Singe ferroelectric and chiral magnetic domain of single-crystalline BiFeO${}_3$ in an electric field

We report polarized neutron scattering and piezoresponse force microscopy studies of millimeter-sized single crystals of multiferroic BiFeO${}_3$. The crystals, grown below the Curie temperature, consist of a single ferroelectric domain. Two unique electric polarization directions, as well as the populations of equivalent spiral magnetic domains, can be switched reversibly by an electric field. A ferroelectric monodomain with a single-$q$ single-helicity spin spiral can be obtained. This level of control, so far unachievable in thin films, makes single-crystal BiFeO${}_3$ a promising object for multiferroics research.