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Monte-Carlo phase diagram of a Hubbard-Peierls model in the search for spin crossover transition in $π$-conjugated polymers

We present a Monte Carlo study of the finite temperature properties of an extended Hubbard-Peierls model describing one dimensional $π$-conjugated polymers. The model incorporates electron-phonon and hyperfine interaction and it is solved at the mean field level for half filling. In particular we explore the model as a function of the strength of electron-electron and electron-phonon interactions. At low temperature the system presents a diamagnetic to antiferromagnetic transition as the electron-electron interaction strength increases. At the same time by increasing the electron-phonon coupling there is a transition from a homogeneous to a Peierls dimerized geometry. As expected such a Peierls dimerized phase disappears at finite temperature as a result of thermal vibrations. More intriguing is the interplay between the electron-phonon and the electron-electron interactions at finite temperature. In particular we demonstrate that for a certain region of the parameter space there is a spin-crossover, where the system transits from a low-spin to a high-spin state as the temperature increases. In close analogy to standard spin-crossover in divalent magnetic molecules such a transition is entropy driven. Finally we discuss the role played by the hyperfine interaction over the phase diagram.