First-principles theory of magnetically induced ferroelectricity in TbMnO3

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.