Understanding the spin-driven polarizations in Bi$M$O$_{\mathrm{3\thinspace }}(M=$3$d$ transition metals) multiferroics.

Bismuth ferrite (BiFeO$_{\mathrm{3}})$, a promising multiferroic, stabilizes in a perovskite type rhombohedral crystal structure (space group R3c) at room temperature. Recently, it has been reported that in its ground state it possess a huge spin-driven polarization [1]. To probe the underlying mechanism of this large spin-phonon response, we examine these couplings within other Bi based 3$d$ transition metal oxides Bi$M$O$_{\mathrm{3\thinspace }}(M=$ Ti, V, Cr, Mn, Fe, Co, Ni) using density functional theory. Our results demonstrate that this large spin-driven polarization is a consequence of symmetry breaking due to competition between ferroelectric distortions and anti-ferrodistortive octahedral rotations. Furthermore, we find a strong dependence of these enhanced spin-driven polarizations on the crystal structure; with the rhombohedral phase having the largest spin-induced atomic distortions along [111]. These results give us significant insights into the magneto-electric coupling in these materials which is essential to the magnetic and electric field control of electric polarization and magnetization in multiferroic based devices. [1] J. H. Lee, and R. S. Fishman, \underline {http://arxiv.org/abs/1504.07106}