Electrostatic Force Microscopy of Fe$_3$O$_4$ nanoparticles

The electronic compressibility is a fundamental property that characterizes the electronic properties of materials submitted to an external electric field. In metals (insulators), the electronic compressibility is large (small) and leads to a small (large) screening length. Variations of the screening length can be observed through measurements of the ``quantum'' capacitance between one material and a metallic counter-electrode. Using an Electrostatic Force Microscope (EFM), we measured maps of the local capacitance of 8 nm magnetite nanoparticles synthesized following the ``benzyl alcohol route'' deposited on a metallic substrate. Magnetite, an inverse spinel structure of composition Fe$_3$O$_4$, is a material with strongly correlated electronic properties and presents a metal-insulator transition at 120 K, the so-called Verwey transition. We present EFM measurements of these nanoparticles as a function of tip-sample distance and temperature.