SPIN POLARIZATION AND MAGNETIC DICHROISM IN PHOTOEMISSION FROM CORE AND VALENCE STATES IN LOCALIZED MAGNETIC SYSTEMS .3. ANGULAR-DISTRIBUTIONS

A general analysis is presented for angle-dependent photoemission from magnetic and oriented atoms using linearly and circularly polarized x-rays. The anisotropy in the angular distribution in a localized material is due to the polarization of the photon, the polarization of the shell from which the electron is emitted, and the Coulomb and exchange interactions of the hole with the polarized valence electrons in the final state of the photoionized atom. The angular dependence of the dipole excited photoemission gives the same information about the multipole orbital and spin magnetic moments of the atom as excitation with quadrupole or octupole radiation. It is shown that the photoemission spectrum at an arbitrary angle is a linear combination of the fundamental spectra, which contain all the physical information of the atom. Redundancy in the measurements makes it possible to obtain these fundamental spectra in completely different ways, allowing to choose the most advantageous geometry and polarization, e.g., the magnetic circular dichroism can be also be measured with linear polarization. Circular dichroism in the angular dependence, magnetic linear dichroism in the angular dependence, and spin polarization are treated using the same analysis. We explain the strong angle dependence observed in the rare-earth 5p photoemission, in the circular dichroism of the 3d transition-metal 2p core-level photoemission and the rare-earth 4f photoemission.