A theoretical description of the sequence of magnetic phases in Co3TeO6 is presented. The strongly first-order character of the transition to the commensurate multiferroic ground state, induced by coupled order parameters corresponding to different wavevectors, is related to a large magnetoelastic effect with an exchange energy critically sensitive to the interatomic spacing. The monoclinic magnetic symmetry C2 of the multiferroic phase permits spontaneous polarization and magnetization as well as the linear magnetoelectric effect. The existence of weakly ferromagnetic domains is verified experimentally by second harmonic generation measurements.
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