Orbital Resolved Soft X-Ray Spectroscopy in NaV2O5

We demonstrate that angle-resolved soft x-ray spectroscopy can resolve absorption by inequivalent oxygen sites and by different orbitals belonging to the same site in ${\mathrm{NaV}}_{2}{\mathrm{O}}_{5}.$ By rotating the polarization direction, we see a dramatic change in the absorption spectra at the oxygen K edge. Our theory identifies the detailed composition of the spectra and predicts a correct energy ordering of the orbitals of three inequivalent oxygen atoms. Because different orbitals dominate absorption spectra at different energies and angles, one can excite at a specific site and ``orbital.'' In contrast, absorption at the vanadium L edge does not show large changes when varying the polarization direction. The reason for this is that different excitation channels (involving different initial states for the excited electron) overlap in energy and vary in compensating ways, obscuring each channel's sensitive polarization dependence.