Extension of the Szigeti equations: Average longitudinal-transverse frequencies and effective charges

Abstract

Combination of the first Szigeti and the Lyddane-Sachs-Teller relations leads to a suitable correlation scheme between spectroscopic, dielectric, and mechanical properties in binary cubic crystals. It can be defined a squared average longitudinal-transverse frequency: ${\ensuremath{\omega}}_{\mathrm{LTO}}^{2}=({\ensuremath{\omega}}_{\mathrm{LO}}^{2}{\ensuremath{\epsilon}}_{\ensuremath{\infty}}+2{\ensuremath{\omega}}_{\mathrm{TO}}^{2})∕({\ensuremath{\epsilon}}_{\ensuremath{\infty}}+2)$, with ${\ensuremath{\omega}}_{\mathrm{LO}}$ and ${\ensuremath{\omega}}_{\mathrm{TO}}$ the corresponding frequencies of the zone-center fundamentals optical lattice modes (the longitudinal and the doubly degenerate transverse, respectively), and ${\ensuremath{\epsilon}}_{\ensuremath{\infty}}$ the high-frequency dielectric constant. This average frequency is equivalent to the mechanical or spring-constant frequency defined in previous models, and exactly scales with the product of the bulk modulus and the equilibrium nearest neighbor distance, so a weighted summation rule for phonon frequencies holds. We find that the general behavior previously observed in longitudinal optical phonons can be completely explained within the present scheme. In addition, effective charges can be calculated only in terms of the dielectric constants and mechanical properties; our estimations are in good agreement with available results based on spectroscopic measurements. Finally, a new relationship between localized, transverse, and Szigeti effective charges is provided.