Phase and amplitude modes of then=4incommensurate phase II of biphenyl: Neutron scattering experiments and theoretical results

We report the only neutron scattering measurement of phase and amplitude modes in an incommensurate system with a four-component order parameter (n=4): the phase II of biphenyl. Experiments have been performed at low temperature and under hydrostatic pressure, where phase II becomes the ground state of biphenyl. This allows a study at very low temperature, where the damping of the modes is extremely reduced. Three propagating excitations have been observed, one of which is twice degenerate. Comparison between their characteristics and that of the soft mode which drives the transition towards phase II proves unambiguously that they are the phase and amplitude modes of biphenyl phase II. We also develop theoretical calculations within the scope of the Ginzburg-Landau theory, including coupling between the order parameter and strains. Calculations lead to the exact assignment of the measured modes to the different possible excitations of phases and amplitudes according to a single-q or to a double-q structure of phase II. Moreover, comparison between theoretical and experimental results gives a strong argument in favor of the single-q structure.