Inelastic neutron-scattering study of methyl tunnelling and the quantum sine-Gordon breather mode in isotopic mixtures of 2,6-dimethyl-pyridine at low temperature

Abstract

The INS spectra of 2,6-lutidine at low temperature reveal bands at 11.7, 15, 23, 30, 53 and 190μeV. The bands at 15 and 23μeV are broad and asymmetric. Both can be decomposed into two components at 14.3 and 16.0μeV, 22.8 and 24.7μeV, respectively. In addition, the band at 190μeV can be decomposed into three components at 182, 190 and 202μeV. At higher energy transfer, four broad bands can be identified at 3.64, 6.14, 7.30 and 9.67meV. INS spectra in the 100–200μeV region of isotopic mixtures containing 5, 15, 30, 40, 60, 73 and 85wt% (weight per cent) of 2,6-lutidine-h 9 into 2,6-lutidine-d 9 give a continuous frequency shift for the main feature from 190μeV (100wt% 2,6-lutidine-h 9) to 119μeV (5wt% 2,6-lutidine-h 9). These bands show upward frequency shifts with temperature above 10 K. For pure 2,6-lutidine-h 9 the frequency variation is consistent with a Boltzmann law and an activation energy ∼ 4.6meV. The bands below 50μeV show no significant temperature effect. These observations reveal collective rotation of the methyl groups. The quantum sine-Gordon theory is used to describe the dynamics in infinite chains of coupled rotors. The observed transitions are interpreted as travelling-states of the breather mode in a periodic potential (self-pinning).