Coupled spin-orbital fluctuations in a three orbital model for $4d$ and $5d$ oxides with electron fillings $n=3,4,5$ -- Application to $\rm NaOsO_3$, $\rm Ca_2RuO_4$, and $\rm Sr_2IrO_4$

TL;DR

This paper develops a unified theoretical framework to analyze coupled spin-orbital excitations in three-orbital models relevant to 4d and 5d oxides, capturing various modes and their relation to complex magnetic behaviors.

Contribution

It introduces a generalized fluctuation propagator within a self-consistent Hartree-Fock approach for realistic three-orbital models, including all Coulomb interactions and multiple excitation modes.

Findings

Identification of low-energy magnon, orbiton, and spin-orbiton modes.

Discovery of high-energy spin-orbit exciton and Hund's coupling induced gapped magnon modes.

Application to real compounds like NaOsO3, Ca2RuO4, and Sr2IrO4.

Abstract

A unified approach is presented for investigating coupled spin-orbital fluctuations within a realistic three-orbital model for strongly spin-orbit coupled systems with electron fillings $n=3,4,5$ in the $t_{2g}$ sector of $d_{yz},d_{xz},d_{xy}$ orbitals. A generalized fluctuation propagator is constructed which is consistent with the generalized self-consistent Hartree-Fock approximation where all Coulomb interaction contributions involving orbital diagonal and off-diagonal spin and charge condensates are included. Besides the low-energy magnon, intermediate-energy orbiton and spin-orbiton, and high-energy spin-orbit exciton modes, the generalized spectral function also shows other high-energy excitations such as the Hund's coupling induced gapped magnon modes. We relate the characteristic features of the coupled spin-orbital excitations to the complex magnetic behavior resulting from the interplay between electronic bands, spin-orbit coupling, Coulomb interactions, and structural distortion effects, as realized in the compounds $\rm NaOsO_3$, $\rm Ca_2RuO_4$, and $\rm Sr_2IrO_4$.