Fundamental physical properties, such as phase transitions, electronic structures, and spin
excitations, in all magnetic ordered materials, were ultimately believed to rely on the …

Symmetries of three-dimensional periodic scalar fields are described by 230 space groups
(SGs). Symmetries of three-dimensional periodic (pseudo) vector fields, however, are …

Spatial, momentum and energy separation of electronic spins in condensed-matter systems
guides the development of new devices in which spin-polarized current is generated and …

Recently, unconventional antiferromagnets that enable the spin splitting (SS) of electronic
states have been theoretically proposed and experimentally realized, where the magnetic …

Symmetry invariants of a group specify the classes of quasiparticles, namely the classes of
projective irreducible co-representations in systems having that symmetry. More symmetry …

Magnetic materials with noncollinear spin textures are promising for spintronic applications.
To realize practical devices, control over the length and energy scales of such spin textures …

Antiferromagnets exhibiting giant anomalous Hall effect (AHE) and anomalous Nernst effect
(ANE) have recently aroused broad interest, not only for their potential applications in future …

In this work, we demonstrate a simple yet effective procedure for identifying the exotic
tetrahedral triple-Q magnetic ordering over the domain averaged collinear single-Q …

We establish the map between symmetries and orbital rules to realize tunable band gap in
quantum anomalous Hall effect material. The band gap is determined by the spin–orbit …

The interplay of symmetry and topology in crystal solids has given rise to various elementary
excitations as quasiparticles. Among these, those with significant Berry-phase-related …