Toroidal ordering in crystals

Phase transitions are discussed occurring to ordered states that correspond to the toroidal family of multipoles known in electrodynamics. The ordering of toroidal moments may either occur simultaneously with their formation (as in superconductivity) or may follow it (at lower temperature). In addition to electrodynamic toroidal moments corresponding to poloidal charge currents or a spin configuration, a toroidal state corresponding to poloidal spin currents is possible.