Complex magnetic transitions and possible orbital ordering in multiferroic $C{o}_3\mathrm{Te}{O}_6$ single crystal

Multiferroic material $C{o}_3\mathrm{Te}{O}_6$ exhibits a sequence of structural and magnetic phase transitions, reflecting the interplay of lattice, orbit, and spin degrees of freedom. Here we report a different avenue to single-crystal growth and related morphology of $C{o}_3\mathrm{Te}{O}_6$, and the compound is studied by magnetic susceptibility, specific heat, high-field magnetization, and electric polarization. We find that both magnetic susceptibility and specific heat in $C{o}_3\mathrm{Te}{O}_6$ develop antiferromagnetic ordering $\sim 26K$ and a first-order phase transition $\sim 18K$. The emergence of an increase of magnetic moment in magnetic susceptibility is compatible with the anomaly in specific heat for $H\parallel b\text{—}\mathrm{we}$ suppose that is ascribed to the orbital physics because of the degenerate state of $t_{2g}$ in $C{o}^{2+}$ ions. Low-field magnetization shows complex magnetic transitions and strong anisotropy in the system. Two spin flop transitions have been observed in high-field magnetization curve when magnetic field up to 55 T is applied along the $b$ axis. The changes of electric polarization are compatible with the magnetic transitions in magnetization. Those results reveal that the complex transitions arise from the competing interactions among spin, lattice, orbit, and external magnetic field.