Reentrant ferroelectricity and the multiferroic phase diagram of Mn$_{1-x}$Fe$_{x}$WO$_{4}$

Recently MnWO$_{4}$ has attracted attention because of its multiferroic properties. In MnWO$_{4}$ the Mn$^{2+}$ ions can be substituted by Fe$^{2+}$ since MnWO$_{4}$ and FeWO$_{4}$ are isomorphic. This opens the possibility to tune the magnetic orders by Fe-substitution for a better understanding of the microscopic interactions resulting in the multiferroic properties. We report the discovery of reentrant ferroelectricity in the phase diagram of multiferroic Mn$_{1-x}$Fe$_{x}$WO$_{4}$ single crystals. At zero magnetic field (H) the spin-spiral ferroelectric (FE) state is completely suppressed at Fe substitutions (x) exceeding 0.04. For x<0.04 a ferroelectric phase exists in a narrow temperature (T) range at zero magnetic field. This FE phase shows a reentrant behavior at lower T above a critical magnetic field H$_{c}$(x). The reentrant FE transition is explored by polarization, dielectric constant, and magnetization measurements. The complete multiferroic x-T-H phase diagram of Mn$_{1-x}$Fe$_{x}$WO$_{4}$ is derived.