Zone-Center Dynamical Matrix in Magnetoelectrics

TL;DR

This paper derives a comprehensive expression for the zone-center dynamical matrix in magnetoelectric crystals, accounting for coupled electric and magnetic fields, extending the known theory from ordinary dielectrics to magnetoelectrics.

Contribution

It provides the first general symmetric expression for the dynamical matrix at the zone center in magnetoelectric materials, including nonanalytic behavior due to E and H couplings.

Findings

Dynamical matrix is nonanalytic of degree zero in q in magnetoelectrics.

The derived expression is exact within the harmonic approximation.

Addresses implementation issues with different field variables (E, B, H) in calculations.

Abstract

In ordinary dielectrics the dynamical matrix at the zone center in general is a nonanalytic function of degree zero in the wavevector q. Its expression (for a crystal of arbitrary symmetry) is well known and is routinely implemented in first principle calculations. The nonanalytic behavior occurs in polar crystals and owes to the coupling of the macroscopic electric field E to the lattice. In magnetoelectric crystals both electric and magnetic fields, E and H, are coupled to the lattice, formally on equal footing. We provide the general expression for the zone center dynamical matrix in a magnetoelectric, where the E and H couplings are accounted for in a symmetric way. As in the ordinary case, the dynamical matrix is a nonanalytic function of degree zero in q, and is exact in the harmonic approximation. For the sake of completeness, we address other issues, and in particular we solve a problem which might arise in first-principle implementations, where-differently than here-the basic fields are E and B (not H).