Coordinate-Invariant Lyddane-Sachs-Teller Relationship for Polar Vibrations in Materials with Monoclinic and Triclinic Crystal Systems

A coordinate-invariant generalization of the Lyddane-Sachs-Teller relation is presented for polar vibrations in materials with monoclinic and triclinic crystal systems. The generalization is derived from an eigendielectric displacement vector summation approach, which is equivalent to the microscopic Born-Huang description of polar lattice vibrations in the harmonic approximation. An expression for a general oscillator strength is also described for materials with monoclinic and triclinic crystal systems. A generalized factorized form of the dielectric response characteristic for monoclinic and triclinic materials is proposed. The generalized Lyddane-Sachs-Teller relation is found valid for monoclinic $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$, where accurate experimental data became available recently from a comprehensive generalized ellipsometry investigation [Phys. Rev. B 93, 125209 (2016)]. Data for triclinic crystal systems can be measured by generalized ellipsometry as well, and are anticipated to become available soon and results can be compared with the generalized relations presented here.

Figure 1

Unit vector $\widehat{\mathbf{e}}$, characteristic for a dielectric eigenpolarizability vibration ${\mathbf{P}}_{\widehat{e}}$, whose frequency response is rendered by a complex-valued response function $\varrho$.