Calculation of Raman- and infrared-active modes of ${\mathrm{Tl}}_2$${\mathrm{CaBa}}_2$${\mathrm{Cu}}_2$${\mathrm{O}}_8$

We present the frequencies and polarizaton vectors of the infrared- and Raman-active modes for ${\mathrm{Tl}}_2$ ${\mathrm{CaBa}}_2$ ${\mathrm{Cu}}_2$ ${\mathrm{O}}_8$ (Tl 2:1:2:2). Our calculations are carried out in the framework of shell models, which are based on short-range overlap and long-range Coulomb potentials, as well as ionic polarizabilities. A guiding principle of this work is that the shell models for the different superconducting compounds should be mutually compatible, i.e., the short-range potentials for given ion pairs in equivalent environments should be transferable from one compound to the other. The optical data presented here for Tl 2:1:2:2 are obtained with a model which is applicable not only for six different thallium superconductors, but also for ${\mathrm{Bi}}_2$ ${\mathrm{CaSr}}_2$ ${\mathrm{Cu}}_2$ ${\mathrm{O}}_8$ and ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$. The model for Tl 2:1:2:2 reproduces the measured infrared and Raman data quite well and yields a reliable first approximation for the displacement patterns of the modes at the Γ point. This is far from trivial since a mere force constant fit to the measured eigenvalues may yield rather arbitrary eigenvectors.