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We report an ultrasonic study of the magneto-elastic coupling of thehydrogenated and deuterated (TMTTF)$_2$PF$_6$ organic salts. For both salts thetemperature dependence of the longitudinal velocity along the c* axis displaysa monotonic stiffening of the $C_{33}$ compressibility modulus upon cooling.Below the characteristic temperature scale 40 K the modulus stiffening becomesmarkedly enhanced, in concomitance with the reduction of spin degrees offreedom previously seen in magnetic measurements as low dimensional precursorsof the spin-Peierls transition. The magneto-elastic coupling appears to be muchweaker in the hydrogenated salt due to the highly inhomogeneous elasticbehavior induced by the proximity of the charge ordering transition to thespin-Peierls phase. For the deuterated salt, an important anomaly in theultrasound velocity is observed below the spin-Peierls transition temperature$T_{\rm SP}$ in agreement with scaling of the elastic deformation with thespin-Peierls order parameter. In spite of the weakly inhomogeneous character ofthe spin-Peierls phase transition, the magnetic field dependence of $T_{\rmSP}$ is well captured with the mean-field prediction for the lattice distortedHeisenberg spin chain.

Magneto-elastic coupling in the spin-Peierls ground state of hydrogenated and deuterated (TMTTF)$_2$PF$_6$ salts