We theoretically study quantum size effects in the magnetic response of a spherical metallic nanoparticle (e.g. gold). Using the Jellium model in spherical coordinates, we compute the induced magnetic moment and the magnetic susceptibility for a nanoparticle in the presence of a static external magnetic field. Below a critical magnetic field the magnetic response is diamagnetic, whereas above such field the magnetization is characterized by sharp, step-like increases of several tenths of Bohr magnetons, associated with the Zeeman crossing of energy levels above and below the Fermi sea. We quantify the robustness of these regimes against thermal excitations and finite linewidth of the electronic levels. Finally, we propose two methods for experimental detection of the quantum size effects based on the coupling to superconducting quantum interference devices.
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