Density response of Bloch electrons to a weak magnetic field.*

We consider the action of a weak magnetic with finite frequency and wave vector on a system of Bloch electrons. The density response is computed using a Boltzmann-like formalism and from density-current correlators for both metals and insulators. To linear order, and in the limit of vanishing frequency and wave vector, we recover the Streda formula but obtained additional contributions arising from the magnetic moments of electrons at the Fermi surface.