By means of a model Hamiltonian approach we study the role of volume expansion, Hund's coupling, and electron correlation in the standard hybridization mechanism for ferroelectricity in cubic CaMnO${}_3$, a prototypical non-$d^0$ perovskite. Our results establish that the ferroelectric instability arises from a subtle balance between different energy contributions, explaining the origin of its enhancement under negative pressure. An expansion of the volume is found to cause a strong reduction in the elastic energy, while leaving almost unchanged the tendency of Mn states to form covalent bonds with the surrounding oxygens. Hund's coupling with local spins of magnetic cations can reduce and even suppress the instability toward the ferroelectric state.

• Received 10 August 2011

DOI:https://doi.org/10.1103/PhysRevB.84.134101