Dzyaloshinskii-Moriya interactions and multiferroic behavior in high-symmetry single molecule magnets*

We study analytically the effects of the antisymmetric exchange, or Dzyaloshinskii-Moriya interactions in high-symmetry single molecule magnets with 2-4 magnetic ions per cluster. When the Moriya rules allow it, such as when an ionic bond does not contain a center of inversion, these interactions can lead to interesting observable effects, including the presence of an electric polarization driven by an applied magnetic field, and associated multiferroic behaviors. We will present our results for tetramers with the common S$_4$ molecular group symmetry, and for other ultrasmall single molecule magnets.