Weak ferromagnetism and magnetoelectric coupling in bismuth ferrite

We analyze the coupling between the ferroelectric and magnetic order parameters in the magnetoelectric multiferroic $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$ using density functional theory within the local spin density approximation (LSDA) and the $\mathrm{LSDA}+\mathrm{U}$ method. We show that weak ferromagnetism of the Dzyaloshinskii-Moriya type occurs in this material, and we analyze the coupling between the resulting magnetization and the structural distortions. We explore the possibility of electric-field-induced magnetization reversal and show that, although it is unlikely to be realized in $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$, it is not in general impossible. Finally, we outline the conditions that must be fulfilled to achieve switching of the magnetization using an electric field.