Theory of moir\'e magnetism in twisted bilayer $\alpha$-RuCl$_3$

TL;DR

This paper develops a comprehensive theoretical framework to understand the complex magnetic phases in twisted bilayer $ ext{RuCl}_3$, revealing how twist angle and interlayer exchange influence magnetic order and frustration.

Contribution

It introduces a combined first-principles and atomistic simulation approach to analyze magnetic phases in twisted bilayer $ ext{RuCl}_3$, uncovering new multi-domain structures and tunable magnetic frustration.

Findings

Large twist angles favor single wave vector zigzag order.

Small twist angles lead to complex multi-domain structures.

Magnetic frustration can be tuned via stacking and twist angle.

Abstract

Twisted heterostructures of van der Waals materials have received much attention for their many remarkable properties. Here, we present a comprehensive theory of the long-range ordered magnetic phases of twisted bilayer $\alpha$-RuCl$_3$ via a combination of first-principles calculations and atomistic simulations. While a monolayer exhibits zigzag antiferromagnetic order with three possible ordering wave vectors, a rich phase diagram is obtained for moir\'e superlattices as a function of interlayer exchange and twist angle. For large twist angles, each layer spontaneously picks a single zigzag ordering wave vector, whereas, for small twist angles, the ground state involves a combination of all three wave vectors in a complex hexagonal domain structure. This multi-domain order minimizes the interlayer energy while enduring the energy cost due to the domain wall formation. Our results indicate that magnetic frustration due to stacking-dependent interlayer exchange in moir\'e superlattices can be used to tune the magnetic ground state and enhance quantum fluctuations in $\alpha$-RuCl$_3$.