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

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