Fate Of Soliton Matter Upon Symmetry-Breaking Ferroelectric Order

In a one-dimensional (1D) system with degenerate ground states, their domain boundaries, dubbed solitons, emerge as topological excitations often carrying unconventional charges and spins; however, the soliton excitations are vital in only the nonordered regime. Then a question arises: How do the solitons conform to a three-dimensional (3D) ordered state? Here, using a quasi-1D organic ferroelectric, tetrathiafulvalene-p-chloranil (TTF-CA), with degenerate polar dimers, we pursue the fate of spin-soliton charge-soliton composite matter in a 1D polar-dimer liquid upon its transition to a 3D ferroelectric order by resistivity, nuclear magnetic resonance (NMR), and nuclear quadrupole resonance (NQR) measurements. We demonstrate that the soliton matter undergoes neutral spin-spin soliton pairing and spin-charge soliton pairing to form polarons, coping with the 3D order. Below the ferroelectric transition, the former contributes to the magnetism through triplet excitations, which rapidly fade out on cooling, whereas the latter carries electrical current with paramagnetic spins that more moderately decrease with temperature. The nearly perfect scaling between NMR and NQR relaxation rates in the ferroelectric phase evidences that spin carriers diffuse with lattice distortion, namely, in the form of polarons. From the combined analyses of conductivity and NMR relaxation rate, we derive the excitation energies of polaron excitations and diffusion. Our results reveal the whole picture of soliton matter that condenses into the 3D ordered state.