Mechanisms and origins of half-metallic ferromagnetism in CrO 2

摘要: Using a realistic low-energy model, derived from the first-principles electronic structure calculations, we investigate behavior of interatomic exchange interactions in ${\mathrm{CrO}}_{2}$, which is regarded to be one canonical half-metallic (HM) ferromagnetics. For these purposes employ dynamical mean-field theory (DMFT), based on exact diagonalization effective Anderson impurity Hamiltonian, was further supplemented with infinitesimal spin rotations for interactions. In order elucidate relative roles played by static and dynamic electron correlations, compare obtained results several techniques, including unrestricted Hartree-Fock (HF) approximation, DMFT (corresponding infinite frequency limit self-energy), optimized potential method treating correlation random-phase approximation. Our demonstrate that origin HM ferromagnetism ${\mathrm{CrO}}_{2}$ highly nontrivial. As far as neighboring coordination spheres are concerned, HF methods produce very similar results, due partial cancellation ferromagnetic (FM) double-exchange antiferromagnetic (AFM) superexchange contributions, represent two leading terms ${(\mathrm{\ensuremath{\Delta}}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathrm{\ensuremath{\Sigma}}})}^{\ensuremath{-}1}$ expansion ($\mathrm{\ensuremath{\Delta}}\stackrel{\ifmmode \^{}\fi{}}{\mathrm{\ensuremath{\Sigma}}}$ being intra-atomic splitting). Both contributions weaker approximation to, respectively, additional orbital polarization ${t}_{2g}$ states neglect correlations. The role higher-order twofold. On hand, they give rise FM interactions, tend stabilize state. other AFM long-range make state unstable single-site calculations minimal consisting bands. Thus, robust can easily using approximations, fortuitous this picture largely revised at level more rigorous approach. We argue main ingredients, missing direct magnetic oxygen $2p$ band. evaluate local-spin-density play important stability ground ${\mathrm{CrO}}_{2}$.