Magnetoresistance and spin polarization in the insulating regime of a Si two-dimensional electron system

We have studied the magnetoresistance in a high-mobility Si inversion layer down to low electron concentrations at which the longitudinal resistivity $\rho_{xx}$ has an activated temperature dependence. The angle of the magnetic field was controlled so as to study the orbital effect proportional to the perpendicular component $B_\perp$ for various total strengths $B_{\rm tot}$. A dip in $\rho_{xx}$, which corresponds to the Landau level filling factor of $\nu=4$, survives even for high resistivity of $\rho_{xx} \sim 10^8 \Omega$ at $T= 150 {\rm mK}$. The linear $B_{\rm tot}$-dependence of the value of $B_\perp$ at the dip for low $B_{\rm tot}$ indicates that a ferromagnetic instability does not occur even in the far insulating regime.