Electronic structure of $\boldsymbol{\alpha}$-RuCl$_3$ by fixed-node and fixed-phase diffusion Monte Carlo methods

TL;DR

This study uses advanced quantum Monte Carlo methods to analyze the electronic structure of $oldsymbol{ extalpha}$-RuCl$_3$, demonstrating that electron correlations primarily determine the band gap, with spin-orbit effects being relatively minor.

Contribution

It introduces fixed-node and fixed-phase diffusion Monte Carlo calculations with explicit spin-orbit treatment to accurately study $oldsymbol{ extalpha}$-RuCl$_3$'s electronic structure.

Findings

QMC accurately describes the band gap of $oldsymbol{ extalpha}$-RuCl$_3$

Spin-orbit coupling has a minor effect on the gap (~0.2 eV)

QMC results align well with experiments and hybrid DFT/DFT+U methods.

Abstract

Layered material $\alpha$-RuCl$_3$ has caught wide attention due to its possible realization of Kitaev's spin liquid and its electronic structure that involves the interplay of electron-electron correlations and spin-orbit effects. Several DFT$+U$ studies have suggested that both electron-electron correlations and spin-orbit effects are crucial for accurately describing the band gap. This work studies the importance of these two effects using fixed-node and fixed-phase diffusion Monte Carlo calculations both in spin-averaged and explicit spin-orbit formalisms. In the latter, the Slater-Jastrow trial function is constructed from two-component spin-orbitals using our recent quantum Monte Carlo (QMC) developments and thoroughly tested effective core potentials. Our results show that the gap in the ideal crystal is already accurately described by the spin-averaged case, with the dominant role being played by the magnetic ground state with significant exchange and electron correlation effects. We find qualitative agreement between hybrid DFT, DFT+$U$, and QMC. In addition, QMC results agree very well with available experiments, and we identify the values of exact Fock exchange mixing that provide comparable gaps. Explicit spin-orbit QMC calculations reveal that the effect of spin-orbit coupling on the gap is minor, of the order of 0.2 eV, which corresponds to the strength of the spin-orbit of the Ru atom.