# Deriving models for the Kitaev spin-liquid candidate material $\alpha$-RuCl$_3$ from first principles

## TL;DR

This paper derives a detailed first-principles model for $ ext{RuCl}_3$, revealing significant non-local Coulomb and spin-orbit effects that influence magnetic interactions, aiding the understanding of quantum spin liquids.

## Contribution

It introduces a first-principles Wannier model for $ ext{RuCl}_3$ including non-local Coulomb and spin-orbit interactions, and analyzes their impact on magnetic properties.

## Key findings

- Non-local Coulomb repulsions significantly enhance magnetic interactions.
- Spin-orbit coupling contains notable non-local contributions.
- Results differ from previous experimental fits, indicating complex interactions.

## Abstract

We use the constrained random phase approximation (cRPA) to derive from first principles the Ru-$t_{2g}$ Wannier function based model for the Kitaev spin-liquid candidate material $\alpha$-RuCl$_3$. We find the non-local Coulomb repulsion to be sizable compared to the local one. In addition we obtain the contribution to the Hamiltonian from the spin-orbit coupling and find it to also contain non-negligible non-local terms. We invoke strong coupling perturbation theory to investigate the influence of these non-local elements of the Coulomb repulsion and the spin-orbit coupling on the magnetic interactions. We find that the non-local Coulomb repulsions cause a strong enhancement of the magnetic interactions, which deviate from experimental fits reported in the literature. Our results contribute to the understanding and design of quantum spin liquid materials via first principles calculations.