In light of the forecast of recent topics of magnetic van der Waals materials [Burch et al., Nature (London) 563, 47 (2018); Gong and Zhang, Science 363, 706 (2019)], it was encouraged to explore new magnetic two-dimensional (2D) materials that contain heavy atoms so as to elevate the magnetic transition temperature. Here, relativistic density functional theory calculations, combined with ab initio molecular dynamics simulations, lattice dynamical calculations, and classical Monte Carlo (MC) simulations, were performed on transition metal trihalide (${\mathrm{TMI}}_{3}$; TM = La, Hf, Ta, W, Re, Os, Ir, Pt) layers, for which heavy $5d$-block and $5p$-block elemental atoms were considered owing to their strong spin-orbit coupling. We identified that these newly designed layers are energetically, dynamically, thermally, and thermomagnetically stable at room temperature. Our investigations revealed that most of them possess the intrinsic semiconducting characteristic with tunable band gap, diverse magnetic properties (ferromagnetic, antiferromagnetic, and nonferromagnetic orders), and large magnetic anisotropy energy (generally larger than 1.9 meV/f.u. and up to 29 meV/f.u.). Based on MC simulations, we proposed that ${\mathrm{TaI}}_{3}$, ${\mathrm{OsI}}_{3}$, and ${\mathrm{PtI}}_{3}$ layers have high Curie temperatures of 575, 225, and 170 K, respectively, which are much larger than those of most magnetic 2D materials such as the notable ${\mathrm{CrI}}_{3}$ (45 K), ${\mathrm{CrGeTe}}_{3}$ (28 K), and ${\mathrm{Fe}}_{3}{\mathrm{GeTe}}_{2}$ layers (130 K). Importantly, our calculations evidenced the high stability of the ${\mathrm{TaI}}_{3}$ layer under ambient conditions, large magnetic moment of $2\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{B}$, large magnetic anisotropy energy of $\ensuremath{-}7.3$ meV/f.u., and high Curie temperature of 575 K, making it possible to experimentally study this layer by more ex situ measurements and even to utilize it in future electronic devices.
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