Spin-Orbit Coupling and Ion Displacements in Multiferroic TbMnO3

TL;DR

This study uses relativistic DFT calculations to analyze the spin-spiral planes and ferroelectric polarization mechanisms in TbMnO3, highlighting the importance of ion displacements over purely electronic models.

Contribution

It demonstrates that ion displacements are essential for accurate prediction of ferroelectric polarization in TbMnO3, challenging the adequacy of the pure electronic KNB model.

Findings

Spin-spiral plane can be bc- or ab-plane, but not ac-plane.

Pure electronic KNB model fails to predict the correct polarization direction.

Ion displacements are crucial for determining the magnitude and direction of FE polarization.

Abstract

The electronic and magnetic properties of TbMnO3 leading to its ferroelectric (FE) polarization were investigated on the basis of relativistic density functional theory (DFT) calculations. In agreement with experiment, we show that the spin-spiral plane of TbMnO3 can be either the bc- or ab-plane, but not the ac-plane. As for the mechanism of FE polarization, our work reveals that the "pure electronic" model by Katsura, Nagaosa and Balatsky (KNB) is inadequate in predicting the absolute direction of FE polarization. For the ab-plane spin-spiral state of TbMnO3, the direction of FE polarization predicted by the KNB model is opposite to that predicted by DFT calculations. In determining the magnitude and the absolute direction of FE polarization in spin-spiral states, it is found crucial to consider the displacements of the ions from their ecntrosymmetric positions.