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.
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