Theoretical and experimental studies present that metal halogens in MX$_3$ forms can show very interesting electronic and magnetic properties in their bulk and monolayer phases. Many MX$_3$ materials have layered structures in their bulk phases, while RuBr$_3$ and RuI$_3$ have one-dimensional chains in plane. In this paper, we show that these metal halogens can also form two-dimensional layered structures in the bulk phase similar to other metal halogens, and cleavage energy values confirm that the monolayers of RuX$_3$ can be possible to be synthesised. We also find that monolayers of RuX$_3$ prefer ferromagnetic spin orientation in the plane for Ru atoms. Their ferromagnetic ground state, however, changes to antiferromagnetic zigzag state after U is included. Calculations using PBE+U with SOC predict indirect band gap of 0.70 eV and 0.32 eV for the optimized structure of RuBr$_3$ and RuI$_3$, respectively. Calculation based on the Monte Carlo simulations reveal interesting magnetic properties of RuBr$_3$, such as large Curie temperature against RuI$_3$, both in bulk and monolayer cases. Moreover, as a result of varying exchange couplings between neighboring magnetic moments, magnetic properties of RuBr$_3$ and RuI$_3$ can undergo drastic changes from bulk to monolayer. We hope our findings can be useful to attempt to fabricate the bulk and monolayer of RuBr$_3$ and RuI$_3$.
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