Spin Splitter without Spin-Split Bands: A Reconfigurable Altermagnetic Texture

The altermagnetic spin-splitter effect converts an electric field into a transverse pure spin current, with no net magnetization and no charge-Hall counterpart. In established materials this function is tied to crystal-fixed spin-split bands that lock the polarization axis to the lattice. We show that the noncoplanar counter-spiral ground state of a frustrated honeycomb magnet instead carries the altermagnetic operation through a $\mathbf{Q}$-locked helicity mirror $g$. The mirror selects the spin-current polarization and forbids the perpendicular one, while an antitranslation $\mathrm{\Theta }$ forbids even-parity spin splitting. Band splitting and spin-splitter response therefore rest on different symmetry elements. Either element alone enforces the charge-Hall zero—a redundancy absent from other spin–orbit-free noncollinear routes—and a charge Hall appears only when both elements are removed. Hole doping then realizes a \emph{spin splitter without spin-split bands}—the symmetry-allowed odd-parity residual below $2\times {10}^{-7}$ of the hopping $t$ at the Fermi level—with ${\sigma }_H^{(s_y)}=0.082e^2\mathrm{/}h$ without spin–orbit coupling and with zero charge Hall response. Selecting among the three degenerate $\mathbf{Q}$ orientations rotates the polarization axis in exact ${120}^{\circ }$ steps at fixed magnitude and charge-Hall zero; the selection rules persist in a $32$-site cell accessible to programmable photonic and circuit lattices.