Ferroelectric Ising chain magnet Ca$_3$Co$_{2-x}$Mn$_x$O$_6$ ($xsimeq$0.96) was studied in magnetic fields up to 33 T. Magnetization and neutron scattering measurements reveal successive metamagnetic transitions from the zero-field $uparrow uparrow d
ownarrow downarrow$ spin configuration to the $uparrow uparrow uparrow downarrow$ state with a broad magnetization plateau, and then to the $uparrow uparrow uparrow uparrow$ state. The absence of hysteresis in these plateaus reveals an intriguing coupling between the intra-chain state and the three-dimensional geometrically frustrated magnetic system. Inversion symmetry, broken in the $uparrow uparrow downarrow downarrow$ state, is restored in the $uparrow uparrow uparrow downarrow$ state, leading to the complete suppression of the electric polarization driven by symmetric superexchange.
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 ele
ctric 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.
