Anisotropy of the orbital methods and the magnetic dipole term $T_z$ in $\mathrm{C}\mathrm{r}{\mathrm{O}}_2$: An {\it ab-initio} studt

A systematic study is performed by the {\it ab-initio} density functional theory of the anisotropy of the orbital moments $<l_z>$ and the magnetic dipole term $<T_z>$ in bulk $\mathrm{C}\mathrm{r}{\mathrm{O}}_2$. Two different band-structure techniques are used (FLAPW and LMTO-ASA), and the electronic correlations are treated by the local-spin-density approximation (LSDA), the LSDA+ orbital polarization method, and the LSDA+$U$ method. The calculated anisotropies of $<l_z>$ and $<T_z>$ are very large compared to Fe, Ni and Co but still a factor of 5 and 2 smaller than the anisotropies obtained from a recently suggested analysis of the X-ray magnetic circular dichroism spectra for a thick layer of $\mathrm{C}\mathrm{r}{\mathrm{O}}_2$.