Selection rules in (e, 2e) spectroscopy from ferromagnetic surfaces

Abstract

Electron pair emission from ferromagnetic crystalline surfaces, which occurs due to the collision of an incident low-energy electron with a valence electron, is shown to be governed by spatial and spin selection rules. Valence electron states with spatial parts antisymmetric with respect to the reaction plane are not observable for any spin configuration. If there is a spatial symmetry plane normal to the reaction plane, spin-polarized primary electrons selectively probe equal and opposite spin valence electrons. These analytical findings are further elaborated for ferromagnetic cubic (110) surfaces and illustrated by numerical results for Fe(110).

Spin-Resolved Mapping of Spin Contribution to Exchange-Correlation Holes

“…It has been demonstrated that the concept of the xc hole can be studied by the electron pair emission from surfaces. The xc hole manifests itself through a reduction of the pair emission intensity around the fixed emission direction of one electron, which we may call the depletion zone [3][4][5][6][7][8].…”

Spin-dependent two-electron emission from ferromagnetic Fe(001)

“…9] both arise almost exclusively from collisions with majority-spin valence electrons, except at energies very close to the Fermi energy and, for ϑ = 30 • , around −2.8 eV. This is in contrast to (e,2e) results from Fe(110), 22,37 which show that-for equal energies of the two emitted electrons-I + (I − ) is for most energies associated with minority (majority) valence electrons, i.e., there is mostly singlet scattering between the primary and the valence electron. The reason for this difference between Fe(001) and Fe(110) is that valence states, which are odd with respect to reflection at a plane perpendicular to the scattering plane and thence lead to triplet scattering, occur for Fe(110) only in a very small energy range well below E F , whereas for Fe(001) they are present over a wide energy range (cf.…”

“…Consequently, only valence electron states of even symmetry with respect to this plane are allowed to contribute to the (e,2e) intensity, as has been derived in previous work. 37 We therefore have to restrict the LDOS sum N σ τ to even states.…”

Spin-orbit effects in two-electron emission from ferromagnetic surfaces

“…In view of exploring the relation between the valence electron structure and the pair emission spectra, it is important to recall two (e,2e) selection rules, 49 which hold for our above-specified geometry. Since our reaction plane (x,z) is a mirror plane of the semi-infinite surface system, only valence states with even mirror symmetry are allowed to contribute.…”

“…Ref. 49). Only valence states with spatial parts of (single-group) symmetry types 1 and 3 are relevant: both types can contribute to antiparallel spin intensities, whereas parallel-spin intensities can only originate from 3 .…”