Peierls transition driven ferroelasticity in the two-dimensional d−f hybrid magnets

For broad nanoscale applications, it is crucial to implement more functional properties, especially ferroic orders, into two-dimensional materials. Here, ${\mathrm{GdI}}_{3}$ is theoretically identified as a honeycomb antiferromagnet with a large $4f$ magnetic moment. The intercalation of metal atoms can dope electrons into Gd's $5d$ orbitals, which alters its magnetic state and leads to a Peierls transition. Due to strong electron-phonon coupling, the Peierls transition induces prominent ferroelasticity, making it a multiferroic system. The strain from unidirectional stretching can be self-relaxed via the resizing of triple ferroelastic domains, which can protect the magnet against mechanical breaking in flexible applications.