Orbital magnetization of a metal is not a bulk property in the mesoscopic regime

We find that, in the mesoscopic regime, modification of the material's surface can induce an extensive change of the material's magnetic moment. In other words, perturbation of order-$N^2$ atoms on the surface of a three-dimensional solid can change the magnetic moment proportionally to $N^3$. When the solid's surface is perturbed, it triggers two changes in the magnetization. One arises from variations of the electron wave function and energy, while the other arises from a modification in the kinetic angular momentum operator. In the macroscopic regime of our model, these two bulk effects cancel each other, resulting in no impact of the surface perturbation on the magnetization, consistent with prior work. In the mesoscopic regime, we find a departure from this behavior, as the cancellation of two terms is not complete.