  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.
