Magnetism and Charge ordering in TMTTF${}_2$-PF${}_6$ organic crystals

Using a combination of Density Functional Theory, mean-field analysis and exact diagonalization calculations we reveal the emergence of a dimerized charge ordered state in TMTTF${}_2$-PF${}_6$ organic crystal. The interplay between charge and spin order leads to a rich phase diagram. Coexistence of charge ordering with a structural dimerization results in a ferroelectric phase, which has been observed experimentally. The tendency to the dimerization is magnetically driven revealing TMTTF${}_2$-PF${}_6$ as a multiferroic material.