Spin-Fluctuation-Driven Orbital Nematic Order in Ru-Oxides: Self-Consistent Vertex Correction Analysis for Two-Orbital Model

TL;DR

This paper demonstrates that spin fluctuations induce orbital nematic order in Sr$_3$Ru$_2$O$_7$ through a vertex correction mechanism, linking magnetic quantum criticality to nematicity in multiorbital systems.

Contribution

It introduces a self-consistent vertex correction analysis to show how spin fluctuations drive orbital nematic order, a mechanism overlooked by RPA.

Findings

Vertex correction causes strong spin-orbital fluctuation coupling.

Orbital nematic order is induced by magnetic quantum criticality.

Explains the relation between magnetism and nematicity in Sr$_3$Ru$_2$O$_7$.

Abstract

To reveal the origin of the "nematic electronic fluid phase" in Sr$_3$Ru$_2$O$_7$, 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. Due to this mechanism, orbital nematic order with $C_2$ symmetry is induced by the magnetic quantum criticality in multiorbital systems, while this mechanism is ignored in the random-phase-approximation. The present study naturally explains the intimate relation between the magnetic quantum criticality and the nematic state in Sr$_3$Ru$_2$O$_7$ and Fe-based superconductors.