  We study the polarization induced via spin-orbit interaction by a magnetic
cycloidal order in orthorhombic TbMnO3 using first-principle methods. The case
of magnetic spiral lying in the b-c plane is analyzed, in which the pure
electronic contribution to the polarization is shown to be small. We focus our
attention on the lattice-mediated contribution, and study it's dependence on
the Coulomb interaction parameter U in the LDA+U method and on the wave-vector
of the spin spiral. The role of the spin-orbit interaction on different sites
is also analyzed.
