Analysis of x-ray magnetic circular dichroism in the half-metallic ferromagnet CrO2

We report a theoretical analysis of x-ray magnetic circular dichroism (XMCD) at the Cr-$L$ edge in half-metallic ferromagnetic ${\mathrm{CrO}}₂$. First, since the XMCD spectrum is the difference between the x-ray absorption spectra (XAS) for right- and left-handed circularly polarized x rays, a general perturbative method of calculating XAS spectra is developed by means of the Keldysh Green's function technique for nonequilibrium states. Subsequently, it is applied to the analysis of XMCD of half-metallic ferromagnetic ${\mathrm{CrO}}₂$. Calculated XAS and XMCD spectra are compared with several previous experimental data. It is clearly shown that effects of the atomiclike Coulomb interaction between the $2p$ and $3d$ states are indispensable ingredients to yield good agreement with the experiments. Such strong $2p\text{\ensuremath{-}}3d$ correlation may originate from a peculiarity of the half-metallic ferromagnetic state. Evaluation of the validity of sum rules is made within our framework.