We have studied the structural phase transition of multiferroic $\mathrm{Y}\mathrm{Mn}{\mathrm{O}}_3$ from first principles. Using group-theoretical analysis and first-principles density functional calculations of the total energy and phonons, we perform a systematic study of the energy surface around the prototypic phase. We find a single instability at the zone boundary which couples strongly to the polarization. This coupling is the mechanism that allows multiferroicity in this class of materials. Our results imply that $\mathrm{Y}\mathrm{Mn}{\mathrm{O}}_3$ is an improper ferroelectric. We suggest further experiments to clarify this point.

• Received 26 April 2005

DOI:https://doi.org/10.1103/PhysRevB.72.100103