Spin-polarized low-energy (e, 2e) spectroscopy of non-magnetic surfaces

Abstract

For spin-polarized low-energy electrons impinging on non-magnetic crystalline surfaces, the collision with a valence electron and the ensuing emission of an electron pair are treated in a distorted-wave Born approximation formalism with exchange, in which the four relevant quasi-one-electron states are solutions of the Dirac equation. Numerical calculations for W(001), which were carried out in two coplanar geometries with normal and grazing incidence of a primary beam polarized normal to the reaction plane, show that the (e, 2e) cross section changes significantly upon reversal of the polarization. Originating mainly from spin-orbit coupling in the valence electron state, asymmetries of up to 30% occur in conjunction with sizable intensity. The calculated spectra respond sensitively to changes in the surface structure.

Spin-orbit coupling in tungsten by spin-polarized two-electron spectroscopy

“…Mirror reflection with respect to the E 1 − E 2 = 0 point transforms I + almost perfectly into I − and hence changes the sign of the difference spectrum. This is consistent with the theoretical prediction 17 and can be understood from the symmetry analysis of the experimental geometry (Fig. 1).…”

“…The origin of the spin-dependence in the ͑e ,2e͒ spectra, as pointed out, 17 is the spin-orbit coupling in at least one of the four relevant electron states: incident electron state, two outgoing electron states, and a valence electron state. The contribution of each of them to the observed spin-asymmetry can be revealed by a comparison of the measured spectra at different geometries with the appropriate calculations.…”

“…In such a geometrical arrangement one can expect in general a nonvanishing spin-asymmetry in measured spectra because of symmetry considerations. 17 A sketch of the experimental geometry is shown in Fig. 1.…”

“…15,16 The spin-orbit interaction, in turn, is dominant in the case of a nonmagnetic heavy (large Z) target (tungsten, for example). An extensive theoretical work on spin-polarized low-energy ͑e ,2e͒ spectroscopy of nonmagnetic surfaces 17 predicted an observable spin-asymmetry in the ͑e ,2e͒ cross section from tungsten. The collision of an incident electron with a valence electron of the target was treated in a distorted-wave Born approximation formalism with exchange, the four relevant quasi-one-electron states being solutions of the Dirac equation.…”

Theory of (e,2e) Spectroscopy from Ferromagnetic Surfaces

“…choosing the mirror plane as (x, z) and applying the transformation (y, y ) → (−y, −y ) to the integrals in Eqs. (9.4), (9.5), which by virtue of ϕ aσ 2 2…”