Ferrotoroidic Moment as a Quantum Geometric Phase
  We present a geometric characterization of the ferrotoroidic moment in terms of a set of Abelian Berry phases. We also introduce a fundamental complex quantity which provides an alternative way to calculate the ferrotoroidic moment and its moments, and is derived from a second order tensor. This geometric framework defines a natural computational approach for density functional and many-body theories. 
C. D. Batista, G. Ortiz, and A. A. Aligia