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The magnetic and electrical properties of Co$_3$TeO$_6$ single-crystals withcorundum related structure reveal a magnetic-field induced polarization below21 K. A sharp peak in the specific heat at \approx 18 K indicates areconstructive-type first-order phase transition. From second-harmonicgeneration (SHG) measurements breaking of inversion symmetry is evident and thepoint-group symmetry was determined as m. The temperature and magnetic-fielddependence of the magnetic and electrical polarizations are discussed in thelight of the SHG results.

Complex magnetism and magnetic field-driven electrical polarization in Co$_3$TeO$_6$