Figure 2
Illustration: Alan Stonebraker

Figure 2: Different microscopic mechanisms found in type-I multiferroics. (a) In “mixed” perovskites with ferroelectrically active d0 ions (green circles) and magnetic dn ions (red), shifts of d0 ions from the centers of O6 octahedra (yellow plaquettes) lead to polarization (green arrows), coexisting with magnetic order (red arrows). (b) In materials like BiFeO3 and PbVO3, the ordering of lone pairs (yellow ”lobes”) of Bi3+ and Pb2+ ions (orange), contributes to the polarization (green arrow). (c) In charge ordered systems, the coexistence of inequivalent sites with different charges, and inequivalent (long and short) bonds, leads to ferroelectricity. (d) The “geometric” mechanism of generation of polarization in YMnO3 [24] describes the tilting of a rigid MnO5 block with a magnetic Mn remaining at the center. Because of the tilting, the Y-O bonds form dipoles (green arrows), and there appears two “down” dipoles per one “up” dipole so that the system becomes ferroelectric (and multiferroic when Mn spins order at lower temperatures).