Spin and charge order in doped spin-orbit coupled Mott insulators

TL;DR

This paper investigates how doping and bond angles affect charge and magnetic orders in a minimal model of spin-orbit coupled Mott insulators, revealing dominant magnetic fluctuations and charge density waves.

Contribution

It introduces a minimal Hubbard model with antisymmetric spin-orbit coupling to explain electronic properties of non-centrosymmetric TM oxides, supported by numerical and analytical methods.

Findings

In-plane antiferromagnetic fluctuations dominate at small doping and small bond angles.

Ferromagnetic fluctuations become dominant at larger bond angles.

Charge density wave order can be stabilized by strong Hubbard interactions.

Abstract

We study a two-dimensional single band Hubbard Hamiltonian with antisymmetric spin-orbit coupling. We argue that this is the minimal model to understand the electronic properties of locally non-centrosymmetric transition-metal (TM) oxides such as Sr$_2$IrO$_4$. Based on exact diagonalizations of small clusters and the random phase approximation, we investigate the correlation effects on charge and magnetic order as a function of doping and of the TM-oxygen-TM bond angle $\theta$. For small doping and $\theta$ $\lesssim$ $15^\circ$ we find dominant commensurate in-plane antiferromagnetic fluctuations while ferromagnetic fluctuations dominate for $\theta$ $\gtrsim$ $25^\circ$. Moderately strong nearest-neighbor Hubbard interactions can also stabilize a charge density wave order. Furthermore, we compare the dispersion of magnetic excitations for the hole-doped case to resonant inelastic X-ray scattering data and find good qualitative agreement.