  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.
