Theory of spin polarized photoelectron diffraction

Abstract

We discuss several aspects of the theory of spin-polarized photoelectron diffraction (SPPD). This method makes use of multiplet splittings of core-level binding energies to produce photoelectron peaks with high spin polarization (for example, the two principal peaks associated with Mn 3s emission from Mn 2+). We consider three possible mechanisms for spin-dependent photoelectron scattering and diffraction: exchange scattering by valence electrons (3d 5 for Mn 2+), spin-orbit scattering (which is not expected to yield large effects if the sample does not have a net magnetization), and spin-dependent inelastic scattering (which cannot yet be dealt with in a fully quantitative way, but is estimated to be less important than the other two). The fact that SPPD involves internal sources of polarized electrons references to their respective emitters implies that it can be employed to study magnetic order in both anti-ferromagnets and ferromagnets and at temperatures above their respective Néel or Curie points. The effects of exchange scattering on Mn 3s emission from Mn 2+ in KMnF 3 have been incorporated into a single-scattering cluster model of the diffraction process via either the Dirac-Hara or Kohn-Sham local density approximations. This model is applied to several cases: a single Mn 2+ scatterer, small clusters of Mn 2+ scatterers, and full clusters appropriate to the (110) surface of KMnF 3, with all atoms included. These calculations demonstrate that SPPD should be a short-range probe of magnetic order, a result consistent with conclusions reached in several prior studies of photoelectron diffraction without spin resolution. They also illustrate the perturbative nature of these effects, which are only about ca. 5–15% of the total intensity; this in turn leads to several possible simplifications in the theory. We have in addition phenomenologically modelled the decreases of short-range order with increasing temperature by using a Gaussian modulation of spins; this model produces curves of SPPD spin asymmetry versus Gaussian width which qualitatively agree with those observed experimentally (Phys. Rev. Lett. 55 (1986) 1227). Direct comparisons of the observed angular dependence of these spin asymmetries with theory for (110) KMnF 3 are also encouraging in that trends from one direction to another are in general predicted correctly. However, the maximum degree of asymmetry predicted by theory (13%) is somewhat below that of experiment (17%). Possible reasons for the discrepancies seen between theory and experiment are discussed, together with likely future directions of study.