Peierls transition driven ferroelasticity in the two-dimensional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>d</mml:mi><mml:mtext>?</mml:mtext><mml:mi>f</mml:mi></mml:mrow></mml:math> hybrid magnets

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