  We have directly imaged reversible electrical switching of the cycloidal
rotation direction (magnetic polarity) in a (111)-BiFeO3 epitaxial-film device
at room temperature by non-resonant x-ray magnetic scattering. Consistent with
previous reports, fully relaxed (111)-BiFeO3 epitaxial films consisting of a
single ferroelectric domain were found to comprise a sub-micron-scale mosaic of
magneto-elastic domains, all sharing a common direction of the magnetic
polarity, which was found to switch reversibly upon reversal of the
ferroelectric polarization without any measurable change of the magneto-elastic
domain population. A real-space polarimetry map of our device clearly
distinguished between regions of the sample electrically addressed into the two
magnetic states with a resolution of a few tens of micron. Contrary to the
general belief that the magneto-electric coupling in BiFeO3 is weak, we find
that electrical switching has a dramatic effect on the magnetic structure, with
the magnetic moments rotating on average by 90 degrees at every cycle.
