Quantum Machines Using Cu 3 $\mathrm{Cu}_{3}$ -Like Compounds Modeled by Heisenberg Antiferromagnetic in a Triangular Ring

A theoretical study of an antiferromagnetically coupled spin system, specifically ${\text{Cu}}_3-X\left(\text{X=As, Sb}\right)$, characterized by a slightly distorted equilateral triangle configuration is presented. Using the Heisenberg model with exchange and Dzyaloshinskii–Moriya interactions, g-factors, and an external magnetic field, three quantum machines are investigated using this system as the working substance, assuming reversible processes. For ${\text{Cu}}_3-X$ the magnetocaloric effect (MCE) is significant at low temperatures ($\approx$1K) under a perpendicular magnetic field ($\approx 5T$). Although only the ${\text{Cu}}_3-\text{As}$ compound is considered, since the ${\text{Cu}}_3-\text{Sb}$ compound behaves quite similarly. How MCE influences the Carnot machine, which operates as a heat engine or refrigerator when varying the external magnetic field is analyzed. In contrast, the Otto and Stirling machines can operate as heat engines, refrigerators, heaters, or thermal accelerators, depending on the magnetic field intensity. The results indicate that enhanced MCE broadens the operating regions for these machines, with the Otto and Stirling machines primarily functioning as refrigerators and accelerators. The corresponding thermal efficiencies are also discussed for all operating modes.