A systematic electronic structure study of A2CrB′O6 (A = Ca, Sr; B′ = W, Re, and Os) has been performed by employing the local spin-density approximation (LSDA) as well as the GGA and LSDA + U methods using the fully relativistic spin-polarized Dirac linear muffin-tin orbital band-structure method. We investigated the effects of the subtle interplay among the spin-orbit coupling, electron correlations, and lattice distortion on the electronic structure of the double perovskites. First principles calculations predict that Sr2CrOsO6 is (before considering spin-orbit coupling) actually a ferrimagnetic semimetal with precisely compensating spin moments, or spin-asymmetric compensated semimetallic ferrimagnet in which the electrons and holes are each fully polarized and have opposite spin directions, in spite of a zero net moment and hence no macroscopic magnetic field. Spin-orbit coupling degrades this by giving a nonzero total moment, but the band structure is little changed. Therefore, the observed saturation moment of ferrimagnetic Sr2CrOsO6 is entirely due to spin-orbit coupling. The x-ray absorption spectra and x-ray magnetic circular dichroism at the W, Re, Os, and Cr L2,3, and Cr and O K edges were investigated theoretically from first principles. A qualitative explanation of the XMCD spectra shape is provided by the analysis of the corresponding selection rules, orbital character and occupation numbers of individual orbitals. The calculated results are in good agreement with experimental data. The complex fine structure of the Cr L2,3 XAS in Sr2CrWO6 and Sr2CrReO6 was found to be not compatible with a pure Cr3+ valency state. The interpretation demands mixed valent states. We found that possible oxygen vacancies lead to a mixed valency at the Cr site, double peak structure at the Cr L2,3 edges and reduce the saturation magnetization in Sr2CrWO6 and Sr2CrReO6.
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