Spin Space Groups: Full Classification and Applications,Physical Review X

当前位置： X-MOL 学术 › Phys. Rev. X › 论文详情

Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)

Spin Space Groups: Full Classification and Applications
Physical Review X ( IF 11.6 ) Pub Date : 2024-08-28 , DOI: 10.1103/physrevx.14.031037
Zhenyu Xiao ₁ , Jianzhou Zhao ₂ , Yanqi Li ₁ , Ryuichi Shindou ₁ , Zhi-Da Song _{1,

3,

4}

Affiliation

In this work, we exhaust all the spin space symmetries, which fully characterize collinear, noncollinear, and commensurate spiral as well as incommensurate spiral magnetism, etc., and investigate enriched features of electronic bands that respect these symmetries. We achieve this by systematically classifying the so-called spin space groups (SSGs)—joint symmetry groups of spatial and spin operations that leave the magnetic structure unchanged. Generally speaking, they are accurate (approximate) symmetries in systems where spin-orbit coupling (SOC) is negligible (finite but weaker than the energy scale of interest), but we also show that specific SSGs could remain valid even in the presence of strong SOC. In recent years, SSGs have played increasingly pivotal roles in various fields such as altermagnetism, topological electronic states, and topological magnon, etc. However, due to its complexity, a complete SSG classification has not been completed up to now. By representing the SSGs as O(N) representations, we—for the first time—obtain the complete classifications of 1421, 9542, and 56 512 distinct SSGs for collinear (N=1), coplanar (N=2), and noncoplanar (N=3) magnetism, respectively. SSG not only fully characterizes the symmetry of spin degrees of freedom, but also gives rise to exotic electronic states, which, in general, form projective representations of magnetic space groups (MSGs). Surprisingly, electronic bands in SSGs exhibit features never seen in MSGs, such as (i) nonsymmorphic SSG Brillouin zone, where SSG operations behave as a glide or screw when acting on momentum, (ii) effective π flux, where translation operators anticommute with each other and yield duplicate bands, (iii) higher-dimensional representations unexplained by MSGs, and (iv) unconventional spin texture on a Fermi surface, which is completely determined by SSGs, independent of Hamiltonian details. To apply our theory, we identify the SSG for each of the 1595 published magnetic structures in the MAGNDATA database on the Bilbao Crystallographic Server. Material examples exhibiting the novel features (i)–(iv) are discussed with emphasis. We also investigate new types of SSG-protected topological electronic states that are unprecedented in MSGs. In particular, we propose a 3D Z2 topological insulator state with a fourfold degenerate Dirac point on the surface and a new scenario of anomalous Z2 helical states that appear on magnetic domain walls.

Published by the American Physical Society

2024

中文翻译：

自旋空间组：完整分类和应用

在这项工作中，我们穷尽了所有自旋空间对称性，这些对称性充分表征了共线、非共线和相称的螺旋以及不相称的螺旋磁性等，并研究了尊重这些对称性的电子频段的丰富特征。我们通过系统地对所谓的自旋空间群（SSG）进行分类来实现这一点，SSG 是保持磁性结构不变的空间和自旋操作的联合对称群。一般来说，在自旋轨道耦合（SOC）可以忽略不计（有限但弱于感兴趣的能量尺度）的系统中，它们是精确（近似）对称性的，但我们也表明，即使在存在强 SOC 的情况下，特定的 SSG 也可以保持有效。近年来，SSG 在互通磁、拓扑电子态和拓扑磁振子等各个领域发挥着越来越关键的作用。然而，由于其复杂性，到目前为止尚未完成完整的 SSG 分类。通过将 SSG 表示为 O（N）表示，我们首次获得了 1421、9542 和 56 512 个不同 SSG 的完整分类，分别用于共线（N=1）、共面（N=2）和非共面（N=3）磁性。SSG 不仅完全表征了自旋自由度的对称性，而且还产生了奇异的电子态，这些电子态通常形成磁性空间群（MSG）的投影表示。令人惊讶的是，SSG 中的电子带表现出 MSG 中从未见过的特征，例如（i）非对称的 SSG 布里渊区，其中 SSG 操作在作用于动量时表现为滑行或螺旋，（ii）有效的π通量，其中平移运算符相互反交换并产生重复的带，（iii） MSG 无法解释的高维表示，以及（iv）费米表面上的非常规自旋织构，这完全由 SSG 确定，与哈密顿细节无关。为了应用我们的理论，我们在毕尔巴鄂晶体学服务器的 MAGNDATA 数据库中确定了 1595 个已发表的磁性结构中每个磁性结构的 SSG。重点讨论了表现出新特征（i）-（iv）的材料示例。我们还研究了 MSG 中前所未有的新型 SSG 保护拓扑电子态。特别是，我们提出了一个 3D Z2 拓扑绝缘体状态，表面有一个四倍简并的 Dirac 点，以及一个出现在磁畴壁上的异常 Z2 螺旋态的新场景。美国物理学会 2024 年出版

更新日期：2024-08-28

点击分享查看原文

点击收藏

公开下载

阅读更多本刊新发论文本刊介绍/投稿指南