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The complete magnetic and multiferroic phase diagram ofMn$_{1-x}$Co$_{x}$WO$_4$ single crystals is investigated by means of magnetic,heat capacity, and polarization experiments. We show that the ferroelectricpolarization $\overrightarrow{P}$ in the multiferroic state abruptly changesits direction twice upon increasing Co content, x. At x$_{c1}$=0.075,$\overrightarrow{P}$ rotates from the $b-$axis into the $a-c$ plane and atx$_{c2}$=0.15 it flips back to the $b-$axis. The origin of the multiplepolarization flops is identified as an effect of the Co anisotropy on theorientation and shape of the spin helix leading to thermodynamic instabilitiescaused by the decrease of the magnitude of the polarization in thecorresponding phases. A qualitative description of the ferroelectricpolarization is derived by taking into account the intrachain ($c-$axis) aswell as the interchain ($a-$axis) exchange pathways connecting the magneticions. In a narrow Co concentration range (0.1$\leq$x$\leq$0.15), anintermediate phase, sandwiched between the collinear high-temperature and thehelical low-temperature phases, is discovered. The new phase exhibits acollinear and commensurate spin modulation similar to the low-temperaturemagnetic structure of MnWO$_4$.

The complex multiferroic phase diagram of Mn$_{1-x}$Co$_x$WO$_4$