Understanding spin textures in PT-broken systems through universal symmetry-constrained rules

Abstract: The current understanding of spin-polarization phenomena in crystals relies heavily on the development of specific k.p Hamiltonians. A more fundamental and symmetry-driven understanding, based solely on crystalline symmetries, remains largely incomplete. In this work, we develop a universal theory consisting of five symmetry-constrained rules to capture the key framework of diverse spin textures (STs) in PT-broken systems. These rules comprehensively classify spatial operations and their combinations with anti-unitary operation T in symmetry-preserved k-invariant subspaces. The theory allows us to address puzzling STs and facilitates the ab initio design of unconventional STs in spin-orbit coupled crystals. Key examples include the identification of vertex-like and windmill-like STs in materials with Dn and Cnv point groups, extending beyond the currently known Radial and Rashba STs. By integrating different types of antiferromagnetic configurations, we also achieve radial STs and the Dresselhaus effect in centrosymmetric systems, challenging the long-standing assumption that these effects exist solely in non-centrosymmetric systems. When combined with topological band theory, we further propose that symmetry-constrained three-dimensional persistent STs can widely exist in two types of non-symmorphic crystals, effectively resolving the ongoing debate regarding their existence.