Theory of acoustic anomalies just aboveTλin ammonium halides

The sound-propagation anomalies originating from the critical fluctuations of the order parameter just above the $\lambda$ temperature in ammonium halides are studied theoretically. Based on the viewpoint that ammonium-halide crystals can be regarded as a pseudospin-phonon coupled system with interaction term of volume magnetostriction type, the sound-attenuation coefficient $\alpha \left(\omega \right)$ is calculated by making use of the mode-coupling theory. The present theory contains one numerically unknown quantity ($\frac{\partial J^{\mathrm{eff}}}{\partial R}$) derived from the basic Hamiltonian, which is nonessential for our discussions. The propagation-direction and polarization dependences of $\alpha \left(\omega \right)$ are investigated by distinguishing two cases according to the microscopic mechanism of the phase transition; (a) the direct-coupling case (e.g., N${\mathrm{H}}_4$Cl at 1 atm), and (b) the indirect one (e.g., N${\mathrm{H}}_4$Br at 1 atm). It is shown that in the latter case the $c^{\prime }$ shear-wave anomaly can also be observed, in addition to an ordinary longitudinal sound anomaly for all directions in both cases. It is pointed out that the strength of the attenuation anomaly depends to some extent on the propagation direction and polarization.