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In this work we present a theoretical investigation into anantiferromagnetically coupled spin system, specifically ${\rm Cu}_{3}-X$($\mathrm{X=As,Sb}$), which exhibits an isosceles triangular configuration orslightly distorted equilateral triangular configuration, as previouslyidentified in reference {[}Phys. Rev. Lett. \textbf{96}, 107202 (2006){]}. Thissystem can be effectively represented by the Heisenberg model on a triangularstructure, taking into account the exchange interaction, theDzyaloshinskii-Moriya interaction, g-factors and external magnetic field, asdelineated in the aforementioned reference. By using numerical approach weexplore both zero-temperature and finite-temperature behaviors of a ${\rmCu}_{3}$-like antiferromagnetically coupled spin system. At zero temperature,the system displays a 1/3 quasi-plateau magnetization, when the magnetic fieldis varied. Moreover, we place particular emphasis on magnetic propertiesincluding magnetization, magnetic susceptibility, entropy, and specific heat atfinite temperatures. Furthermore, we investigate the magnetocaloric effect as afunction of an externally imposed magnetic field, oriented both parallel andperpendicular to the plane of the triangular structure. Interestingly, theseconfigurations demonstrate remarkably similar behavior for both orientations ofthe magnetic field. Our investigation also includes an analysis of theadiabatic curve, the Gr\"uneisen parameter, and the variation in entropy whenapplied or removed the magnetic field. The magnetocaloric effect is found to bemore prominent in low the temperature region, typically at $T\sim1$K, for bothparallel and perpendicular magnetic fields at $\sim4.5$T and $\sim5$T,respectively.

Magnetocaloric effect in $\mathrm{Cu}_{3}$-type compounds using the Heisenberg antiferromagnetic model in a triangular ring