The Symmetry of Multiferroics
  This paper represents a detailed instruction manual for constructing the Landau expansion for magnetoelectric coupling in incommensurate ferroelectric magnets. The first step is to describe the magnetic ordering in terms of symmetry adapted coordinates which serve as complex valued magnetic order parameters whose transformation properties are displayed. In so doing we use the previously proposed technique to exploit inversion symmetry, since this symmetry had been universally overlooked. Having order parameters of known symmetry which describe the magnetic ordering, we are able to construct the trilinear interaction which couples incommensurate magnetic order to the uniform polarization in order to treat many of the multiferroic systems so far investigated. The role of this theory in comparison to microscopic models is discussed. 
A. Brooks Harris