Theory of ferroelectricity in Bi-based multiferroics

An electron-phonon (vibronic) theory of the Bi-based multiferroics is developed. It is shown that the electron-lattice covalency hybridization between the Bi 6s(2) lone electron pair and empty oxygen 2p states causes instability of R-25 and R-15 polar vibrations in the reference cubic phase. The cubic perovskite structure is distorted by displacements of oxygen ions corresponding to the condensation of the R-25 mode at the boundary point R = pi / a(1,1,1) of the Brillouin zone (alpha is the cell constant of the cubic phase). These oxygen displacements correspond to the rotation of the FeO6 octahedron in BiFeO3 about the cube space diagonal. The triply degenerate mode Gamma(1u) participates in the s-p mixing of Bi lone electron pair states and 2p oxygen states. The ferroelectric instability holds in the R3c phase and the observed ferroelectric transition R3c -> R3c is connected with the softening of the A(2u) mode. The Gamma(1u) mode in the R3c phase splits in E-u and A(2u) modes. We have calculated the spontaneous polarization P-s=30-40 mu C/cm(2) (p, =1.5 mu C/cm(2) is also possible), T-c = 1105 K and dielectric constants. It is shown that the phase transition of the first order is in agreement with the experiment. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim