标题： $\mathrm{Nb}_3\mathrm{(Cl, Br, I)}_8$透气 Kagomé 单层的磁电行为的第一性原理计算 显示英文标题

标题： Magnetoelectric behavior of breathing kagomé monolayers of $\mathrm{Nb}_3\mathrm{(Cl, Br, I)}_8$ from first-principles calculations

摘要： 我们应用密度泛函理论来探讨二维$\mathrm{Nb}_3\mathrm{(Cl,Br,I)}_8$的磁电（ME）性质。 这些化合物最近被提出具有耦合的铁电和铁磁序，从而导致可开关的反常谷霍尔效应（AVHE）。 通过自旋螺旋和自洽自旋-轨道耦合计算，我们预测三聚自旋的面内$120^\circ$旋波为$\mathrm{Nb}_3\mathrm{Cl}_8$的基态。 对于$\mathrm{Nb}_3\mathrm{Br}_8$和$\mathrm{Nb}_3\mathrm{I}_8$，我们发现长周期非共线螺旋序。 我们计算了多种磁性性质，如交换常数、轨道磁化和威斯温度。 随后表明，尽管同时破坏了反演对称性和时间反演对称性，但由于基态中存在螺旋序，所提出的 AVHE 和线性 ME 响应是被禁止的。 此外，计算的开关轨迹表明，由于垂直偶极矩的异常状态方程，单层的极性态不太可能通过均匀电场进行开关。 然而，我们强调，在强电场存在的情况下，$\mathrm{Nb}_3\mathrm{Cl}_8$中的三聚自旋将表现出从$120^\circ$旋波到垂直方向铁磁序的磁相变，这恢复了 AVHE 和线性 ME 效应所需的对称性。 显示英文摘要

摘要： We apply density functional theory to explore the magnetoelectric (ME) properties of two-dimensional $\mathrm{Nb}_3\mathrm{(Cl,Br,I)}_8$. These compounds have recently been proposed to exhibit coupled ferroelectric and ferromagnetic order leading to a switchable anomalous valley Hall effect (AVHE). Using both spin-spiral and self-consistent spin-orbit coupled calculations, we predict an in-plane $120^\circ$ cycloid of trimerized spins as the ground state for $\mathrm{Nb}_3\mathrm{Cl}_8$. For $\mathrm{Nb}_3\mathrm{Br}_8$ and $\mathrm{Nb}_3\mathrm{I}_8$ we find long period incommensurate helical order. We calculate a number of magnetic properties such as the exchange constants, orbital magnetization, and Weiss temperatures. It is then shown that, despite having both broken inversion and time-reversal symmetry, the proposed AVHE and linear ME response are forbidden by the presence of helical order in the ground state. In addition, the computed switching trajectory demonstrates that it is unlikely that the polar state of the monolayers can be switched with a homogeneous electric field due to an unusual equation of state of the out-of-plane dipole moment. Nevertheless, we highlight that in the presence of a strong electric field, the trimerized spins in $\mathrm{Nb}_3\mathrm{Cl}_8$ will exhibit a magnetic phase transition from the $120^\circ$ cycloid to out-of-plane ferromagnetic order, which restores the symmetry required for both AVHE and linear ME effects.