Magnetic field-induced spontaneous polarization reversal in multiferroic Mn$_{0.85}$Co$_{0.15}$WO$_{4}$*

In this work, we report the effect of c-axis magnetic field in magnetic and ferroelectric properties of multiferroic Mn$_{1-x}$Co$_{x}$WO$_{4}$ for $x$=0.15,0.135, and 0.17. For $x$=0.15, which is the critical doping that separates ground state AF5 and AF2/4 magnetic phases, the positive b-axis polarization($P_{b}$) is reversed spontaneously at $\sim$ 7K, when the magnetic field along c-axis is $\geq20 kOe$ even for the positive poling voltage. From the polarization measurement for $x$=0.135 and 0.17, we found that $P_{b}$ originates from both AF5 and AF2/4 phases, however, c-axis magnetic field of $\geq 20 kOe$ is needed for former case which is the effect of spin flop transition. Magnetic data for $x$=0.135 clearly show the existence of spin flop transition in a c-axis magnetic field. By comparing similar data for $x$=0.15 we conclude that the spin flop also happens in the AF5 phase which coexists with AF2/4 magnetic structure. The polarization reversal is explained by a coupling of different domains preserving the chirality of the spiral spin structure.