Constructions and Applications of Irreducible Representations of Spin-Space Groups

Abstract

Spin-space groups (SSGs), including the traditional space groups (SGs) and magnetic space groups (MSGs) as subsets, describe the complete symmetries of magnetic materials with weak spin-orbit coupling (SOC). In the present work, we systematically study the irreducible representations (irreps) of SSGs by focusing on the projective irreps of the little co-group $L(k)$ of any momentum point $k$. We analysis the factor systems of $L(k)$, and then reduce the projective regular representation of $L(k)$ into direct sum of irreps using the Hamiltonian approach. Especially, for collinear SSGs which contain continuous spin rotation operations, we adopt discrete subgroups to effectively capture their characteristics. Furthermore, we apply the representation theory of SSGs to study the band structure of electrons and magnons in magnetic materials. After identifying the SSG symmetry group, we extract relevant irreps and determine the $k\cdot p$ models. As an example, we illustrate how our approach works for the material \ch{Mn3Sn}. Degeneracies facilitated by SSG symmetry are observed, underscoring the effectiveness of application in material analysis. The SSG recognition and representation code is uploaded to GitHub, the information of irreps of all SSGs is also available in the online Database. Our work provides a practical toolkit for exploring the intricate symmetries of magnetic materials and paves the way for future advances in materials science.

References in corpus (36)

• Topological quantum chemistry
• The (High Quality) Topological Materials In The World
• Altermagnetism: spin-momentum locked phase protected by non-relativistic symmetries
• Anomalous Hall effect arising from noncollinear antiferromagnetism
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• The space group classification of topological band insulators
• Topological classification of crystalline insulators through band structure combinatorics
• Linear spin wave theory for single-Q incommensurate magnetic structures
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Topological Weyl semimetals in the chiral antiferromagnetic materials Mn3Ge and Mn3Sn
• Irvsp: to obtain irreducible representations of electronic states in the VASP
• Cluster multipole theory for anomalous Hall effect in antiferromagnets
• Anomalous Nernst and Righi-Leduc effects in Mn${}_3$Sn: Berry curvature and entropy flow
• Magnetic Topological Quantum Chemistry
• Spin-group symmetry in magnetic materials with negligible spin-orbit coupling
• Anomalous transport due to Weyl fermions in the chiral antiferromagnets Mn${}_3$$X$, $X$ = Sn, Ge
• Anomalous Hall effect and topological defects in antiferromagnetic Weyl semimetals: Mn${}_3$Sn/Ge
• Enumeration and representation theory of spin space groups
• Anomalous Hall Effect in Thin Film of the Weyl Antiferromagnet Mn${}_3$Sn
• Spin Space Groups: Full Classification and Applications
• Enumeration of spin-space groups: Towards a complete description of symmetries of magnetic orders
• Quantum Anomalous Hall Effect in Antiferromagnetism
• Anomalous and topological Hall effects in epitaxial thin films of the noncollinear antiferromagnet Mn${}_3$Sn
• Topological correspondence between magnetic space group representations
• Calculating the energy spectra of magnetic molecules: application of real- and spin-space symmetries
• Topological classification and diagnosis in magnetically ordered electronic materials
• Symmetry invariants and classes of quasiparticles in magnetically ordered systems having weak spin-orbit coupling
• The Crystallographic Spin Point Groups and their Representations
• Chiral Dirac-like fermion in spin-orbit-free antiferromagnetic semimetals
• Combined use of translational and spin-rotational invariance for spin systems
• Symmetry-protected Nodal Points and Nodal Lines in Magnetic Materials
• MSGCorep: A package for corepresentations of magnetic space groups
• Irreducible Projective Representations and Their Physical Applications
• A $k\cdot p$ effective Hamiltonian generator
• A Hamiltonian Approach for Obtaining Irreducible Projective Representations and the $k\cdot p$ Perturbation for Anti-unitary Symmetry Groups
• Representation Theory for Massless Quasiparticles in Bogoliubov-de Gennes Systems

Cited by in corpus (2)

• Projective Representations, Bogomolov Multiplier, and Their Applications in Physics
• Topological nontrivial berry phase in altermagnet CrSb