Historical Milestones on the Route to Maximal Single Phase Multiferroic Complexity.
Some milestones since the nineteen fifties, having lead to the present day level of understanding of complex single phase multiferroics, will be highlighted, partly based on experience gained with the crystal family of boracites M3B7O13X, where M stands for a bivalent 3d-transition metal ion and X for an ion of the halogens F, Cl, Br or I1.Multiferroics have originally been defined as materials with two or more so-called primary ferroic properties - ferro(i)magnetism, ferroelectricity, ferroelasticity - occurring in a single phase1. In recent times ferrotoroidicity, characterized by a spontaneous toroidal moment, was recognized to complete this family of analogues2.The presence of two or more ferroic properties in a single phase is ruled by stringent symmetry and structural requirements. The occurrence of a spontaneous polarization, magnetization and toroidization (toroidal moment)2 in a common phase is restricted to 9 Heesch-Shubnikov point groups, out of a total of 122. Additional ferroelasticity with centro- or noncentrosymmetry of the prototype phase plays a key role for partial or full coupling between named primary ferroic spontaneous quantities and the associated coupled or non-coupled domain switching, respectively3. However, ferroelasticity can sometimes act as a troublemaker.When considering induced toroidal moments, several novel secondary ferroic phenomena can be postulated, such as electrotoroidic, magnetotoroidic, piezotoroidic effects, toroidal optical SHG and toroidal optical rectification2. No experimental evidence for these effects has been reported so far.Measurements of the linear magnetoelectric effect with strong asymmetry of the off-diagonal tensor components have brought evidence in several substances for the presence of a spontaneous or spin-flop-induced toroidal moment4. The recent first monitoring of ferrotoroidic domains5 has brought further, compelling support for this novel type of primary ferroic. Multiferroic complexity increases with the highest allowed number of ferroic domains of an Aizu-species (prototype/ferroic phase point group pair). This number increases with increasing number of types of ferroic order in a single phase and with decreasing symmetry of that phase. Thus a triclinic triple-ferroic-phase perovskite would reach a maximum of 96 domain states in principle. In case of the additional presence of ferrotoroidic domains5,6 that number would be doubled in principle. As a consequence, applications of coupled switching appear feasible only, if Aizu species with a small number of domain states are used. 1. H. Schmid, Ferroelectrics, 162, 317-338(1994); 2. H. Schmid, Ferroelectrics, 252, 41(2001); 3. H. Schmid, Ferroelectrics, 221, 9-17(1999);; 4. Ref. in: H. Schmid in: M. Fiebig et al(eds.), Magnetoelectric Interaction Phenomena in Crystals, 1-34(2004), Kluwer Academic Pub. 5. Bas B. van Aken, M. Fiebig, J.-P. Rivera and H. Schmid, Symposium T; 6. D.G. Sannikov, Ferroelectrics, 291, 157(2003).