Lattice symmetry breaking and strain control of single-$\mathbf{q}$ magnetism in Na${}_3$Co${}_2$SbO${}_6$

Distinguishing single-$\mathbf{q}$ from multi-$\mathbf{q}$ magnetism constrains microscopic spin Hamiltonians. Here we determine the ground state of the candidate Kitaev magnet Na${}_3$Co${}_2$SbO${}_6$ through its coupling to the lattice. High-resolution neutron diffraction reveals a spontaneous monoclinic-to-triclinic distortion at the magnetic transition, in contrast to the absence of detectable lattice-symmetry breaking in triple-$\mathbf{q}$ Na${}_2$Co${}_2$TeO${}_6$. Together with strain-selective magnetic responses, this identifies single-$\mathbf{q}$ order in Na${}_3$Co${}_2$SbO${}_6$ over the proposed symmetry-preserving double-$\mathbf{q}$ state. Uniaxial compression along a low-symmetry in-plane direction achieves the domain selection that magnetic-field training could not, revealing the intrinsic field-induced phase boundaries of the dominant domain. These results establish strain as a symmetry-conjugate field for magnetic domains and highlight magnetoelastic coupling as a route to diagnose, manipulate, and potentially tune magnetic states.