Neutron investigation of the dynamical properties of the mercury-chain compoundHg3−δ AsF6

Abstract

We present in this paper the results of a detailed neutron scattering investigation at various temperatures of the dynamical properties of the linear-mercury-chain compound ${\mathrm{Hg}}_{3-\delta } \mathrm{As}{\mathrm{F}}_6$. The main emphasis has been put on the nature of the response function of the Hg chains at higher temperatures ($T\gtrsim 150$ K). The results are analyzed and discussed in terms of new theoretical results obtained by Emery and Axe, and it is found that the behavior of the Hg chains in this temperature region is one-dimensional liquidlike, in accordance with theoretical predictions. Below $T_c=120\mathrm{}$ K where three-dimensional long-range order is established among the Hg ions, the transverse phononlike excitations in the Hg chains with displacement along the chain develop a small (∼ 0.1 meV) energy gap at finite wave vector. This feature makes it straightforward to demonstrate the absence of elastic scattering in the sheets of scattering from the Hg chains. We have measured at room temperature acoustic As${\mathrm{F}}_6$ sublattice phonons in the $\Delta \left(\zeta 00\right)$ and the $\Lambda \left(00\mathrm{}\zeta \right)$ directions. The observed dispersion slope of the transverse branch along $\Delta$ polarized along $\Lambda$ is about 25% smaller than that of the transverse branch along $\Lambda$ polarized along $\Delta$, in apparent disagreement with elasticity theory which predicts both modes to be governed by $C_{44}$. We show that this behavior can be qualitatively explained by the anisotropic coupling between Hg chains and the host lattice, leading to a much smaller elastic regime in the $\Lambda$ direction than in the $\Delta$ direction.