A systematic study is performed by the ab initio density-functional theory of the anisotropy of the orbital moments ͗l z ͘ and the magnetic dipole term ͗T z ͘ in bulk CrO 2 . Two different band-structure techniques are used ͑full potential linearized-augmented-plane-wave method and linear-muffin-tin-orbital method in the atomic-sphere approximation͒, and the electronic correlations are treated by the local-spin-density approximation ͑LSDA͒, the LSDAϩ orbital polarization method, and the LSDAϩU 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 CrO 2 . DOI: 10.1103/PhysRevB.69.132409 PACS number͑s͒: 75.30.Gw, 71.15.Mb Recent research within the fields of magnetic tunneling and spin injection involves CrO 2 as a promising material for electrodes.1 Besides its potential importance for applications, this material also exhibits interesting physics originating from its half metallic nature and consequently the ferromagnetism due to the double-exchange coupling, 2 as well as from its orbital magnetism 3,4 which is related to the spinorbit coupling and the electronic orbital correlation effects. Consequently, there are already several experimental 3,4 and theoretical 4 -7 investigations of the orbital moments ͗l z ͘ in CrO 2 .However, much less information is available on the anisotropy of the orbital moments, i.e., on its dependence of the orientation of the sample magnetization ͑in the following the z axis of the external coordinate system is always chosen to be parallel to the magnetization direction͒. It has been pointed out first by Bruno 8 and later worked out in more detail by van der Laan 9 that the anisotropy of the orbital moment is closely related to the magnetocrystalline anisotropy energy. Furthermore, van der Laan has shown that there is an additional contribution to the anisotropy energy arising from the anisotropy of the magnetic dipole term T z , which is the expectation value of the magnetic dipole operator:In Eq. ͑1͒ r is the unit vector in the direction of the position vector r and is the vector of the Pauli matrices. In fact, it turns out ͑see below͒ that for CrO 2 the two contributions are very large and of similar magnitudes but opposite in sign.A suitable method to investigate the anisotropy of ͗l z ͘ and ͗T z ͘ is the angle-resolved variant 10 of the x-ray magnetic circular dichroism 11 ͑XMCD͒ which measures the XMCD spectra for various orientations of the sample magnetization.The orbital moments ͗l z ͘ then may be determined directly from the application of the XMCD orbital sum rule.12 In contrast, the application of the spin sum rule 13 yields a combination of the spin moment ͗ z ͘ and the ͗T z ͘ term. A separation of these two contributions is possible by applying the spin sum rule to XMCD spectra for various orientations of the sample magnetization. Cr atom in a thick l...