Resonant magnetic x-ray scattering spectra in spin-density-wave state of Cr fromab initioband structure calculations

Abstract

Using ab initio band structure calculation based on the local density approximation, $\mathrm{Cr}\phantom{\rule{0.2em}{0ex}}K$-edge resonant x-ray magnetic scattering spectra are analyzed in the spin-density-wave (SDW) state of chromium. We perform a band structure calculation, assuming an ideal bcc lattice structure with the experimental lattice constant and a commensurate SDW state with the propagation vector close to the observed value at the spin-flip temperature. Taking account of the spin-orbit interaction, we obtain the orbital moment on each Cr site induced in proportion to the local spin moment, which is quite small, at most a tenth of those in nickel or iron. In spite of the tiny $3d$ orbital moment, the orbital polarization is found to have large fluctuations as a function of energy. We obtain the scattering intensity at the $\mathrm{Cr}\phantom{\rule{0.2em}{0ex}}K$-edge on the SDW magnetic Bragg spot, which shows resonant enhancement in good agreement with the experiment. The $3d$ orbital polarization is found to be highly correlated with the intensity of the resonant main peak, indicating that the $4p$ orbital polarization is induced mainly by the $3d$ orbital polarization through $p\text{\ensuremath{-}}d$ hybridization.