Inelastic-neutron-scattering study of methyl tunneling and the quantum sine-Gordon breather in isotopic mixtures of 4-methyl-pyridine at low temperature

The inelastic-neutron-scattering spectra in the 500-μeV region of a series of mixtures of totally hydrogenated and totally deuterated 4-methyl-pyridine molecules (4MP-${\mathit{h}}_7$ and 4MP-${\mathit{d}}_7$, respectively) with relative concentrations in 4MP-${\mathit{h}}_7$ of 100, 85, 65, 50, 26, 20, and 5 % are presented at various temperatures: 2.5, 4.5, 6.5, 8.5, 11 and 15 K. In pure 4MP-${\mathit{h}}_7$ at 2.5 K, the spectrum shows three partially resolved bands at 468, 510, and 535 μeV. These frequencies are unaffected by temperature up to 15 K where the bands become rather weak. At 2.5 K, the main peak shows a continuous frequency shift with increasing concentration in 4MP-${\mathit{d}}_7$ down to 360 μeV (5% 4MP-${\mathit{h}}_7$) indicating collective motions of the methyl groups. This frequency shift is very sensitive to temperature and vanishes above 10 K. These unusual aspects of the methyl-group dynamics are quantitatively represented by the quantum sine-Gordon equation describing a one-dimensional infinite chain of coupled methyl groups. Accordingly, the weak side bands at 468 and 535 μeV are assigned to in-phase and out-of-phase tunneling transitions, respectively. The main peak at 510 μeV in pure 4MP-${\mathit{h}}_7$ is due to the excitation of the first quantized traveling state of the breather mode. Isotopic dilution effects are understood in terms of breathers trapped in clusters of 4MP-${\mathit{h}}_7$ molecules surrounded by 4MP-${\mathit{d}}_7$ molecules which act as reflective walls. Temperature effects are due to the thermal excitation of breather-roton states in relationship with the zero-point energy difference for 4MP-${\mathit{h}}_7$ and 4MP-${\mathit{d}}_7$ clusters. Finally, some previous spectroscopic data are reconsidered on the basis of the quantum sine-Gordon theory.