Magnetic-thermodynamic phase transition in strained phosphorous-doped graphene

Abstract

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 $\epsilon$. This leads to a magnetic quantum phase transition (MQPT) at zero temperature modulated by $\epsilon$. The system transitions from a magnetic phase, characterized by an out-of-plane $s{p}^3$ type hybridization of the P-carbon (P-C) bonds, to a non-magnetic phase when these bonds switch to in-plane $s{p}^2$ hybridization. Employing a Fermi-Dirac statistical model, we calculate key thermodynamic quantities as the electronic entropy $S_e$ and electronic specific heat $C_e$. At finite temperatures, we find the MQPT is reflected in both $S_e$ and $C_e$, which display a distinctive $\hat{I}›$-shaped profile as a function of $\epsilon$. These thermodynamic quantities sharply increase up to $\epsilon =5\%$ in the magnetic regime, followed by a sudden drop at $\epsilon =5.5\%$, transitioning to a linear dependence on $\epsilon$ in the nonmagnetic regime. Notably, $S_e$ and $C_e$ capture the MQPT behavior for low and moderate temperature ranges, providing insights into the accessible electronic states in P-doped graphene. This controllable magnetic-to-nonmagnetic switch offers potential applications in electronic nanodevices operating at finite temperatures.