Electronic and magnetic properties of monolayer α-RuCl₃: a first-principles and Monte Carlo study

Recent experiments revealed that monolayer α-RuCl₃ can be obtained by a chemical exfoliation method and exfoliation or restacking of nanosheets can manipulate the magnetic properties of the materials. In this paper, the electronic and magnetic properties of an α-RuCl₃ monolayer are investigated by combining first-principles calculations and Monte Carlo simulations. From first-principles calculations, we found that the spin configuration of FM corresponds to the ground state for α-RuCl₃, however, the other excited zigzag oriented spin configuration has an energy of 5 meV per atom higher than the ground state. The energy band gap is found to be 3 meV using PBE functionals. When the spin-orbit coupling effect is taken into account, the corresponding energy gap is determined to be 57 meV. We also investigate the effect of the Hubbard U energy terms on the electronic band structure of the α-RuCl₃ monolayer and revealed that the band gap increases approximately linearly with increasing U value. Moreover, spin-spin coupling terms (J₁, J₂, and J₃) have been obtained using first-principles calculations. By benefiting from these terms, Monte Carlo simulations with a single site update Metropolis algorithm have been implemented to elucidate the magnetic properties of the considered system. Thermal variations of magnetization, susceptibility and also specific heat curves indicate that monolayer α-RuCl₃ exhibits a phase transition between ordered and disordered phases at the Curie temperature of 14.21 K. We believe that this study can be utilized to improve two-dimensional magnetic materials.