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The structural distortion and magnetoelastic coupling induced throughcommensurate magnetism has been investigated by neutron diffraction instructurally related MnWO$_4$ and NaFe(WO$_4$)$_2$. Both systems exhibit acompetition of incommensurate spiral and commensurate spin up-up-down-downordering along the magnetic chains. In the latter commensurate phases, thealternatingly parallel and antiparallel arrangement of Fe$^{3+}$ respectivelyMn$^{2+}$ moments leads to sizeable bond-angle modulation and thus to magneticdimerization. For NaFe(WO$_4$)$_2$ this structural distortion has beendetermined to be strongest for the low-field up-up-down-down arrangement, andthe structural refinement yields a bond-angle modulation of $\pm 1.15(16)$degrees. In the commensurate phase of MnWO$_4$, superstructure reflectionssignal a comparable structural dimerization and thus strong magneto-elasticcoupling different to that driving the multiferroic order. Pronouncedanharmonic second- and third-order reflections in the incommensurate andmultiferroic phase of MnWO$_4$ result from tiny commensurate fractions that candepin multiferroic domains.

Structural dimerization in the commensurate magnetic phases of NaFe(WO$_4$)$_2$ and MnWO$_4$