Molecular displacements in the spin-dimerized state of (tetrathiafulvalene)Cu${\mathrm{S}}_4$${\mathrm{C}}_4$${\left(\mathrm{C}{\mathrm{F}}_3\right)}_4$ at 4.2 K

We have carried out a crystallographic study of the dimerized state of the spin-Peierls compound (TTF)Cu(BDT). X-ray data taken below the dimerization transition at $T_c=12\mathrm{}$ K were analyzed using a model which assumes rigid molecular displacements. We find that pairing is accomplished by a simple longitudinal translation of spin-½ ${\mathrm{}\left(\mathrm{TTF}\right)\mathrm{}}^{+}$ units along the ${\overrightarrow{\mathrm{c}}}_p$ axis in the primitive triclinic cell. We use our quantitative measurement of the displacement magnitude ($\Delta x=0.072\mathrm{}$ Å) within the mean-field spin-Peierls model to show that the unrenormalized energy of the dimerization phonon is about 1 meV. This result is consistent with previous observations of preexisting soft modes in x-ray diffuse-scattering studies. Implications for the observation of this transition in other materials are discussed.