Cupric oxide is a unique magnetic ferroelectric material with a transition temperature significantly higher than the boiling point of liquid nitrogen. However, the mechanism of high-T$_c$ multiferroicity in CuO remains puzzling. In this paper, we cla
rify the mechanism of high-T$_c$ multiferroicity in CuO, using combined first-principles calculations and an effective Hamiltonian model. We find that CuO contains two magnetic sublattices, with strong intrasublattice interactions and weakly frustrated intersublattice interactions, which may represent one of the main reasons for the high ordering temperature of the compound. The weak spin frustration leads to incommensurate spin excitations that dramatically enhance the entropy of the mutliferroic phase and eventually stabilize that phase in CuO.
Magnetic ferroelectric has been found in a wide range of spiral magnets. However, these materials all suffer from low critical temperatures, which are usually below 40 K, due to strong spin frustration. Recently, CuO has been found to be multiferroic
at much higher ordering temperature ($sim$ 230K). To clarify the origin of the high ordering temperature in CuO, we investigate the structural, electronic and magnetic properties of CuO via first-principles methods. We find that CuO has very special nearly commensurate spiral magnetic structure, which is stabilized via the Dzyaloshinskii-Moriya interaction. The spin frustration in CuO is relatively weak, which is one of the main reasons that the compound have high ordering temperature. We propose that high $T_c$ magnetic ferroelectric materials can be found in double sublattices of magnetic structures similar to that of CuO.
