# Dependence of electronic polarization on octahedral rotations in TbMnO3 from first principles

## TL;DR

This study investigates how octahedral rotations influence electronic polarization in TbMnO3, revealing that electronic contributions vary significantly with structural distortions and are comparable to lattice effects.

## Contribution

The paper introduces a phenomenological model linking electronic polarization to oxygen displacements, highlighting the impact of octahedral rotations on polarization behavior.

## Key findings

- Electronic contribution negligible in b-c plane cycloid
- Electronic contribution significant in a-b plane cycloid
- Electronic polarization varies widely with octahedral rotations

## Abstract

The electronic contribution to the magnetically induced polarization in orthorhombic TbMnO3 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-c or a-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 how 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 MnO6 octahedra, and demonstrate that it can vary over a wide range, comparable with the lattice-mediated contribution, for both b-c and a-b spirals. We introduce 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.