Nuclear magnetic resonance line shapes of methyl-like quantum rotors in low-temperature solids

Abstract

Dissipative dynamics of a tunneling, methyl-like rotor, whose spatial coordinate is weakly coupled to a thermal bath, are described using the reduced density matrix (RDM) approach. It is found that, owing to selection rules imposed on thermally induced transitions by the symmetrization postulate, there are two sorts of coherences between the rotor eigenstates that live long enough to be observed on the nuclear magnetic resonance (NMR) time scale. One comprises degenerate pairs of Kramers sublevels at sequential librational levels of the rotor. The other involves nearly degenerate pairs each of which engages one Kramers sublevel and the remaining sublevel, separated from the Kramers doublet by tunneling quantum. These are the coherences which are seen in the inelastic neutron scattering (INS) patterns of methyl-like rotors. From the RDM equation of motion, augumented with spin-dependent terms relevant in the presence of an external magnetic field, the NMR line shape equation is derived. With no loss of information it can be formulated in terms of only the spin degrees of freedom. Its dissipative part includes two rate constants that describe damping of the long-lived tunneling and Kramers coherences, respectively; coherent tunneling is represented in the Hamiltonian part by an apparent spin-spin coupling. These rate constants are the widths of the inelastic and quasielastic lines, respectively, in the INS spectra of methyl-like rotors; the apparent coupling constant is the shift of the inelastic line. This seems to be the first full exposition of the parallelism between INS and NMR images of tunneling rotors. Rationalization of previous findings involving a CD3 rotor was achieved by use of a simple model of rotor-bath couplings, combined with inferences from numerical simulations of NMR line shapes.