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We present a comprehensive single crystal neutron diffraction investigationof the $\rm Mn_{1-x}Co_{x}WO_4$ with $0.02\leq x \leq0.30$. At lowerconcentration $x \leq 0.05$, the system is quickly driven into the multiferroicphase with spin structure forming an elliptical spiral order similar to theparent compound. The reduction of electric polarization is ascribed to thetilting of the spiral plane. For $x\sim 0.075$, the magnetic structureundergoes a spin flop transition that is characterized by a sudden rotation ofthe spin helix envelope into the $ac$ plane. This spin structure persists forconcentration up to $x=0.15$, where additional competing magnetic orders appearat low temperature. For $0.17 \leq x \leq 0.30$, the system experiences anotherspin flop transition and recovers the low-$x$ spiral spin configuration. Asimple commensurate spin structure with $\vec{q}=(0.5,0,0)$ is found to coexistwith the incommensurate spiral order. The complex evolution of magneticstructure in Co doped $\rm MnWO_4$ contrasts sharply with other transitionmetal ion doped $\rm Mn_{1-x}A_xWO_4$ (A=Zn, Mg, Fe) where the chemicalsubstitutions stabilize only one type of magnetic structure. The rich phasediagram of $\rm Mn_{1-x}Co_{x}WO_4 $ results from the interplay betweenmagnetic frustration and spin anisotropy of the Co ions.

Magnetic orders and spin-flop transitions in the cobalt doped multiferroic $\rm Mn_{1-x}Co_{x}WO_4$