Octupolar vortex crystal and toroidal moment in twisted bilayer MnPSe$_3$

TL;DR

This paper explores higher-order multipole moments in twisted bilayer MnPSe$_3$, revealing vortex-like octupolar patterns and toroidal moments that could enable indirect detection of complex antiferromagnetic textures.

Contribution

It introduces the concept of octupolar vortex crystals and toroidal moments in twisted bilayer MnPSe$_3$, advancing understanding of multi-domain antiferromagnetic textures.

Findings

Octupolar moments are significant at domain walls.

Vortex patterns form in octupolar moments around antiferromagnetic domains.

Toroidal moments suggest potential for magnetoelectric effects.

Abstract

Experimental detection of antiferromagnetic order in two-dimensional materials is a challenging task due to the absence of net dipole moments. Identifying multi-domain antiferromagnetic textures via the current techniques is even more difficult. In order to address this challenge, we investigate the higher order multipole moments in twisted bilayer MnPSe$_3$. While the monolayers of MnPSe$_3$ exhibit in-plane N\'eel antiferromagnetic order, our atomistic simulations indicate that the moir\'e superlattices display a two-domain phase on each layer. We show that the octupolar moments $M_{33}^+$ and $M_{33}^-$ are significant in this multi-domain phase at the domain walls. In addition, when $[M_{33}^+,M_{33}^-]$ are represented by the $x$ and $y$ components of a vector, the resultant pattern of these octupole moments winds around the antiferromagnetic domains and forms to vortex crystals which leads to octupolar toroidal moments, $T_{xyz}$ and $T_{z}^{\beta}$. $T_{xyz}$ and $T_{z}^{\beta}$ can give rise to a magnetoelectric effect and gyrotropic birefringence that may provide indirect ways of detecting multi-domain antiferromagnetic order. Our results highlight the importance of higher-order multipole moments for identification of complex spin textures in moir\'e magnets.