Magnetic quantum phase transition extension in strained P-doped graphene

We explore quantum-thermodynamic effects in a phosphorous (P)-doped graphene monolayer subjected to biaxial tensile strain. Introducing substitutional P atoms in the graphene lattice generates a tunable spin magnetic moment controlled by the strain control parameter ε. This leads to a magnetic quantum phase transition (MQPT) at zero temperature modulated by ε. The system transitions from a magnetic phase, characterized by an out-of-plane sp³ type hybridization of the P–carbon (P–C) bonds, to a non-magnetic phase when these bonds switch to in-plane sp² hybridization. Employing a Fermi–Dirac statistical model, we calculate key thermodynamic quantities such as the electronic entropy S_e and electronic specific heat C_e. At finite temperatures, we find a MQPT extension characterized by S_e and C_e, where both display a distinctive Λ-shape profile as a function of ε. These thermodynamic quantities sharply increase up to ε = 5% in the magnetic regime, followed by a sudden drop at ε = 5.5%, transitioning to a linear dependence on ε in the nonmagnetic regime. This controllable magnetic-to-nonmagnetic switch offers potential applications in electronic nanodevices operating at finite temperatures.