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

Abstract

The structural distortion and magnetoelastic coupling induced through commensurate magnetism has been investigated by neutron diffraction in structurally related MnWO${}_4$ and NaFe(WO${}_4$)${}_2$. Both systems exhibit a competition of incommensurate spiral and commensurate spin up-up-down-down ordering along the magnetic chains. In the latter commensurate phases, the alternatingly parallel and antiparallel arrangement of Fe${}^{3+}$ respectively Mn${}^{2+}$ moments leads to sizeable bond-angle modulation and thus to magnetic dimerization. For NaFe(WO${}_4$)${}_2$ this structural distortion has been determined to be strongest for the low-field up-up-down-down arrangement, and the structural refinement yields a bond-angle modulation of $\pm 1.15(16)$ degrees. In the commensurate phase of MnWO${}_4$, superstructure reflections signal a comparable structural dimerization and thus strong magneto-elastic coupling different to that driving the multiferroic order. Pronounced anharmonic second- and third-order reflections in the incommensurate and multiferroic phase of MnWO${}_4$ result from tiny commensurate fractions that can depin multiferroic domains.