Spin-lattice relaxation and molecular reorientations near Tc with application to NH4Cl

Abstract

Reorientations of the ammonium tetrahedra around C₂ axes in the neighborhood of the structural phase transition in a NH₄Cl crystal are described by a master equation. Within each group of two sterically different tetrahedral configurations characterized by a pseudospin variable $\text{σ=± 1}$ distinction is made of a=12 sterically equivalent positions. Cooperative dynamical behavior is introduced by extending Glauber's theory of the dynamics of an Ising system to the tetrahedral motion in molecular crystals. The (approximate) solution of the master equation yields a critical slowing down behavior for the pseudospin correlation function. This explains quadrupole spin‐lattice relaxation $T_1^Q$ experiments. In addition the decay time τ for the probability P(σa;t) of finding a tetrahedron in a given position σ, α∈ 12 is found to depend on the equilibrium pair correlation function g=<σ_iσ_i+1>. By relating this quantity to the thermal expansion, the proton spin‐lattice relaxation time $T_1^P$ can be expressed in terms of the anomalous thermal expansion. The theory explains the anomalous behaviour found experimentally for $T_1^P$ around the phase transition at low pressure and high pressure.