We performed magnetic and ferroelectric measurements, first principle calculations and Landau theory analysis on hexagonal YMnO3. The polarization and the AFM order parameter were found to present different temperature dependence at TN. A linear coupling between these two order parameters is thus forbidden in the Landau theory and P63cm cannot be the magnetic group. The only compatible magnetic group is P63. In this group however, Landau theory predicts the possibility of a ferromagnetic component and of a linear coupling between the dielectric constant and the AFM order parameter. On one hand we performed dielectric constant measurements under magnetic field that clearly exhibit a metamagnetic transition, and thus confirm these predictions. On the other hand careful magnetization measurements show a small by non null FM component along the c-axis direction. Finally the Landau analysis within the P63 magnetic group shows that only the polarization square is coupled to the magnetic orders and thus neither the magnetization nor the AFM order can be reversed by an applied electric field.
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