Spin Polarised Relativistic Kkr
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SPIN POLARISED RELATIVISTIC KKR J.B.STAUNTON', M.MATSUMOTO** and P.STRANGEt *Department of Physics, University of Warwick, Coventry CV4 7AL, U.K. *-University of Library and Information Science,Tsukuba 305, Japan tDepartment of Physics, University of Keele, Keele ST5 5BG, U.K.
ABSTRACT We review spin polarised multiple scattering theory and show how it can provide a description of magnetic anisotropic effects in metallic systems. An interpretation in terms of the leading relativistic corrections is given; namely the interaction between spin-orbit coupling and spin polarisation. It is pointed out that it is straightforward to vary the direction of spin polarisation within this formalism. As simple illustrations, the cases of two and three impurities in a non-interacting relativistic' electron gas are outlined and the origin of pseudo-dipolar and Dzyaloshinski-Moriya anisotropy highlighted. We go on to compare and contrast estimates of magneto-crystalline anisotropies of transition metals with those from alternative methods. Finally we discuss the paramagnetic spin susceptibility of metals within this framework and show that this work is complementary to magnetic anisotropy energy calculations. A generalised Stoner condition for the onset and direction of the magnetisation is given. Calculations for h.c.p. metals cobalt, scandium and yttrium are presented. We conclude by pointing out that this approach can be extended to set up a theory for the dynamical susceptibility with consequent implications for anisotropy of spin wave excitations.
Introduction When the relativistic effects of an interacting gas of electrons in a metal are treated accurately, one of their most pertinant consequences is the linkage of the equilibrium direction of the magnetisation with the crystallographic axes. It is well known that the magnetic properties of metals are driven predominantly by the exchange interactions between electrons but these are apparently independent of any spatial direction. It is only when the electrons' orbital motions are coupled to their spin degrees of freedom that magnetic anisotropy effects appear. In this paper we review a multiple scattering approach to these sorts of problems. In the first section, the scattering of a relativistic electron from a single spherically symmetric target potential with a magnetic component will be covered. This will be extended to many scatterers. The following section will set out a formalism for calculating the magnetic anisotropy energy with simple illustrations of two and three magnetic impurities embedded in relativistic jellium. Magneto-crystalline energy calculations within the multipie scattering framework will be briefly cited. Finally we will describe our recent work on the paramagnetic spin susceptibility of metals highlighting the magnetic anisotropy effects.
Relativistic,Spin Polarised Multiple Scattering Theory. An inhomogeneous relativistic electron gas subjected to external fields can be examined with an appropriate generalisation of Density Functional theory. Raja
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