Tunable magnetic transition and electronic structure in monolayer iron trihalides Fe X 3 ( X = F ,   Cl ,   Br ,   I )

Two-dimensional (2D) iron trihalides $(\mathrm{Fe}{X}_{3}, X=\mathrm{F}, \mathrm{Cl}, \mathrm{Br}, \mathrm{I})$ are an emerging family of van der Waals magnets whose fundamental physical properties are not yet fully understood. In this work, we present a systematic first-principles study incorporating hybrid functional (HSE06) calculations and Hubbard U corrections to unravel the spin state, magnetic order, electronic structure, and doping response in monolayer $\mathrm{Fe}{X}_{3}$. The high-spin $(S=5/2)$ state is unequivocally established as the universal local ground state across the series. A chemical tuned magnetic transition is identified: ${\mathrm{FeF}}_{3}$ adopts N\'eel-type antiferromagnetic (AFM) order, while ${\mathrm{FeCl}}_{3}$, ${\mathrm{FeBr}}_{3}$, and ${\mathrm{FeI}}_{3}$ are ferromagnetic (FM) semiconductors with Curie temperatures $({T}_{C})$ monotonically increasing from 154 K to 238 K. This trend is driven by the competition between direct AFM exchange and halogen-mediated FM superexchange. Electronically, ${\mathrm{FeCl}}_{3}$ and ${\mathrm{FeBr}}_{3}$ are identified as bipolar magnetic semiconductors, exhibiting a perfect linear scaling of the band gap with halogen electronegativity. An effective tight-binding model derived from maximally Wannier functions reveals a progressive increase in crystal-field splitting $({\mathrm{\ensuremath{\Delta}}}_{\mathrm{oct}})$ from 3.36 eV to 4.22 eV, underpinning the evolving orbital hierarchy across iron trihalides. Crucially, electron doping induces a nonmonotonic magnetic evolution, from FM to geometrically frustrated AFM (zigzag/stripy), culminating in a reentrant FM state, driven by the competition between kinetic energy minimization and orbital-selective electron correlations. Finally, bilayer systems exhibit a universally robust interlayer AFM coupling driven by ${p}_{z}$ orbital-mediated superexchange across the van der Waals gap. Our work provides a complete microscopic picture of the basic magnetic and electronic properties of the 2D $\mathrm{Fe}{X}_{3}$, establishing them as a highly versatile material platform for tunable magnetism and spintronics.