First-principles prediction of coexistence of magnetism and ferroelectricity in rhombohedral Bi2FeTiO6

First principles calculations based on the density functional theory within the local spin density approximation plus U(LSDA+U)scheme, show rhombohedral Bi$_2$FeTiO$_6$ is a potential multiferroic in which the magnetism and ferroelectricity coexist . A ferromagnetic configuration with magnetic moment of 4 $\mu_B$ per formula unit have been reported with respect to the minimum total energy. Spontaneous polarization of 27.3 $\mu$ C/cm$^2$, caused mainly by the ferroelectric distortions of Ti, was evaluated using the berry phase approach in the modern theory of polarization. The Bi-6s stereochemical activity of long-pair and the `d$^0$-ness' criterion in off-centring of Ti were coexisting in the predicted new system. In view of the oxidation state of Bi$^{3+}$,Fe$^{2+}$,Ti$^{4+}$, and O$^{2-}$ from the orbital-resolved density of states of the Bi-6p, Fe-3d,Ti-3d, and O-2p states,the valence state of Bi$_2$FeTiO$_6$ in the rhombohedral phase was found to be Bi$_2$$^{3+}$Fe$^{2+}$Ti$^{4+}$O$_6$.