Canted-spin-caused electric dipoles: a local symmetry theory
  A pair of magnetic atoms with canted spins Sa, Sb can give rise to an electric dipole moment P. Several forms for the behavior of such a moment have appeared in the theoretical literature, some of which have been invoked to explain experimental results found in various multiferroic materials. The forms specifically are P1 ~ R x (Sa x Sb); P2 ~ Sa x Sb, and P3 ~ Sa (R . Sa) - Sb (R . Sb), where R is the relative position of the atoms and Sa, Sb are unit vectors. To unify and generalize these various forms we consider P as the most general quadratic function of the spin components that vanishes whenever Sa and Sb are collinear, i.e. we consider the most general expressions that require spin canting. The study reveals new forms. We generalize to the vector P, Moriya's symmetry considerations regarding the (scalar) Dzyaloshinskii-Moriya energy D. Sa x Sb (which led to restrictions on D). This provides a rigorous symmetry argument which shows that P1 is allowed no matter how high the symmetry of the atoms plus environment, and gives restrictions for all other contributions. The analysis leads to the suggestion of terms omitted in the existing microscopic models, suggests a new mechanism behind the ferroelectricity found in the 'proper screw structure' of CuXO2, X=Fe, Cr, and predicts an unusual antiferroelectric ordering in the antiferromagnetically and ferroelectrically ordered phase of RbFe(MoO4)2. 
T. A. Kaplan, S. D. Mahanti