A relativistic treatment of interacting spin-aligned electron systems: application to ferromagnetic iron, nickel and palladium metal

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Abstract
The authors use a relativistically extended version of the one-particle formalism. The electron-electron interaction is assumed to be non-relativistic Coulombic as before. As a consequence, the one-particle Dirac-type equations which now stand in place of the formerly employed Kohn-Sham type equations, contain a diagonal 4*4 matrix whose elements represent the various potential contributions including spin-dependent local potentials describing exchange and correlation as in the non-relativistic case. If asphericity effects of the resulting potential are negligible, these Dirac equations can exactly be reduced to relativistic two-component Pauli-type equations with a diagonal exchange-correlation matrix and a spin-orbit coupling matrix. The latter equations are used to self-consistently calculate the electronic structure of nickel, iron and palladium metal. In addition, the calculation provides magnetic anisotropy energies. The band structure of iron is discussed in detail and compared with other theoretical studies based on different band theoretical methods. The calculations on Pd metal lead without spin-orbit coupling to ferromagnetic spin alignment when the metal is expanded by approximately 5% of the lattice constant. If spin-orbit coupling is included in the self-consistent calculations, the alignment disappears. This effect can only be counteracted by further expanding the lattice up to approximately 10%.

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