Soft-mode-driven lattice instabilities in Cs2HgCl4 crystal: phenomenological treatment and far-infrared spectroscopy of the structurally modulated phases

Abstract

This paper reports a comprehensive phenomenological description and experimental infrared (IR) investigations of the soft-mode-driven lattice instabilities into various commensurately and incommensurately modulated phases of Cs2HgCl4 crystals. Our theoretical analysis shows that the lattice instabilities along the a and c crystallographic directions are related to low-frequency transverse optical (TO) phonon branches of Σ2 and Λ3 symmetry, respectively, which merge together in the center of the Brillouin zone at the point of B3g symmetry. As the temperature decreases both branches fall down, leading first to the direct condensation of the soft TO Σ2 mode in the symmetric Σ direction (k ∥ a*). On the other hand, coupling of the TO and transverse acoustic (TA) modes of Λ3 symmetry causes, at somewhat lower temperatures, a series of frozen modulated commensurate and incommensurate states developing along the symmetric Λ direction (k ∥ c*). Polarized far-infrared (FIR) reflectivity spectra (15–600 cm−1) of Cs2HgCl4 crystals were measured in a broad temperature region, 10–297 K. Despite a rich sequence of structurally modulated phases existing above 163 K we observed rather moderate temperature evolution of IR spectra where only a few new modes of different polarizations have been activated. However, the commensurately modulated phases occurring below 163 K made an essential impact on the spectra of all three polarizations. The process of activation of both the Raman- and the IR-active phonons in the structurally modulated phases is subjected to the phenomenological analysis.