Peierls transition driven ferroelasticity in two-dimensional $d$-$f$ hybrid magnet

For broad nanoscale applications, it is crucial to implement more functional properties, especially those ferroic orders, into two-dimensional materials. Here GdI$_3$ is theoretically identified as a honeycomb antiferromagnet with large $4f$ magnetic moment. The intercalation of metal atoms can dope electrons into Gds $5d$-orbitals, which alters its magnetic state and lead to Peierls transition. Due to the strong electron-phonon coupling, the Peierls transition induces prominent ferroelasticity, making it a multiferroic system. The strain from undirectional stretching can be self-relaxed via resizing of triple ferroelastic domains, which can protect the magnet aganist mechnical breaking in flexible applications.