Direct coupling of ferromagnetic moment and ferroelectric polarization in BiFeO$_3$

The spin-driven component of electric polarization in a single crystal of multiferroic BiFeO$_{3}$ was experimentally investigated in pulsed high magnetic fields up to 41 T. Sequential measurements of electric polarization for various magnetic field directions provide clear evidence of electric polarization normal to the hexagonal $c$ axis (${bf P}_{rm t}$) in not only the cycloidal phase, but also the field-induced canted antiferromagnetic phase. The direction of ${bf P}_{rm t}$ is directly coupled with the ferromagnetic moment in the canted antiferromagnetic phase, and thus controlled by changing the direction of the applied magnetic field. This magnetoelectric coupling is reasonably reproduced by the metal-ligand hybridization model.