Ferroelectricity and magnetism in the hexagonal manganite YMnO$_3$ from first principles

The hexagonal manganites are a class of multiferroic materials that are simultaneously ferroelectric and antiferromagnetic. Here, we describe a first-principles study of the structural energetics and polarization in magnetic YMnO$_3$, with the LSDA+U as implemented in VASP. For selected collinear magnetically ordered structures, the lowest symmetry-allowed terms in the Taylor expansion of the energy as a function of zone-center and zone-boundary distortions are identified and computed. The implications for the phase transitions in YMnO$_3$ will be discussed.