Predicting magnetic ordering in kagome compounds offers the possibility of harnessing topological or flat-band physical properties through tuning of the magnetism. Here, we examine the magnetic interactions and phases of ErMn₆Sn₆ which belongs to a family of RMn₆Sn₆, R = Sc, Y, Gd–Lu, compounds with magnetic kagome Mn layers, triangular R layers, and signatures of topological properties. Using results from single-crystal neutron diffraction and mean-field analysis, we find that ErMn₆Sn₆ sits close to the critical boundary separating the spiral-magnetic and ferrimagnetic ordered states typical for non-magnetic versus magnetic R layers, respectively. Finding interlayer magnetic interactions and easy-plane Mn magnetic anisotropy consistent with other members of the family, we predict the existence of a number of temperature and field dependent collinear, noncollinear, and noncoplanar magnetic phases. We show that thermal fluctuations of the Er magnetic moment, which act to weaken the Mn-Er interlayer magnetic interaction and quench the Er magnetic anisotropy, dictate magnetic phase stability. Our results provide a starting point and outline a multitude of possibilities for studying the behavior of Dirac fermions in RMn₆Sn₆ compounds with control of the Mn spin orientation and real-space spin chirality.

预测戈薇化合物中的磁有序性提供了通过调整磁性来利用拓扑或平带物理特性的可能性。在这里，我们研究了 ErMn ₆ Sn ₆ 的磁相互作用和相，它属于 RMn ₆ Sn ₆ 家族，R = Sc、Y、Gd–Lu，具有磁性 kagome Mn 层、三角形 R 层和拓扑特性特征的化合物。利用单晶中子衍射和平均场分析的结果，我们发现 ErMn ₆ Sn ₆ 位于分离螺旋磁和亚铁磁有序态典型的临界边界附近。分别为非磁性 R 层与磁性 R 层。发现层间磁相互作用和易平面 Mn 磁各向异性与该族的其他成员一致，我们预测存在许多依赖于温度和场的共线、非共线和非共面磁相。我们表明，Er 磁矩的热波动会削弱 Mn-Er 层间磁相互作用并淬灭 Er 磁各向异性，从而决定磁相稳定性。我们的结果为研究狄拉克费米子在 RMn ₆ Sn ₆ 化合物中的行为提供了一个起点，并概述了通过控制 Mn 自旋方向和实空间自旋手性来研究狄拉克费米子的行为。 。