  Intriguing lattice dynamics has been predicted for aperiodic crystals that
contain incommensurate substructures. Here we report inelastic neutron
scattering measurements of phonon and magnon dispersions in Sr14Cu24O41, which
contains incommensurate one-dimensional (1D) chain and two-dimensional (2D)
ladder substructures. Two distinct pseudoacoustic phonon modes, corresponding
to the sliding motion of one sublattice against the other, are observed for
atomic motions polarized along the incommensurate axis. In the long wavelength
limit, it is found that the sliding mode shows a remarkably small energy gap of
1.7-1.9 meV, indicating very weak interactions between the two incommensurate
sublattices. The measurements also reveal a gapped and steep linear magnon
dispersion of the ladder sublattice. The high group velocity of this magnon
branch and weak coupling with acoustic and pseudoacoustic phonons can explain
the large magnon thermal conductivity in Sr14Cu24O41 crystals. In addition, the
magnon specific heat is determined from the measured total specific heat and
phonon density of states, and exhibits a Schottky anomaly due to gapped magnon
modes of the spin chains. These findings offer new insights into the phonon and
magnon dynamics and thermal transport properties of incommensurate magnetic
crystals that contain low-dimensional substructures.
