Magnetic phase diagram of HoMnO3

The phase diagram of hexagonal ${\mathrm{HoMnO}}_3$ in the magnetic-field/temperature plane is investigated by second harmonic generation (SHG). Four different magnetic phases of the frustrated Mn sublattice are identified on the basis of the selection rules for SHG. In-plane or interplane reordering of Mn spins at the phase boundaries occurs almost independent of each other which leads to a tetracritical point in the phase diagram. Interactions of the Mn and Ho sublattices are discussed as possible origin of the phase transitions.