Recent experiments revealed that monolayer α-RuCl 3 can be obtain by chemical exfoliation method and exfoliation or restacking of nanosheets can manipulate the magnetic properties of the materials. In this present paper, the electronic and magnetic properties of α-RuCl 3 monolayer are investigated by combining first-principles calculations and Monte Carlo simulations. From first-principles calculations, we found that the spin configuration FM corresponds to the ground state for α-RuCl 3 , however, the other excited zigzag oriented spin configuration has energy of 5 meV/atom higher than the ground state. Energy band gap has been obtained as 3 meV using PBE functionals. When spin-orbit coupling effect is taken into account, corresponding energy gap is determined to be as 57 meV. We also investigate the effect of Hubbard U energy terms on the electronic band structure of α-RuCl 3 monolayer and revealed band gap increases approximately linear with increasing U value. Moreover, spin-spin coupling terms (J 1 , J 2 , J 3 ) have been obtained using first principles calculations. By benefiting from these terms, Monte Carlo simulations with single site update Metropolis algorithm have been implemented to elucidate magnetic properties of the considered system. Thermal variations of magnetization, susceptibility and also specific heat curves indicate that monolayer α-RuCl 3 exhibits a phase transition between ordered and disordered phases at the Curie temperature 14.21 K. We believe that this study can be utilized to improve two-dimensional magnet materials.

We have presented dynamic phase transition features and stationary-state behavior of a ferrimagnetic small nanoparticle system with a core-shell structure. By means of detailed Monte Carlo simulations, a complete picture of the phase diagrams and magnetization profiles have been presented and the conditions for the occurrence of a compensation point Tcomp in the system have been investigated. According to Néel nomenclature, the magnetization curves of the particle have been found to obey P-type, N-type and Q-type classification schemes under certain conditions. Much effort has been devoted to investigation of hysteretic response of the particle and we observed the existence of triple hysteresis loop behavior which originates from the existence of a weak ferromagnetic core coupling Jc/J sh , as well as a strong antiferromagnetic interface exchange interaction Jint/J sh . Most of the calculations have been performed for a particle in the presence of oscillating fields of very high frequencies and high amplitudes in comparison with exchange interactions which resembles a magnetic system under the influence of ultrafast switching fields. Particular attention has also been paid on the influence of the particle size on the thermal and magnetic properties, as well as magnetic features such as coercivity, remanence and compensation temperature of the particle. We have found that in the presence of ultrafast switching fields, the particle may exhibit a dynamic phase transition from paramagnetic to a dynamically ordered phase with increasing ferromagnetic shell thickness.

Theoretical and experimental studies present that metal halogens in MX3 forms can show very interesting electronic and magnetic properties in their bulk and monolayer phases. Many MX3 materials have layered structures in their bulk phases, while RuBr3 and RuI3 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 RuX3 can be possible to be synthesised. We also find that monolayers of RuX3 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 RuBr3 and RuI3, respectively. Calculation based on the Monte Carlo simulations reveal interesting magnetic properties of RuBr3, such as large Curie temperature against RuI3, both in bulk and monolayer cases. Moreover, as a result of varying exchange couplings between neighboring magnetic moments, magnetic properties of RuBr3 and RuI3 can undergo drastic changes from bulk to monolayer. We hope our findings can be useful to attempt to fabricate the bulk and monolayer of RuBr3 and RuI3.

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