8.3 Requirements of a Magnetoelectric and Multiferroic Material

There are many material requirements which need to be fulfilled for a material to be called as multiferroic. For instance, for ferroelectricity, a material must be non-centrosymmetric to possess spontaneous electrical polarization and there are only a limited number of point groups (out of 32) which allow an unique polar direction. Similarly, spontaneous magnetic moment is permitted by 31 point groups. Out of these, 13 point groups allow occurrence of both the properties simultaneously. Since this is not a small number; it is probably unlikely that symmetry plays an important role in determining a multiferroic.

Electrically, while a ferroelectric material must be an insulator, it is not a constraint for a ferromagnetic material. For most ferromagnets, electronically speaking, the conductivity is due to high density of states at the Fermi level while the same is not true for ferroelectrics and insulators. However, there are a few magnetic oxides, such as half metallic magnets and ferrimagnetic oxides which show reasonable spontaneous magnetism while simultaneously being semiconducting or insulating.

As far as the chemistry of the material is concerned, most ferroelectrics require ions whose shells are filled and in case of perovskites the B-atom at the centre of BO₆ octahedra must have d⁰ type electron configuration. In contrast, magnetic systems require d-orbitals to be partially occupied for magnetic ordering to develop. Latter also puts constraints to maintaining the center of symmetry in these systems.

Among type I multiferroics, multiple mechanisms of ferroelectricity have been proposed⁵. For example, in mixed perovskites, it has been suggested that d⁰ ions being ferroelectrically active shift from the center of O₆ octaehdra while magnetic order is maintained by dn ions. In contrast, in materials like BiFeO₃, ferroelectricity is believed to arise due to the ordering of lone pairs of Bi in one direction such as [111]. Another proposed mechanism for ferroelectricity is charge ordering i.e. if after charge ordering has occurred, the sites have different charges and bonds turn out to be of unequal lengths. This is seen in materials like TbMn₂O₅. Finally, materials like YMnO₃ exhibit geometric ordering due to tilting of rigid MnO₅ polyhedra, resulting in Y and O atoms coming closer to each other forming dipoles.

Another factor that could be analyzed is the size of small cation, especially in the perspective of perovskites. However, upon comparison, one finds that this is not a valid argument as sizes vary considerably for different kinds of compounds.

Another contrast between ferroelectric and ferromagnetically ordered systems is that the way structure is distorted. While ferroelectrics undergo a phase transition as temperature changes, low temperature phase being non-centrosymmetric, ferromagnetic materials show significant Jahn-Teller distortion arising from partially filled d-shells. The latter is almost absent in most ferroelectrics as it has been postulated that Jahn-Teller distorted structure may have less driving force for off-center displacement of B-ions in the octahedra.

Another condition which ferroelectric materials show is that they possess a time reversal symmetry but do not exhibit a space inversion symmetry (i.e. polarization reverses in space). On the other hand, ferromagnetic materials possess space inversion symmetry but do not exhibit time inversion symmetry.