标题： 八极涡旋晶体和扭曲双层MnPSe的环状矩在$_3$ 显示英文标题

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

摘要： 二维材料中反铁磁序的实验检测是一项具有挑战性的任务，这是由于缺乏净偶极矩。 通过现有技术识别多畴反铁磁结构更加困难。 为了解决这一挑战，我们研究了扭曲双层MnPSe$_3$中的高阶多极矩。 虽然MnPSe$_3$单层表现出面内Néel反铁磁序，但我们的原子模拟表明，摩尔超晶格在每一层上显示两畴相。 我们表明，在畴壁处，八极矩$M_{33}^+$和$M_{33}^-$在这种多畴相中是显著的。 此外，当$[M_{33}^+,M_{33}^-]$由矢量的$x$和$y$成分表示时，这些八极矩的总体模式围绕反铁磁畴旋转并形成涡旋晶体，从而导致八极矩的旋转向量矩，$T_{xyz}$和$T_{z}^{\beta}$。 $T_{xyz}$和 $T_{z}^{\beta}$可以产生磁电效应和旋光双折射，这可能为检测多畴反铁磁序提供间接方法。 我们的结果突显了高阶多极矩在识别莫尔磁体中复杂自旋纹理的重要性。 显示英文摘要

摘要： 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.