Common interatomic potential model for the lattice dynamics of several cuprates

Abstract

A common empirical model is developed for the lattice dynamics of the cuprates ${\mathrm{La}}_2$ ${\mathrm{CuO}}_4$, (La,Sr${)}_2$ ${\mathrm{CuO}}_4$, ${\mathrm{Nd}}_2$ ${\mathrm{CuO}}_4$, ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_6$, and ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$, which is also consistent with their crystal structures. Starting from the idea that the binding in these compounds is primarily ionic in character, the interatomic interactions were modeled using shell models with short-range repulsive potentials of the Born-Mayer type. For the metallic members of the series, screening of the ionic forces by free carriers was taken into account. There is clear evidence for an anisotropic Cu-O potential whereas the polarizabilities could be kept isotropic. The Cu(1)-O(4) bond in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_6$ could not be treated on a common footing, as there is too little charge on the Cu(1). The present study demonstrates that the lattice dynamics of all the compounds investigated can be described quite satisfactorily by a common model and it offers a basis for extensions to related compounds. On the other hand, we found clear indications that a description of the lattice vibrations with purely ionic forces has its limits for this class of compounds.