Spin flop transition in the multiferroic Mn$_{1-x}$Co$_{x}$WO$_{4}$ studied by neutron diffraction

Elastic neutron diffraction is employed to investigate the ground state magnetic structure of the multiferroic Mn$_{1-x}$Co$_{x}$WO$_{4}$. Unlike the undoped MnWO$_{4 }$that has low-$T$ collinear spin structure, the doped MnWO$_{4}$ exhibits complex evolution of magnetic structure. Samples at lower concentration ($x<$0.10) have similar elliptical spiral structure as MnWO$_{4}$ in the multiferroic phase. With increasing $x$, the magnetic structure undergoes a sudden spin-flop transition which switches electric polarization from crystalline $b$-axis to $a$-axis. Polarized neutron scattering is also used to study the correlation between the bulk electricity and magnetic helicity.