Mechanisms and origins of half-metallic ferromagnetism inCrO2

Abstract

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