Strain- and Field-Tunable Nonrelativistic Spin Splitting and Wave-Symmetry-Dependent Spin Transport in Twisted Bilayer Altermagnets

Abstract: Magnetism-driven nonrelativistic spin splitting (NRSS) provides a pathway toward efficient, spin-orbit-free spintronics. In centrosymmetric two-dimensional antiferromagnets, spin-polarized transport is symmetry-forbidden due to the combined space-time inversion ($PT$) symmetry. Here, by employing first-principles density functional theory and spin-group symmetry analysis, we demonstrate that twisting two antiferromagnetic or ferromagnetic monolayers of CoCl$2$, AX$_2$ (A = Mn, V; X = Cl, Br, I), NiF$_2$, NiBr$_2$, FeS, CoS, MnTe$_2$, MnSe$_2$, and RuSe induces finite NRSS even in the absence of spin-orbit coupling. The relative twist breaks $[C_2||P]$ and $[E||C{nz}]$ symmetries, giving rise to momentum-dependent spin polarization with distinct $d$-, $g$-, and $i$-wave altermagnetic patterns across the Brillouin zone. Using symmetry-invariant $k\cdot p$ modeling, we extract linear spin-splitting coefficients $α^{(1)}$ ranging from 800-1100 meVÅ, comparable to SOC-induced Rashba-Dresselhaus strengths observed in noncentrosymmetric semiconductors. An out-of-plane electric field ($\mathcal{E}z$) introduces Zeeman-type band splitting up to 110 meV at 10 MV/cm, while biaxial strain tunes the NRSS magnitude nearly linearly without altering symmetry. Crucially, the strain $u{xx-yy}$ reduces the spin point group symmetry and drives reversible $g/i \rightarrow d$ wave-type transitions, resulting in finite spin conductivity and an enhanced spin-splitter angle (up to 18$^\circ$). These results extend the concept of altermagnetism to twisted bilayer geometries and establish a general route for realizing exchange-driven, nonrelativistic spin currents through symmetry engineering without requiring heavy elements or spin-orbit coupling.