The crystal and magnetic structure of multiferroic LiFe(WO$_4$)$_2$ were investigated by temperature and magnetic-field dependent specific heat, susceptibility and neutron diffraction experiments on single crystals. Considering only the two nearest-neighbour magnetic interactions, the system forms a $J_1$, $J_2$ magnetic chain but more extended interactions are sizeable. Two different magnetic phases exhibiting long-range incommensurate order evolve at $T_{text{N}1}approx 22.2 text{ K}$ and $T_{text{N}2}approx 19 text{ K}$. First, a spin-density wave develops with moments lying in the $ac$ plane. In its multiferroic phase below $T_{text{N}2}$, LiFe(WO$_4$)$_2$ exhibits a spiral arrangement with an additional spin-component along $b$. Therefore, the inverse Dzyaloshinskii-Moriya mechanism fully explains the multiferroic behavior in this material. A partially unbalanced multiferroic domain distribution was observed even in the absence of an applied electric field. For both phases only a slight temperature dependence of the incommensurability was observed and there is no commensurate phase emerging at low temperature or at finite magnetic fields up to $6text{ T}$. LiFe(WO$_4$)$_2$ thus exhibits a simple phase diagram with the typical sequence of transitions for a type-II multiferroic material.
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