Non- d0 ferroelectricity from semicovalent superexchange in bismuth ferrite

Abstract

Empirical ${d}^{0}$ rule, i.e., magnetic unpairing $d$ occupation tends to be chemically incompatible for ferroelectrics, has for long inhibited the availability of room-temperature single-phase multiferroics. Here, we readdress the ferroelectricity of type-I multiferroic $\mathrm{BiFe}{\mathrm{O}}_{3}$, and conclusively clarify hybrid origins of lone-pair electrons' instability. Surprisingly, the sole lone-pair mechanism cannot account for overall polarization. Thus, beyond the popular belief, we propose that, with half-filling ${t}_{2g}^{3}{e}_{g}^{2}$ configuration and stereochemical activity of Bi's lone pair preparticipating, renormalized nonempty Fe $3d$ orbitals render $\mathrm{BiFe}{\mathrm{O}}_{3}$ a strong p-d charge-transfer insulator, and further induce non-${d}^{0}$ ferroelectricity through antiferromagnetic semicovalent superexchange. The magnetoelectric coupling scenario is numerically elaborated by mean-field p-d model, and first-principles generalized gradient approximation $\mathrm{GGA}+U$ calculations. The magnetically induced ferroelectricity also reconciles the competitivity of octahedral rotations and ferroelectricity, which turns into cooperative behavior as octahedral rotations straighten the $\mathrm{Fe}\text{\ensuremath{-}}\mathrm{O}\text{\ensuremath{-}}\mathrm{Fe}$ bonds and strengthen superexchange interactions. Such mechanism is in principle ubiquitous in magnets with superexchange interaction and manipulatable to hybridization engineering.