polarised bands and wavefunctions have been obtained. The technique is used together with the local spin density approximation for exchange and cor-relation to calculate the self-consistent charge and spin density of a neutral G d atom. The calculated magnetic form factor agrees extremely well with experiment. Comparison with a paramagnetic RAPW calculation shows the procedure should be both accurate and fast for general band structure determinations. 1.

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