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. K₂V₃O₈ is a mixed valence (V⁴⁺/V⁵⁺) 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 <i>Cmm</i>2(β,0,1/2)0<i>s</i>0 [No. 196]. What initially appeared as two independent modulation vectors, <b>q</b>₁ = 0.3132(6)[110] + 1/2<i>c</i>* and <b>q</b>₂ = 0.3132(6)[11̅0] + 1/2<i>c</i>*, are more naturally described as a single one-dimensional modulation wave <b>q</b> = 0.626(1)<i>a</i>* + 1/2<i>c*</i> in a <i>C</i>-centered orthorhombic lattice, related to the parent tetragonal cell by the transformation <i>a</i> + <i>b</i>, -<i>a</i> + <i>b</i>, <i>c.</i> Refinement with a 4-fold rotational twin inherited from the <i>P</i>4<i>bm</i> parent structure solves oxygen-dominated framework distortions and K⁺ displacements. A de Wolff section (<i>t</i> = 0.40) enables a symmetry-mode decomposition, identifying three dominant <i>mm</i>2 (<i>C</i>_2<i>v</i>) modes: GM3 for framework tilt, A5 for interlayer shear, and Z5 for <i>c</i>-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 <i>S</i> = 1/2 two-dimensional quantum spin compound.