Irrelevance of the boundary on the magnetization of metals

TL;DR

This paper demonstrates through simulations that, unlike insulators, the magnetization of metals can be accurately determined solely from bulk electron distribution, showing the boundary has no effect.

Contribution

It provides evidence that the boundary does not influence magnetization in metals, allowing for bulk-only calculations similar to insulators.

Findings

Magnetization in metals can be computed from bulk electron distribution.

Boundary effects are negligible for metal magnetization.

Bulk electron distribution suffices for accurate magnetization evaluation.

Abstract

The macroscopic current density responsible for the mean magnetization $\mathbf{M}$ of a uniformly magnetized bounded sample is localized near its surface. In order to evaluate $\mathbf{M}$ 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 $\mathbf{M}$ in insulators: therein, $\mathbf{M}$ admits an alternative expression, not based on currents. $\mathbf{M}$ 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 $\mathbf{M}$ value can be retrieved in terms of the bulk electron distribution only.