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Spin polarization and magnetic dichroism in photoemission from core and valence states in localized magnetic systems. II. Emission from open shells.

With the use of many-particle theory general equations are derived for the six fundamental spectra, which are special linear combinations of the spin-polarized photoemission spectra measured with left-, Z-, and right-circularly polarized radiation. These fundamental spectra, which are the isotropic spectrum, spin spectrum, magnetic circular dichroism, spin-orbit spectrum, anisotropic spectrum, and anisotropic spin spectrum give the correlation between the spin, orbital, and quadrupole momenta in the ground state and spin and orbit of the hole created after photoemission. For emission from an incompletely filled shell the integrated intensities of the fundamental spectra are proportional to the expectation values of the number of electrons, spin magnetic moment, orbital magnetic moment, the alignment between orbital and spin magnetic moment, the quadrupole moment, and the correlation between quadrupole and spin magnetic moment, respectively. This can be used to study the magnetic anisotropy of localized magnetic systems. We calculated the fundamental spectra for the 4f photoemission of the rare-earth ions and show that the multiplet structure displays a strong polarization dependence in agreement with our analysis in terms of correlations of moments and the rules for the integrated intensities. Finally we present the relation between the polarization effects in inverse photoemission and normal photoemission and we discuss the magnetic dichroism in metallic iron, cobalt, and nickel.