The Modulated Crystal Structure of K 2 V 3 O 8

Weak lattice distortions can tune exchange pathways and magnetic interactions in square-lattice quantum magnets. K 2 V 3 O 8 is a mixed valence (V 4+ /V 5+ ) fresnoite oxide that exhibits strong spin–lattice coupling at low temperature. We combine single-crystal neutron diffraction (90 K) and laboratory X-ray diffraction (50 K) to solve the low-temperature structure as an orthorhombic (3 + 1)D incommensurately modulated phase in superspace group Cmm 2(β,0,1/2)0 s 0 [No. 196]. What initially appeared as two independent modulation vectors, q 1 = 0.3132(6)[110] + 1/2 c * and q 2 = 0.3132(6)[11̅0] + 1/2 c *, are more naturally described as a single one-dimensional modulation wave q = 0.626(1) a * + 1/2 c* in a C -centered orthorhombic lattice, related to the parent tetragonal cell by the transformation a + b, − a + b, c. Refinement with a 4-fold rotational twin inherited from the P 4 bm parent structure solves oxygen-dominated framework distortions and K + displacements. A de Wolff section ( t = 0.40) enables a symmetry-mode decomposition, identifying three dominant mm 2 ( C 2 v ) modes: GM3 for framework tilt, A5 for interlayer shear, and Z5 for c -axis breathing. The mode-resolved structure provides a unified, symmetry-based explanation for reported low-temperature Raman and IR anomalies and clarifies the structural origin of the spin–lattice coupling in the S = 1/2 two-dimensional quantum spin compound.