Mixed spin-charge solitons and thermodynamics of (TMTTF)$_2$X

The (TMTTF)$_2$X salts are quasi-one-dimensional materials that undergo two phase transitions as the temperature is lowered from 300 K under ambient pressure. The high temperature transition at T$_{CO}$ $\sim$ 100 K is to a charge-ordered (CO) state. The low temperature transition is often to a spin-Peierls (SP) state that appears at T$_{SP}$ $\sim$ 10 K, and that competes with the CO state. We have investigated the thermodynamics of these systems within an extended Hubbard Hamiltonian that includes (a) on-site and nearest neighbor Coulomb interactions, and (b) bond- and site-coupled quantum phonons. From calculations of charge, bond and spin-susceptibilities we are able to explain the transition from the CO to the SP state. The CO state corresponds to the charge occupancy scheme ...1010... (where `1' and `0' denote charge-rich and charge-poor sites respectively), while the SP state has charge occupancy ...1100.... The transition from the CO to the SP phase as temperature is lowered is driven by spin effects: At high temperatures, high-spin states dominate the free energy, and favor the ...1010... CO configuration. At low temperatures, spin singlet states dominate the free energy and instead favor a singlet SP state with the ...1100... charge pattern. In the temperature region T$_{SP} < T < T_{CO}$ there occur mixed spin-charge solitons that are domain walls between the ...1010... and ...1100... charge patterns.