The recent discoveries of strikingly large zero-field Hall and Nernst effects in antiferromagnets Mn₃X (X = Sn, Ge) have brought the study of magnetic topological states to the forefront of condensed matter research and technological innovation. These effects are considered fingerprints of Weyl nodes residing near the Fermi energy, promoting Mn₃X (X = Sn, Ge) as a fascinating platform to explore the elusive magnetic Weyl fermions. In this review, we provide recent updates on the insights drawn from experimental and theoretical studies of Mn₃X (X = Sn, Ge) by combining previous reports with our new, comprehensive set of transport measurements of high-quality Mn₃Sn and Mn₃Ge single crystals. In particular, we report magnetotransport signatures specific to chiral anomalies in Mn₃Ge and planar Hall effect in Mn₃Sn, which have not yet been found in earlier studies. The results summarized here indicate the essential role of magnetic Weyl fermions in producing the large transverse responses in the absence of magnetization.

Giant electric polarization of more than 150 µC/cm² is predicted for PbVO₃ and BiCoO₃ on the basis of the first-principles Berry-phase method. The stable crystal structure is tetragonally distorted with a large c/a ratio and significant ionic displacements breaking centrosymmetry. In PbVO₃, the key factor that stabilizes such a highly distorted structure and realizes an insulating electronic structure, leading to giant polarization, is the coexistence of ferro-orbital and antiferro-spin orderings in the V⁴⁺ d¹ configuration. It is shown that the same electronic mechanism works also for BiCoO₃ with Co³⁺ d⁶ configuration.

Energy-saving spintronics are believed to be implementable on systems hosting the persistent spin helix (PSH) since they support an extraordinarily long spin lifetime of carriers. However, achieving the PSH requires a unidirectional spin configuration in the momentum space, which is practically nontrivial due to the stringent conditions for fine-tuning the Rashba and Dresselhaus spin-orbit couplings. Here, we predict that the PSH can be intrinsically achieved on a two-dimensional (2D) group-IV monochalcogenide $MX$ monolayer, a new class of the noncentrosymmetric 2D materials having in-plane ferroelectricity. Due to the $C_{2v}$ point-group symmetry in the $MX$ monolayer, a unidirectional spin configuration is preserved in the out-of-plane direction and thus maintains the PSH that is similar to the [110] Dresselhaus model in the [110]-oriented quantum well. Our first-principle calculations on various $MX$ ($M=$ Sn, Ge; $X=$ S, Se, Te) monolayers confirmed that such typical spin configuration is observed, in particular, at near the valence-band maximum where a sizable spin splitting and a substantially small wavelength of the spin polarization are achieved. Importantly, we observe reversible out-of-plane spin orientation under opposite in-plane ferroelectric polarization, indicating that an electrically controllable PSH for spintronic applications is plausible.

Spin splitting bands that arise in the conduction band minimum (CBM) of the ${\text{WS}}_2$ monolayer (ML) play an important role in the spin-orbit phenomena such as spin-valley coupled electronics. However, application of strain strongly modifies electronic properties of the ${\text{WS}}_2$ ML, which is expected to significantly affect the properties of the spin splitting bands. Here, by using fully-relativistic first-principles calculations based on density-functional theory, we show that a substantial spin splitting band observed in the CBM is effectively controlled and tuned by applying the biaxial strain. We also find that these spin splitting bands induce spin textures exhibiting fully out-of-plane spin polarization in the opposite direction between the $K$ and $Q$ points and their time reversals in the first Brillouin zone. Our study clarifies that the strain plays a significant role in the spin-orbit coupling of the ${\text{WS}}_2$ ML, which has very important implications in designing future spintronics devices.