Broken Symmetries, Non-reciprocity and Multiferroicity
When the motion of an object in one direction is different from that in the opposite direction is called non-reciprocal directional dichroism (or simply a non-reciprocal effect). The object can be electron, phonon (lattice wave), magnon (spin wave), or light in crystalline solids, and the best known example is non-reciprocal charge transport (i.e. diode) effects in p-n junctions, where a built-in electric field ( E ) breaks the directional symmetry. In addition to p-n junctions, numerous technological devices such as optical isolators or spin current diodes can utilize non-reciprocal effects. We, fist, introduce the concept of symmetry-Operational Similarity (SOS). Then, we will discuss how non-reciprocal effects can be understood in terms of SOS. Furthermore, we will demonstrate that the SOS approach can readily explain various mechanisms for multiferroicity with magnetism-induced electric polarization. We will also discuss the predicting power of the SOS concept.