For cubic (001), ( 110) and ( 111) surface systems with in-plane or perpendicular magnetization, valence-band photoemission along the surface normal is studied analytically by evaluating electric dipole transition matrix elements between half-space initial and final states of the appropriate double-group symmetry. Explicit expressions are obtained for the spin-polarization vector of the photoelectrons, and the spin-averaged intensity and its change upon reversal of the magnetization direction, i.e. magnetic dichroism, for circularly and linearly polarized incident light. These results firstly elucidate the origin of spin polarization and dichroism in terms of an interplay between spin-orbit coupling and exchange, and secondly provide a systematic overview of possible effects. In particular, we predict new types of magnetic linear dichroism for s-polarized light in the case of magnetization perpendicular to surfaces with a twofold rotation axis and in the case of in-plane magnetization of fcc (111) or hcp (0001) surfaces.

The simultaneous ejection of two electrons from the ͑001͒ surface of W due to the collision of incident low-energy electrons with valence electrons has been studied experimentally and theoretically. Energy and momenta of the ejected electrons were measured simultaneously by a combination of coincidence and timeof-flight techniques. Calculations were performed in a relativistic distorted-wave Born approximation including exchange, in which the primary electron and the two emitted electrons are described by quasiparticle multiple scattering states. The valence electron is represented by linear combinations of Bloch waves matched at the surface. Screened Coulomb interaction matrix elements between these four states are evaluated. Experimental and calculated energy distributions from W͑001͒ for very-low-energy primary electrons at normal and grazing incidence are in fairly good overall agreement. Although some features of one-dimensional bulk densities of states are roughly reflected, Coulomb matrix elements with low-energy-electron-diffraction-type states play a vital role. Further analysis reveals in detail the importance of elastic scattering of the primary electron and of the two ejected electrons. Some observed features can be attributed to occupied surface states. ͓S0163-1829͑98͒05848-2͔

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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.

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