First-principles study of improper ferroelectricity in TbMnO3
  We have carried out a first-principles theoretical study of the magnetically induced polarization in orthorhombic TbMnO3, a prototypical material in which a cycloidal spin structure generates an electric polarization via the spin-orbit interaction. We compute both the electronic and the lattice-mediated contributions to the polarization and find that the latter is strongly dominant. We analyze the spin-orbit induced forces and lattice displacements from both atomic and mode-decomposition viewpoints, and show that a simple model based on nearest Mn--Mn neighbor Dzyaloshinskii-Moriya interactions is not able to account fully for the results. The direction and magnitude of our computed polarization are in good agreement with experiment. 
Andrei Malashevich and David Vanderbilt