Lyddane-Sachs-Teller relationship in linear magnetoelectrics

TL;DR

This paper generalizes the Lyddane-Sachs-Teller relationship to linear magnetoelectrics, linking phonon splitting to response matrices at different frequencies, and provides a simple harmonic crystal case.

Contribution

It introduces a generalized Lyddane-Sachs-Teller relationship for magnetoelectrics, relating response matrices at zero and infinite frequencies.

Findings

Response matrices at 0 and ∞ satisfy the generalized relationship.

The RHS is expressed as weighted averages over excitations.

Simplifies to a form for harmonic crystals.

Abstract

In a linear magnetoelectric the lattice is coupled to electric and magnetic fields: both affect the longitudinal-transverse splitting of zone-center optical phonons on equal footing. A response matrix relates the macroscopic fields (D,B) to (E,H) at infrared frequencies. It is shown that the response matrices at frequencies 0 and \infty fulfill a generalized Lyddane-Sachs-Teller relationship. The rhs member of such relationship is expressed in terms of weighted averages over the longitudinal and transverse excitations of the medium, and assumes a simple form for an harmonic crystal.