自旋空间群:完整分类与应用

IF 11.6 1区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY Physical Review X Pub Date : 2024-08-28 DOI:10.1103/physrevx.14.031037
Zhenyu Xiao, Jianzhou Zhao, Yanqi Li, Ryuichi Shindou, Zhi-Da Song
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引用次数: 0

摘要

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磁性、非共线磁性、同相螺旋磁性以及非同相螺旋磁性等,并研究了尊重这些对称性的电子带的丰富特征。为此,我们对所谓的自旋空间群(SSGs)--空间和自旋操作的联合对称群--进行了系统分类,使磁性结构保持不变。一般来说,在自旋轨道耦合(SOC)可忽略不计(有限但弱于感兴趣的能量尺度)的系统中,它们是准确(近似)的对称,但我们也证明,即使存在强 SOC,特定的 SSGs 仍然有效。近年来,SSGs 在各种领域发挥着越来越关键的作用,如改变磁性、拓扑电子态和拓扑磁子等。然而,由于 SSG 的复杂性,迄今为止尚未完成完整的 SSG 分类。通过将 SSG 表示为 O(N) 表示,我们首次获得了对偶(N=1)、共面(N=2)和非共面(N=3)磁分别有 1421、9542 和 56 512 个不同 SSG 的完整分类。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,一般来说,这些电子态形成了磁空间群(MSG)的投影表示。令人惊奇的是,SSG 中的电子带呈现出 MSG 中从未有过的特征,例如:(i) 非非线性 SSG 布里渊区,其中 SSG 运算在作用于动量时表现为滑行或螺旋;(ii) 有效 π 通量,其中平移算子相互反交并产生重复带;(iii) MSG 无法解释的高维表示;以及 (iv) 费米面上的非常规自旋纹理,这完全由 SSG 决定,与哈密顿细节无关。为了应用我们的理论,我们为毕尔巴鄂晶体学服务器 MAGNDATA 数据库中已发表的 1595 种磁性结构中的每一种确定了 SSG。我们重点讨论了表现出 (i)-(iv) 新特征的材料实例。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,我们提出了一种在表面具有四倍退化狄拉克点的三维 Z2 拓扑绝缘体态,以及一种出现在磁畴壁上的反常 Z2 螺旋态的新方案。
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Spin Space Groups: Full Classification and Applications
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.
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来源期刊
Physical Review X
Physical Review X PHYSICS, MULTIDISCIPLINARY-
CiteScore
24.60
自引率
1.60%
发文量
197
审稿时长
3 months
期刊介绍: Physical Review X (PRX) stands as an exclusively online, fully open-access journal, emphasizing innovation, quality, and enduring impact in the scientific content it disseminates. Devoted to showcasing a curated selection of papers from pure, applied, and interdisciplinary physics, PRX aims to feature work with the potential to shape current and future research while leaving a lasting and profound impact in their respective fields. Encompassing the entire spectrum of physics subject areas, PRX places a special focus on groundbreaking interdisciplinary research with broad-reaching influence.
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