From magnetoelectric response to optical activity

We apply a microscopic theory of polarization and magnetization to crystalline insulators at zero temperature, and consider the orbital electronic contribution of the linear response to non-uniform and non-static electromagnetic fields. These microscopic fields can be decomposed into “site” polarization and magnetization fields, from which “site multipole moments” can be constructed. Macroscopic polarization and magnetization fields follow, and we identify the relevant contributions to them. Within the independent particle and frozen-ion approximations, a description of optical activity and related magneto-optical phenomena then immediately follows; both optical rotary dispersion and circular dichroism can be described with this strategy. Earlier expressions describing the magnetoelectric effect are recovered as the zero frequency limit of our more general equations. Since our site quantities are introduced with the use of Wannier functions, the site multipole moments and their macroscopic analogs are generally gauge dependent. However, the resulting macroscopic charge and current densities, together with the optical effects to which they lead, are gauge invariant, as would be physically expected.