Multiferroic crossover in perovskite oxides

The coexistence of ferroelectricity and magnetism in ABO₃ perovskite oxides is rare, a phenomenon that has become known as the ferroelectric ``d⁰ rule.'' Recently, the perovskite BiCoO₃ has been shown experimentally to be isostructural with PbTiO₃, while simultaneously the d⁶4pt0exCo³⁺ ion has a high-spin ground state with C-type antiferromagnetic ordering. It has been suggested that the hybridization of Bi $6s$ states with the O $2p$ valence band stabilizes the polar phase, however, we have recently demonstrated that Co³⁺ ions in the perovskite structure can facilitate a ferroelectric distortion via the Co $3d$--O $2p$ covalent interaction [L. Weston, et al., Phys. Rev. Lett. 114, 247601 (2015)]. In this paper, using accurate hybrid density functional calculations, we investigate the atomic, electronic, and magnetic structure of BiCoO₃ to elucidate the origin of the multiferroic state. To begin with, we perform a more general first-principles investigation of the role of d electrons in affecting the tendency for perovskite materials to exhibit a ferroelectric distortion; this is achieved via a qualitative trend study in artificial cubic and tetragonal LaBO₃ perovskites. We choose La as the A cation so as to remove the effects of Bi $6s$ hybridization. The lattice instability is identified by the softening of phonon modes in the cubic phase, as well as by the energy lowering associated with a ferroelectric distortion. For the LaBO₃ series, where B is a d⁰--d⁸ cation from the $3d$ block, the trend study reveals that increasing the d orbital occupation initially removes the tendency for a polar distortion, as expected. However, for high-spin d⁵--d⁷ and d⁸ cations a strong ferroelectric instability is recovered. This effect is explained in terms of increased pseudo-Jahn-Teller (PJT) p-d vibronic coupling. The PJT effect is described by the competition between a stabilizing force (K₀) that favors the cubic phase, and a vibronic term that drives the ferroelectric state (Kᵥ). The recovery of the lattice instability for high-spin d⁵--d⁷ and d⁸ cations is due to (i) a reduction in K₀ due to a significant volume increase arising from population of the σ-bonded axial d4pt0exeg orbitals, and (ii) an increase in the Kᵥ contribution arising from increased p-d hybridization; our calculations suggest that the former mechanism is dominant. Surprisingly, we are able to show that, in some cases unpaired electron spins actually drive ferroelectricity, rather than inhibit it, which represents a shift in the understanding of how ferroelectricity and magnetism interact in perovskite oxides. It follows, that for the case of BiCoO₃, the Co³⁺ ion plays a major role in the ferroelectric lattice instability. Importantly, the ferroelectric polarization is greatly enhanced when the Co³⁺ ion is in the high-spin state, when compared to the nonmagnetic, low-spin state, and a large coupling of the electric and magnetic polarization is present. Generally, for d⁵--d⁷ B cations in ABO₃ perovskites, an inherent and remarkably strong magnetoelectric coupling exists via the multiferroic crossover effect, whereby switching the spin state strongly affects the ferroelectric polarization and, potentially, manipulation of the polarization with an externally applied electric field could induce a spin-state transition. This novel effect is demonstrated for BiCoO₃, for which the ground spin state is switched by reducing the internal ferroelectric polarization. These results provide a deeper insight into perovskite ferroelectrics and multiferroics.