Anomalous temperature dependence of the frequency and damping constant of phonons near Tλ in ammonium halides

The mechanism which gives rise to the anomalous temperature dependence of nonsoft phonons near the lambda transition point in ammonium halides is discussed. The orientation of an ammonium ion in its unit cell is treated as a pseudo-Ising spin, and the Hamiltonian of a pseudospin–phonon coupled system is derived from simple assumptions. Perturbation theory is used to evaluate pseudospin–phonon scattering terms in the Hamiltonian. The resulting expressions for the frequency and the damping constant of phonons are seen to include a long-range order parameter and a correlation function of the pseudo-Ising spins, which are well known to show characteristic temperature variations near a lambda point. The results qualitatively explain the anomalous temperature variation in the frequency and the damping constant of nonsoft optical phonons near the lambda point, as measured by means of Raman scattering experiments in NH4Cl and NH4Br. The difference between the temperature dependences of the frequency in these two materials is also discussed.