Pseudosymmetry and infrared activity in the incommensurate phase ofA2BX4compounds

We observe, upon cooling just below the paraelectric-incommensurate phase-transition temperature $T_i$, vibrational modes in the infrared reflection spectra of ${\mathrm{K}}_2$ ${\mathrm{ZnCl}}_4$ and ${\mathrm{RbZnCl}}_4$ which are forbidden by symmetry for the high-temperature paraelectric phase but allowed for the lowest-temperature ferroelectric one. This result is consistent with previous results obtained for ${\mathrm{K}}_2$ ${\mathrm{SeO}}_4$. Such a phenomenon can be treated using a superspace group approach. The results can be understood by considering only the progressive distortion triggered by the amplitude-mode motion upon cooling in both the incommensurate and ferroelectric phases. This motion gives rise to structure modulation below $T_i$ and tripling of the $D_{2h}^{16} \mathrm{}\left(\mathrm{Pnam}\right)\mathrm{}$ unit cell at $T_c$, neglecting the incommensurate correction $\Delta$ to the wave vector $q_c=\frac{1}{3}$ and the loss of inversion center at $T_c$.