# Orbital Magnetic Field Effects in Mott Insulators with Strong Spin-Orbit Coupling

## TL;DR

This paper investigates how magnetic fields influence the exchange interactions in Mott insulators with strong spin-orbit coupling, revealing a mechanism that modulates magnetic properties relevant to Kitaev spin liquids.

## Contribution

It introduces a novel mechanism where Peierls phases affect magnetic exchange in Mott insulators with strong SO coupling, applicable to Kitaev models and extensions.

## Key findings

- Peierls phases modulate exchange interactions at leading order.
- Variation of exchange constants with magnetic flux is explicitly calculated.
- Implications for experimental detection of Kitaev spin liquids are discussed.

## Abstract

We study the effect of a magnetic field on the low energy description of Mott insulators with strong spin-orbit (SO) coupling. In contrast to the standard case of the Hubbard model without SO coupling, we show that Peierls phases can modulate the magnetic exchange at leading order in the interaction. Our mechanism crucially depends on the existence of distinct exchange paths between neighboring magnetic ions enclosing a well-defined area. Thus it will generically be present in any solid state realisation of the Kitaev model and its extensions. We explicitly calculate the variation of the exchange constants of the so-called $JK\Gamma$ model as a function of the magnetic flux. We discuss experimental implications of our findings for various settings of candidate Kitaev spin liquids.