Orthorhombic BiFeO3: Theoretical studies on magnetoelectric effects of the multiferroic phase

The rhombohedral $\mathrm{BiFe}{\mathrm{O}}_{3}$ (BFO), as a star multiferroics, has been of particular interest, but yet it exhibits zero magnetization, which limits its practical application. Remarkably, net magnetization and magnetoelectric (ME) coupling was reported in orthorhombic BFO at room temperature in a recent experiment. However, the underlying mechanism of its ME coupling has not been fully understood. Here, we systematically investigated magnetic structures and ME coupling of the orthorhombic BFO using density functional theory and symmetry analysis. We find it can host large electric polarization and weak ferromagnetism simultaneously, the possible coupling between them is $\mathbit{\ensuremath{\omega}}\ifmmode\cdot\else\textperiodcentered\fi{}(\mathbit{L}\ifmmode\times\else\texttimes\fi{}\mathbit{M})$. More interestingly, its polarization $P$ and magnetization $M$ can be switched simultaneously under an electric field, and it shows a linear ME effect when an external magnetic field is applied. Thus, our study provides a substantially deeper understanding of the ME effect of the orthorhombic BFO and confirm it is a multiferroic with the linear ME coupling.