Abstract
Neutron diffraction, magnetic susceptibility, specific heat, and dielectric constant measurements of single-crystal Co${}_{3}$TeO${}_{6}$ have been measured to study the interplay between the ferroelectricity and magnetic order. Long-range incommensurate magnetic order develops below ${T}_{\mathrm{M}1}$ $=$ 26 K, which is followed by three additional zero-field phase transitions at ${T}_{\mathrm{M}2}$ $=$ 19.5 K, ${T}_{\mathrm{M}3}$ $=$ 18 K, and ${T}_{\mathrm{M}4}$ $=$ 16 K where the incommensurate order changes and commensurate order develops. In magnetic fields up to 14 T we find that the magnetic intensities and incommensurate wave vector are dramatically altered as ferroelectricity develops, with a fifth abrupt transition around 10 T. The overall behavior characterizes Co${}_{3}$TeO${}_{6}$ as a type-II multiferroic.
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