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

The magnetic and electrical properties of Co${}_3$TeO${}_6$ single-crystals with corundum related structure reveal a magnetic-field induced polarization below 21 K. A sharp peak in the specific heat at \approx 18 K indicates a reconstructive-type first-order phase transition. From second-harmonic generation (SHG) measurements breaking of inversion symmetry is evident and the point-group symmetry was determined as m. The temperature and magnetic-field dependence of the magnetic and electrical polarizations are discussed in the light of the SHG results.