Thermodynamic magnetization of two-dimensional electron gas measured over wide range of densities

We report measurements of $\partial m/\partial n$ in Si MOSFET, where $m$ is the magnetization of the two-dimensional electron gas and $n$ is its density. We extended the density range of measurements from well in the metallic to deep in the insulating region. The paper discusses in detail the conditions under which this extension is justified, as well as the corrections one should make to extract $\partial m/\partial n$ properly. At low temperatures, $\partial m/\partial n$ was found to be strongly nonlinear already in weak magnetic fields, on a scale much smaller than the characteristic scales, expected for interacting two-dimensional electron gas. Surprisingly, this nonlinear behavior exists both in the dielectric, and in the metallic region. These observations, we believe, provide evidence for strong coupling of the itinerant and localized electrons in Si-MOSFET.