Spin-fluctuation-driven orbital nematic order in Ru-oxides: Self-consistent vertex correction analysis for two-orbital model

To reveal the origin of the "nematic electronic fluid phase" in Sr₃Ru₂O₇, we apply the self-consistent vertex correction analysis to the (d_xz, d_yz)-orbital Hubbard model. It is found that the Aslamazov-Larkin type vertex correction causes the strong coupling between spin and orbital fluctuations, which corresponds to the Kugel-Khomskii spin-orbital coupling in the local picture. Owing to this mechanism, orbital nematic order with C₂ symmetry is induced by the magnetic quantum criticality in multiorbital systems, whereas this mechanism is ignored in the random-phaseapproximation (RPA). This study provides a natural explanation for the close relationship between the magnetic quantum criticality and nematic state in Sr₃Ru₂O₇ and Fe-based superconductors.