Role of orbital off-diagonal spin and charge condensates in a three orbital model for $\rm Ca_2RuO_4$ -- Coulomb renormalized spin-orbit coupling, orbital moment, and tunable magnetic order

TL;DR

This paper investigates how orbital off-diagonal spin and charge condensates influence spin-orbit coupling, orbital moments, and magnetic order in Ca2RuO4, revealing tunable magnetic phases driven by structural distortions and SOC strength.

Contribution

It introduces a fully self-consistent approach that captures anisotropic SOC renormalization and orbital magnetic moments, elucidating the tunability of magnetic order in ruthenates.

Findings

Strong anisotropic SOC renormalization observed.

Magnetic order can be tuned between AFM and FM by structural parameters.

Self-consistent solutions reveal planar FM order relevant for Ca3Ru2O7.

Abstract

Strongly anisotropic spin-orbit coupling (SOC) renormalization and strongly enhanced orbital magnetic moments are obtained in the fully self consistent approach including the orbital off-diagonal spin and charge condensates. For moderate tetragonal distortion as in $\rm Ca_2 RuO_4$, dominantly planar antiferromagnetic (AFM) order with small canting of moments in and about the crystal $c$ axis are obtained. For reduced tetragonal distortion, we find a tunable regime wherein the magnetic order can be tuned (AFM or FM) by the bare SOC strength and octahedral tilting magnitude. In this regime, with decreasing tetragonal distortion, AFM order is maintained by progressively decreasing octahedral tilting, as observed in $\rm Ca_{2-x}Sr_x RuO_4$. For purely planar order, the only self consistent solution is FM order along crystal $b$ axis, which is relevant for the bilayer ruthenate compound $\rm Ca_3 Ru_2 O_7$.