Contrasting roles of the superexchange and direct exchange interactions in the metal-insulator transitions of the 2D ferromagnetic $1T$-Fe$X_2$ ($X$=Cl, Br, I) monolayers
Within the rapidly growing family of two-dimensional (2D) materials, 2D ferromagnetic (FM) materials have attracted a great deal of recent attention. The ferromagnetism in 2D FM materials originates from the underlying exchange interactions. In particular, metal-insulator transitions (MITs) in 2D FM materials induced via various modulation strategies is critical to the design of 2D electronic devices with reduced sizes (e.g. transistor). However, the critical behaviors of exchange interactions and their effects on the Curie temperatures near MITs remains to be clarified. By taking the 2D FM 1T-FeX2 (X=Cl, Br, I) monolayers as the testbeds, we computationally study the critical behaviors of the exchange interactions in the vicinity of the MITs driven by the on-site Coulomb electron-electon interactions. The FM superexchange interactions and the direct exchange interactions are found to energetically favor the halfmetallic and semiconducting states, respectively. In addition, the halfmetallic states have the stronger FM couplings and thus the higher Curie temperatures. This study provides a comprehensive understanding of the interrelations between MITs and exchange interactions and could be useful for the device design requiring both MITs and exchange-interaction related magnetic properties, particularly robust magnetic ordering and higher Curie temperatures, in 2D FM materials.