In this Rapid Communication, we present the order of the phonon modes and the appearance of the reststrahlen bands for monoclinic symmetry materials with polar lattice vibrations. Phonon modes occur in associated pairs of transverse and longitudinal optical modes, and pairs either belong to inner or outer phonon modes. Inner modes are nested within outer modes. Outer modes cause polarization-dependent reststrahlen bands. Inner modes cause polarization-independent reststrahlen bands. The directional limiting frequencies within the Born-Huang approach are bound to within outer mode frequency regions not occupied by inner mode pairs. Hence, an unusual phonon mode order can occur where both lower-frequency as well as upper-frequency limits for the directional modes can be both transverse and/or longitudinal modes. We exemplify our findings using experimental data for the recently unraveled case of monoclinic symmetry $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$ [Phys. Rev. B 93, 125209 (2016)] and demonstrate excellent agreement with results from density functional theory calculations.

• Received 22 July 2018

DOI:https://doi.org/10.1103/PhysRevB.99.041201