text: To be defined as ferroelectric, a material must have a spontaneous electric polarization that is switchable by an applied electric field. Usually such an electric polarization arises via an inversion-symmetry-breaking structural distortion from a parent centrosymmetric phase. For example, in the prototypical ferroelectric barium titanate, BaTiO, the parent phase is the ideal cubic ABO perovskite structure, with the B-site Ti ion at the center of its oxygen coordination octahedron and no electric polarisation. In the ferroelectric phase the Ti ion is shifted away from the center of the octahedron causing a polarization. Such a displacement only tends to be favourable when the B-site cation has an electron configuration with an empty d shell (a so-called d configuration), which favours energy-lowering covalent bond formation between the B-site cation and the neighbouring oxygen anions.
  This "d0-ness" requirement is a clear obstacle for the formation of multiferroics, since the magnetism in most transition-metal oxides arises from the presence of partially filled transition metal d shells. As a result, in most multiferroics, the ferroelectricity has a different origin. The following describes the mechanisms that are known to circumvent this contraindication between ferromagnetism and ferroelectricity.