The electronic contribution to the magnetically induced polarization in orthorhombic ${\text{TbMnO}}_3$ is studied from first principles. We compare the cases in which the spin cycloid, which induces the electric polarization via the spin-orbit interaction, is in either the $b\text{−}c$ or $a\text{−}b$ plane. We find that the electronic contribution is negligible in the first case, but much larger, and comparable to the lattice-mediated contribution, in the second case. However, we show that this behavior is an artifact of the particular pattern of octahedral rotations characterizing the structurally relaxed $Pbnm$ crystal structure. To do so, we explore how the electronic contribution varies for a structural model of rigidly rotated ${\text{MnO}}_6$ octahedra and demonstrate that it can vary over a wide range, comparable with the lattice-mediated contribution, for both $b\text{−}c$ and $a\text{−}b$ spirals. We present a phenomenological model that is capable of describing this behavior in terms of sums of symmetry-constrained contributions arising from the displacements of oxygen atoms from the centers of the Mn-Mn bonds.

• Received 29 August 2009

DOI:https://doi.org/10.1103/PhysRevB.80.224407