We report thermodynamic magnetization measurements of two-dimensional electrons in several high mobility Si metal-oxide-semiconductor field-effect transistors. We provide evidence for an easily polarizable electron state in a wide density range from insulating to deep into the metallic phase. The temperature and magnetic field dependence of the magnetization is consistent with the formation of large-spin droplets in the insulating phase. These droplets melt in the metallic phase with increasing density and temperature, although they survive up to large densities. PACS numbers: 71.30.+h,73.40.Qv, Magnetic ordering of a low-density electron system is determined by the interplay between the electronic Coulomb interaction and Pauli principle. As the density decreases, the ratio between the interaction and Fermi energies increases, pushing the system towards a ferromagnetic instability.In the Hartree-Fock approximation, the Bloch instability, a first-order transition from unpolarized to fully polarized state, happens at an unrealistically small r s ≈ 2. In the opposite limit of short-range interaction the Stoner instability, a second-order phase transition characterized by divergent spin susceptibility, is expected. The hierarchy of these transitions is discussed in Ref.[1] within the RPA approximation. Numerical simulations for a clean single-valley two-dimensional electron system (2DES) [2] predict a Bloch instability at r s ≈ 25 followed by Wigner crystallization [3] at r s ≈ 37.However, at very low densities a realistic system cannot be treated as a clean one: even small potential fluctuations due to inevitably present disorder become dominant and lead to Anderson localization. At higher densities intricate interplay between disorder and interactions manifests itself as a metal-insulator transition (MIT) at some density n c [4]. Experimental observations [5] and theoretical arguments [6,7] suggest that a 2DES becomes strongly nonuniform at densities lower than n c ; for n < n c a 2DES can be considered as consisting of weakly coupled disordered quantum dots. Disorder is also expected to drive a 2D system further towards ferromagnetic instability [8,9]. In particular, a disordered quantum dot is predicted to have a finite spin in the ground state, a phenomenon analogous to the Stoner instability [10,11]. Experiments on quantum dots [12] in GaAs indeed found spontaneous spin polarization at r s ∼ 7.6, much smaller than the expected value for a clean system [2].Coulomb interactions lead to renormalization of the Fermi-liquid constants, notably the density of states and the effective g-factor, g = g 0 /(1 + F σ 0 ) with Stoner instability expected at F σ 0 = −1. Negative F σ 0 can indeed be deduced for different 2DESs from measurements of Shubnikov-de Haas (ShdH) oscillations [13,14] and the temperature-dependent resistivity [15][16][17]. Scaling analysis of the magnetoresistance led the authors of Refs. [18,19] to suggest a quantum phase transition into a ferromagnetic state at n c . This conjecture was contested in...

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