Irrelevance of the Boundary on the Magnetization of Metals

The macroscopic current density responsible for the mean magnetization M of a uniformly magnetized bounded sample is localized near its surface. In order to evaluate M one needs the current distribution in the whole sample: bulk and boundary. In recent years it has been shown that the boundary has no effect on M in insulators: therein, M admits an alternative expression not based on currents. M can be expressed in terms of the bulk electron distribution only, which is "nearsighted" (exponentially localized); this virtue is not shared by metals, having a qualitatively different electron distribution. We show, by means of simulations on paradigmatic model systems, that even in metals the M value can be retrieved in terms of the bulk electron distribution only.