Acoustical properties of(TMTSF)2PF6in the spin-density-wave ground state

Abstract

We have carried out ultrasonic investigations of ${(\mathrm{TMTSF})}_{2}{\mathrm{PF}}_{6}$ in the spin-density-wave (SDW) ground state. Some features for the elastic behavior of the SDW state are found. One of the acoustic modes shows a jump in the sound velocity at the critical temperature of the SDW transition ${(T}_{\mathrm{SDW}}\ensuremath{\approx}12\mathrm{K})$ and a relaxation peak in the attenuation of sound just below ${T}_{\mathrm{SDW}}.$ From this peak we have estimated the characteristic relaxation time of the spin fluctuations along the b axis to be ${t}_{0}=2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\mathrm{s}.$ The sound velocity of another acoustic mode changes with temperature as the square of the order parameter. Besides a maximum just below ${T}_{\mathrm{SDW}}$ the attenuation of this mode has an exponential behavior at low temperatures and yields an energy gap value equal to $2\ensuremath{\Delta}(0)\ensuremath{\approx}96\mathrm{K},$ which is much larger than the BCS value $2\ensuremath{\Delta}(0)\ensuremath{\approx}43\mathrm{K}.$ In addition there is an acoustic mode which displays a slow decrease of the sound velocity in the SDW state. We have also studied the influence of a magnetic field applied along the ${c}^{*}$ axis on the acoustic properties of ${(\mathrm{TMTSF})}_{2}{\mathrm{PF}}_{6}:$ ${T}_{\mathrm{SDW}}$ increases in the magnetic field. We discuss our experimental results in the frame of theoretical considerations which are based on the assumption that phonons influence the exchange interaction between the spins of the conducting electrons and thus couple to the SDW (magnetoelastic coupling). In our model, the temperature behavior of the sound velocity and the attenuation of sound is related to the real and imaginary parts of the dynamical spin susceptibility. This model allows us to classify the temperature behavior of different acoustic modes and to explain the observed anomalies in the sound velocity and the attenuation of sound in the SDW ground state.