This study utilizes the Kane-Mele (KM) and Hubbard models to investigate the thermodynamic and magnetic properties of the α-T3 system, a two-dimensional (2D) material with unique electronic characteristics. The α-T3 system features a distinct flat band in its electronic structure, influencing its behavior under various external conditions such as spin–orbit coupling (SOC), on-site Coulomb repulsion (OSCR), temperature, and doping. The research demonstrates how SOC and OSCR significantly change the electronic density of states, electronic heat capacity, and Pauli magnetic susceptibility. Notably, SOC induces band splitting, while increased OSCR shifts and splits the flat band, enhancing thermodynamic properties. The results display that the α-T3 system exhibits paramagnetic behavior for a SOC strength (λ) of 0.5 eV and an α value of 0.5. An intriguing observation is that OSCR induces a transition from a paramagnetic phase to an antiferromagnetic phase. These findings highlight the potential of the α-T3 system for applications in spintronics, thermal management, and nanoelectronics, offering new avenues for technological advancements in energy storage and sensing.
