Thermodynamic Magnetization of Strongly Correlated 2d Electrons in Perpendicular Magnetic Fields

We will report measurements of thermodynamic magnetization ($M$) of strongly correlated 2D electrons in silicon in perpendicular magnetic fields. We see sawtooth oscillations of the magnetization as a function of the electron density, $n_s$. Near the integer filling factors, the slope $\partial M/ \partial n_s$ exceeds the maximum possible non-interacting value pointing to the existence of the regions with the negative thermodynamic compressibility. Comparing $\partial M/ \partial n_s$ on both sides of the spin gaps, we deduce the $g$-factor. The latter is found to be close to its bare value $g=2$ even at low electron densities, where the critical behavior of the spin susceptibility has been observed in similar systems. This indicates that it is the effective mass, rather than the $g$-factor, that is responsible for the giant enhancement of the spin susceptibility near the metal-insulator transition.