Symmetry-protected full-space persistent spin texture in two-dimensional materials

Persistent spin texture (PST) is an interesting phenomenon that a material maintains a uniform spin configuration in the momentum space. Recently, it was proposed that the PST can be enforced by the nonsymmorphic space group symmetry at certain high symmetry points in the Brillouin zone [Tao et al., Nat. Commun. 9, 2763 (2018)]. In this Letter, through group theory analysis, we report that the PST could occur in the whole Brillouin zone of a two-dimensional material, as long as it keeps $xy$ mirror (or glide-plane) symmetry but breaks the combination of inversion symmetry and time-reversal symmetry. By performing first-principles calculations, we demonstrate that this full-space persistent spin texture (FPST) can occur in both nonmagnetic material (e.g., monolayer ${\mathrm{MoS}}_{2}$) and magnetic material (e.g., superlattice ${\mathrm{LaGa}}_{0.5}{\mathrm{Mn}}_{0.5}{\mathrm{O}}_{3}$). Furthermore, our $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ Hamiltonian analysis demonstrates that the FPST is robust for nondegenerate bands with an energy gap. The FPST proposed in this work may lead to promising spintronic applications as it may result in an extremely long spin-relaxation time.