Lyddane-Sachs-Teller Relationship in Linear Magnetoelectrics

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 1 fulfill a generalized Lyddane-Sachs-Teller relationship. The right-hand side 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 a harmonic crystal.