发表机构
University of California, Irvine; Laboratoire Léon Brillouin, CEA, CNRS, Université Paris-Saclay; University of Windsor（加州大学欧文分校; 巴黎-萨克雷大学法国国家科学研究中心法国原子能委员会莱昂·布里渊实验室; 温莎大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构建了非相对论磁性系统的朗道理论，涵盖共面和非共面序，揭示了与自旋空间群的直接联系，并计算了关键可观测量。
AI 中文摘要
在这项工作中，我们研究了非相对论磁性系统的唯象朗道理论，将共线情况的工作推广到共面和非共面序。聚焦于由晶体点群的单一不可约表示描述的零波矢（$\oldsymbol{k}=0$）磁性序，我们构造了所有可能的多维不可约有序通道的对称允许自由能至四阶。我们发现四方、三角/六角和立方对称性具有不同的朗道理论。与自旋向列流体的情况类似，我们发现两种自然结果：坍缩到低对称性的共线相，或真正的共面或非共面序，其中序参量在自旋空间中形成相互正交的集合——让人联想到${}^3$He中的$A$和$B$相。我们普遍证明，这种对称破缺相实现了与序参量的空间表示相关联的自旋空间群，该空间表示与顺磁相共享相同的母空间群。这为朗道方法和自旋空间群方法提供了直接联系。我们使用这种朗道方法计算关键可观测量，包括净磁化强度、自旋电导率、多极矩和压磁效应，将我们的结果与底层自旋空间群的约束联系起来。对每种情况，我们详细给出了共面和非共面磁性序的例子。最后，我们讨论了低对称性共线相与通常共线自旋群的关系，以及与原子交错磁性、超流${}^3$He和电子向列相的联系。
英文摘要
In this work we study phenomenological Landau theories of non-relativistic magnetic systems, generalizing work on the collinear case to coplanar and non-coplanar orders. Focusing on zero-wavevector ($\boldsymbol{k}=0$) magnetic orders described by a single irreducible representation of the crystallographic point group, we construct the symmetry-allowed free energies to quartic order for all possible multi-dimensional irreducible ordering channels. We find distinct Landau theories for tetragonal, trigonal/hexagonal, and cubic symmetry. Similar to the case of spin-nematic fluids, we find two natural outcomes: a collapse to a lower-symmetry collinear phase or a genuinely coplanar or non-coplanar order where the order parameters form a mutually orthogonal set in spin space -- reminiscent of the $A$ and $B$ phases in ${}^3$He. We show in general that this symmetry-broken phase realizes the spin space group associated with the spatial representation of the order parameter sharing the same parent space group as the paramagnetic phase. This provides a direct link between the Landau and spin space group approaches. We calculate key observables using this Landau approach, including net magnetization, spin conductivity, multipolar moments, and piezomagnetism, connecting our results to constraints from the underlying spin space group. Examples of coplanar and non-coplanar magnetic orders for each case are worked out in detail. Finally, we discuss the relationship of the lower-symmetry collinear phases to the usual collinear spin groups, as well as connections to atomic altermagnetism, superfluid ${}^3$He and electronic nematic phases.
Comments35 pages, 7 figures, 11 tables
