Unconventional spin texture driven by higher-order spin-orbit interactions

Spin splitting and the resulting spin texture are central to emerging spintronic applications. In non-centrosymmetric non-magnetic materials containing heavy elements, spin textures are typically governed by low-order, momentum-dependent spin-orbit interactions, such as Rashba spin-orbit interaction with linear or cubic order in crystal momentum. In this work, we use \textit{ab initio} calculations to reveal a previously unidentified spin texture in the conduction bands of a prototypical ferroelectric nitride LaWN$_3$. In addition to the usual $\Gamma$-centered vortex, we find six new vortices and anti-vortices located at non-high-symmetry points near the Brillouin zone center. Furthermore, by combining group-theoretical analysis and $\textbf{k}\cdot\textbf{p}$ perturbation modeling, we show that, constrained by the $C_{3v}$ point group to which ferroelectric LaWN$_3$ belongs, a 7th-order Weyl spin-orbit interaction is essential to reproduce the unconventional spin structure observed in first-principles calculations. We also find that weak electron doping of LaWN$_3$ leads to a Fermi surface whose spin-arrow contour exhibits an unusual epicycloid pattern--a distinctive signature that is experimentally accessible. Our work demonstrates that higher-order spin-orbit interactions are more than perturbative corrections. They can play a dominant role in shaping the spin texture of non-centrosymmetric materials. Our results open up new avenues for designing spintronic devices that exploit multi-chiral spin textures beyond the conventional spin-orbit paradigm.