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Mechanism of Ferroelectricity in $d^3$ Perovskites - a Model Study

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. Expansion of volume is found to cause a strong reduction of 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 towards the ferroelectric state.