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

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 Sigma(2) and Lambda(3) symmetry, respectively, which merge together in the center of the Brillouin zone at the point of B-3g symmetry. As the temperature decreases both branches fall down, leading first to the direct condensation of the soft TO Sigma(2) mode in the symmetric Sigma direction (k parallel to a*). On the other hand, coupling of the TO and transverse acoustic (TA) modes of Lambda(3) symmetry causes, at somewhat lower temperatures, a series of frozen modulated commensurate and incommensurate states developing along the symmetric 3 direction (k parallel to 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.