Non collinear magnetism and single ion anisotropy in multiferroic perovskites

TL;DR

This study explores how crystal distortions in multiferroic perovskites influence magnetic interactions, revealing relationships between structural features, weak ferromagnetism, and single-ion anisotropy through density-functional calculations.

Contribution

It provides a detailed analysis of the interplay between oxygen octahedra rotations, ferroelectricity, and magnetic interactions, highlighting the sensitivity of single-ion anisotropy to A-site cation chemistry.

Findings

Weak ferromagnetism is induced by Dzyaloshinsky-Moriya interaction due to oxygen rotations.

Single-ion anisotropy can be unexpectedly large and sensitive to A-site chemistry.

The relative size of ferroelectric distortions and oxygen rotations can tune weak ferromagnetism.

Abstract

The link between the crystal distortions of the perovskite structure and the magnetic exchange interaction, the single-ion anisotropy (SIA) and the Dzyaloshinsky-Moriya (DM) interaction are investigated by means of density-functional calculations. Using BiFeO$_3$ and LaFeO$_3$ as model systems, we quantify the relationship between the oxygen octahedra rotations, the ferroelectricity and the weak ferromagnetism (wFM). We recover the fact that the wFM is due to the DM interaction induced by the oxygen octahedra rotations. We find a simple relationship between the wFM, the oxygen rotation amplitude and the ratio between the DM vector and the exchange parameter such as the wFM increases with the oxygen octahedra rotation when the SIA does not compete with the DM forces induced on the spins. Unexpectedly, we also find that, in spite of the $d^5$ electronic configuration of Fe$^{3+}$, the SIA is very large in some structures and is surprisingly strongly sensitive to the chemistry of the $A$-site cation of the $A$BO$_3$ perovskite. In the ground $R3c$ state phase we show that the SIA shape induced by the ferroelectricity and the oxygen octahedra rotations are in competition such as it is possible to tune the wFM "on" and "off" through the relative size of the two types of distortion.