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.
@article{arxiv.2202.02304,
title = {Influence of the triangular Mn-O breathing mode on the magnetic ordering in multiferroic hexagonal manganites},
author = {Tara N. Tošić and Quintin N. Meier and Nicola A. Spaldin},
journal= {arXiv preprint arXiv:2202.02304},
year = {2022}
}