Complex magnetism and magnetic-field-driven electrical polarization of Co<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi /><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>Te<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mn>6</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

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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.

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