Magnetic properties of half metal from the paramagnetic phase: DFT+DMFT study of exchange interactions in CrO$_2$

We study magnetic properties of CrO$_2$ within the density functional theory plus dynamical mean-field theory (DFT+DMFT) approach in the paramagnetic phase. We consider the 3-orbital (per Cr site) model, containing only $t_{2g}$ states, the $5$-orbital model, including all $d$-states, as well as the model including also the oxygen $p$-states. Using the recently proposed approach of calculation of exchange interactions in paramagnetic phase, we extract exchange interaction parameters and magnon dispersions for these models. While the magnon dispersion in the 3-orbital model possesses negative branches in accordance with previous studies in ferromagnetic phase, this drawback is removed in the $5$-orbital model. The model including oxygen states (with purely local interaction at chromium sites) overestimates the exchange interactions and spin wave stiffness. While this overestimate is partly corrected by including non-local interaction between chromium and oxygen states within mean-field approximation, the $5$-orbital model appears as most adequate for describing magnetic properties of CrO$_2$ with local Coulomb interaction. The possibility of describing magnetic properties of this material starting from paramagnetic phase points to the correspondence of magnetic properties in this phase and ferromagnetic phase, as well as important contributions of double exchange in paramagnetic phase of CrO$_2$.