  We extend a microscopic theory of polarization and magnetization to include
the spin degree of freedom of the electrons, introducing a general spin orbit
coupling and Zeeman interaction term in the Hamiltonian. At finite frequencies
and including spin, the magnetoelectric polarizability tensor is replaced by
two separate tensors, one that relates the polarization \textbf{P} to the
magnetic field \textbf{B} and a separate tensor that relates the magnetization
\textbf{M} to the electric field \textbf{E}. When combined with other relevant
response tensors a third rank tensor that relates the induced current density
to gradients in the electric field can be introduced; it is gauge invariant, in
a form suitable for numerical calculations, and describes optical activity --
including spin effects -- even in materials that may lack time reversal
symmetry.
