Helical and collinear spin density wave order in the S=12 one-dimensional frustrated chain compound NaCuMoO4(OH) investigated by neutron scattering

We performed neutron diffraction experiments on a single crystal of an $S=\frac{1}{2}$ frustrated ferromagnetic chain compound ${\mathrm{NaCuMoO}}_{4}$(OH) at zero and finite magnetic fields. Three magnetic Bragg peaks with the propagation vector of $\mathbit{q}=(0,\ensuremath{\delta},0)$ $[\ensuremath{\delta}=0.481(1)]$ were observed at the zero field, which means that an incommensurate helical magnetic order was realized. Using the ratio of the intensities between these magnetic peaks, a proper-screw structure was suggested, where the spiral plane is the crystallographic $ac$ plane. While the $\ensuremath{\delta}$ is unchanged at lower fields, it decreases linearly with the field where ${\ensuremath{\mu}}_{0}H\ensuremath{\ge}2.5\phantom{\rule{0.16em}{0ex}}\mathrm{T}$. The field dependence is consistent with that of the field-induced spin density wave state that originated from the formation of the bound state of two magnons in the $S=\frac{1}{2}$ frustrated ferromagnetic chain.