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, Cr 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 Cr 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-d hybridization.

Magnetic x-ray microdiffraction

“…Resonant effects appear mainly as the development of a small probability of scattering while rotating the polarization [36]. Density functional theory calculations using the local density approximation show that the orbital moment in Cr is approximately a factor of ten smaller than in ferromagnetic Fe, Co or Ni and that the orbital magnetic moment arises through a spin orbit interaction with the SDW [98]. In practical terms, the overall resonant enhancement of scattering does not outweigh the increase in the absorption and fluorescence at the resonance.…”

4p States and X-Ray Spectroscopy

“…The OP is induced by the coupling to the OP in the 3d bands at neighboring sites through p-d hybridization. We explain this scenario by taking up the spin density wave (SDW) phase in Cr metal [39].…”

“…This period is very close to the observed value at T SF . We carry out the band calculation self-consistently with a large unit cell [39]. Within the LDA method and the MT approximation, we obtain the LSDW and TSDW phases as stable solutions with the magnetic moment written as…”

Ab InitioStudy ofL-edge X-ray Resonant Scattering from Chromium in Spin Density Wave State

“…13) For details of the calculation, we refer to ref. 16. A stable solution of the SDW state is obtained.…”

“…8) These K-edge spectra have been fully analyzed by ab initio band structure calculation. 16) Figure 1 depicts the superlattice in the SDW state. The local spin moments are approximately described by…”