Hidden spin polarization in the 1T-phase layered transition-metal dichalcogenides MX₂ (M = Zr, Hf; X = S, Se, Te)

The recent discovery of hidden spin polarization emerging in layered materials of specific nonmagnetic crystal is a fascinating phenomenon, though hardly explored yet. Here, we have studied hidden spin textures in layered nonmagnetic 1T-phase transition-metal dichalcogenides MX₂ (M = Zr, Hf; X = S, Se, Te) by using first-principles calculations. Spin-layer locking effect, namely, energy-degenerate opposite spins spatially separated in the top and bottom layer respectively, has been identified. In particular, the hidden spin polarization of β-band can be easily probed, which is strongly affected by the strength of spin-orbit coupling. The hidden spin polarization of ξ-band locating at high symmetry M point (conduction band minimum) has a strong anisotropy. In the bilayer, the hidden spin polarization is preserved at the upmost Se layer, while being suppressed if the ZrSe₂ layer is taken as the symmetry partner. Our results on hidden spin polarization in 1T-phase dichalcogenides, verifiable by spin-resolved and angle-resolved photoemission spectroscopy (ARPES), enrich our understanding of spin physics and provide important clues to search for specific spin polarization in two dimensional materials for spintronic and quantum information applications.