Spin polarization of photoelectrons from the 5d shell of polarized Gd atoms: Application to the Gd 5dz2 surface state

The angular distribution of photoelectrons with defined spin orientation ejected from the 5d3/2 shell of polarized Gd atoms has been investigated theoretically. For free-atom calculations, a particular geometry of the experiment was chosen where the direction of the light beam is parallel (or antiparallel) to the direction of atomic polarization n. In this particular case, the angular distributions are the functions of the electron ejection angle θ relative to the direction n. In addition, we implied that the light is circularly polarized because in this case the degree of spin polarization is the highest. The calculations have been performed for the Gd ground state 4f75d(9D) in the nonrelativistic Hartree-Fock approximation, and many-electron correlation has been included using the random-phase approximation with exchange as developed for open-shell atoms. It is shown that in normal emission the photoelectron spin polarization has a well-defined value independent of photon energy, which is different for different kinds of alignment or orientation. The dependences of photoelectron spin polarization on the ejection angle are presented for different kinds of atomic polarization. The results can be applied to the investigation of the surface state of solid Gd that is known to be the 5d state, but not much is known about the character of this state. The influence of scattering from neighboring atoms on the results of the atomic calculations is investigated within a spin-dependent single scattering approximation in a two-step photoemission model. The calculations correspond to an experimental geometry with normal light incidence and to the polarization of the 5d electron being either in the direction of the surface normal or in the surface plane. It is shown that the results of the atomic model are strongly modulated by scattering processes. Some of the main peculiarities remain unchanged, but certain features arise that cannot be predicted in pure atomic theory