Octupolar Vortex Crystal and Toroidal Moment in Twisted Bilayer MnPSe<sub>3</sub>.

Akram, Muhammad; Yang, Fan; Birol, Turan; Erten, Onur · Nano Lett · 2025

basic_science · Level V

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Abstract

Experimental detection of antiferromagnetic order in two-dimensional materials is a challenging task. Identifying multidomain antiferromagnetic textures via the current techniques is even more difficult. Therefore, we investigate the higher-order multipole moments in twisted bilayer MnPSe<sub>3</sub>. While the monolayers of MnPSe<sub>3</sub> exhibit antiferromagnetic order, the moiré superlattices display a two-domain phase. We show that the octupolar moments <i>M</i><sub>33</sub><sup>+</sup> and <i>M</i><sub>33</sub><sup>-</sup> are significant in this multidomain phase. In addition, when [<i>M</i><sub>33</sub><sup>+</sup>,<i>M</i><sub>33</sub><sup>-</sup>] are represented by the <i>x</i> and <i>y</i> components of a vector, the resultant pattern of these octupole moments forms vortex crystals which leads to octupolar toroidal moments, <i>T</i><sub><i>xyz</i></sub> and <i>T</i><sub><i>z</i></sub><sup>β</sup>. <i>T</i><sub><i>xyz</i></sub> and <i>T</i><sub><i>z</i></sub><sup>β</sup> can give rise to a magnetoelectric effect and gyrotropic birefringence that may provide indirect ways of detecting multidomain antiferromagnetic order. Our results highlight the importance of higher-order multipole moments for identification of complex spin textures in moiré magnets.