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Gadolinium halide monolayers: a fertile family of two-dimensional 4f magnets

Two-dimensional (2D) magnets have great potentials for applications in next-generation information devices. Since the recent experimental discovery of intrinsic 2D magnetism in monolayer CrI$_3$ and few-layer Cr$_2$Ge$_2$Te$_6$, intensive studies have been stimulated in pursuing more 2D magnets and revealing their intriguing physical properties. In comparison to the magnetism based on $3d$ electrons, $4f$ electrons can provide larger magnetic moments and stronger spin-orbit coupling, but have been much less studied in the 2D forms. Only in very recent years, some exciting results have been obtained in this area. In this mini-review, we will introduce some recent progress in 2D Gd halides from a theoretical aspect. It is noteworthy that $4f$ and $5d$ orbitals of Gd both play key roles in these materials. For Gd$X_2$ ($X$=I, Br, Cl and F) monolayers and related Janus monolayers, robust ferromagnetism with large exchanges comes from the $4f^7$+$5d^1$ hybridization of Gd$^{2+}$. The spatially expanded $5d$ electrons act as a bridge to couple localized $4f$ spins. For Gd$X_3$ monolayers, the intercalation of metal atoms can dope electrons into Gd's $5d$ orbitals, which leads to numerous intriguing physical properties, such as ferroelasticity, ferromagnetism, and anisotropic conductance. In brief, Gd halides establish an effective strategy to take advantage of $f$-electron magnetism in 2D materials.