Inelastic-neutron-scattering study at low temperature of the quantum sine-Gordon breather in 4-methyl-pyridine with partially deuterated methyl groups

Abstract

Inelastic-neutron-scattering spectra of 4-methyl-pyridine (4MP) molecules with partially deuterated methyl groups, referred to as 4MP-${\mathit{ch}}_{2}$d and 4MP-${\mathit{chd}}_{2}$, are reported. At 1.6 K, the observed frequencies for the ${\mathrm{CH}}_{2}$D and ${\mathrm{CHD}}_{2}$ derivatives are 388 \ensuremath{\mu}eV (3.13 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) and 337 \ensuremath{\mu}eV (2.72 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$), respectively. 4MP-${\mathit{ch}}_{2}$d shows an additional band at 436 \ensuremath{\mu}eV (3.51 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$). Between 1.6 and 5.0 K, the band at 3.13 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ progressively merges into the band at 3.51 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. At a higher temperature, 7.5 K, the frequency shifts upwards to 477 \ensuremath{\mu}eV (3.84 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$). Three different models for the methyl-group dynamics are considered: single-particle model, coupled-pair model, and an infinite chain of coupled methyl groups. All the data strongly support the quantum sine-Gordon theory used to describe the dynamics of an infinite chain of coupled methyl groups.At low temperature the bands are assigned to transitions between the quantized traveling states of the sine-Gordon breather mode. The potential for 4MP-${\mathit{ch}}_{2}$d is the same (to first order) as that previously proposed for the fully hydrogenated material. However, small perturbations are introduced, which account for the break of threefold symmetry in the partially deuterated systems. In this case, the breather band splitting at very low temperature corresponds to the coexistence of different chain conformations, or phase correlations, with respect to the methyl-group torsional coordinates. Between 1.6 and 5.0 K, one of the chain conformations is progressively converted into the other. This conversion is monitored by the tunneling states of the chains. It corresponds to the recovery of the threefold symmetry for the on-site potential. Finally, the breather-frequency shift above about 5K, which is in marked contrast to the fully hydrogenated compound, is attributed to the ``imbalance'' character of the partially deuterated methyl group. Therefore, there is a coupling of the methyl-group torsion coordinate with other librational modes in the crystal. Above about 5 K this coupling averages out the on-site potential. A part of the breather rest energy (mass) is converted into kinetic energy and the traveling frequency increases. The breather is progressively converted into rotons in an almost freely rotating chain of coupled methyl groups.