Orbital degeneracy, orbital polarization and x-ray absorption linear dichroism in transition-metal oxides

On the basis of exact diagonalization of a single-ion Hamiltonian, we calculate Mn and Ti L-2,L-3 x-ray absorption linear dichroism (XLD) spectra for manganites with trivalent Mn ion and YTiO3, where antiferro-orbital ordering among the degenerate e(g) and t(2g) states, respectively, are reported. For the orbital polarization given by a superposition of the doubly degenerate e(g) states, the superposition is shown to be reflected in the integrated XLD intensity, while not in XLD spectral shape. In the case of the triply degenerate t(2g) states, on the other hand, the superposition is shown to be reflected in both the integrated intensity and the spectral shape. In both e(g) and t(2g) systems, XLD is shown to be a promising method in identifying orbital polarization.