Influence of the triangular Mn-O breathing mode on the magnetic ordering in multiferroic hexagonal manganites

TL;DR

This study investigates how a specific breathing mode distortion in hexagonal manganites influences their magnetic ordering, revealing the mode's impact on magnetic interactions and ground state configurations.

Contribution

The paper combines symmetry analysis, phenomenological modeling, and first-principles calculations to elucidate the role of the Mn-O breathing mode in magnetic ordering of hexagonal manganites.

Findings

Breathing mode affects magnetic interactions and anisotropy.

Magnetic ground state depends on rare-earth ion and breathing mode.

Developed a phase diagram linking magnetic structure to structural parameters.

Abstract

We use a combination of symmetry analysis, phenomenological modelling and first-principles density functional theory to explore the interplay between the magnetic ground state and the detailed atomic structure in the hexagonal rare-earth manganites. We find that the magnetic ordering is sensitive to a breathing mode distortion of the Mn and O ions in the $ab$ plane, which is described by the K\textsubscript{1} mode of the high-symmetry structure. Our density functional calculations of the magnetic interactions indicate that this mode particularly affects the single-ion anisotropy and the inter-planar symmetric exchanges. By extracting the parameters of a magnetic model Hamiltonian from our first-principles results, we develop a phase diagram to describe the magnetic structure as a function of the anisotropy and exchange interactions. This in turn allows us to explain the dependence of the magnetic ground state on the identity of the rare-earth ion and on the K\textsubscript{1} mode.