What are the ground states of an interacting, low-density electron system? In the absence of disorder, it has long been expected that as the electron density is lowered, the exchange energy gained by aligning the electron spins should exceed the enhancement in the kinetic (Fermi) energy, leading to a (Bloch) ferromagnetic transition. At even lower densities, another transition to a (Wigner) solid, an ordered array of electrons, should occur. Experimental access to these regimes, however, has been limited because of the absence of a material platform that supports an electron system with very high quality (low disorder) and low density simultaneously. Here we explore the ground states of interacting electrons in an exceptionally clean, two-dimensional electron system confined to a modulation-doped AlAs quantum well. The large electron effective mass in this system allows us to reach very large values of the interaction parameter $r_s$, defined as the ratio of the Coulomb to Fermi energies. As we lower the electron density via gate bias, we find a sequence of phases, qualitatively consistent with the above scenario: a paramagnetic phase at large densities, a spontaneous transition to a ferromagnetic state when $r_s$ surpasses 35, and then a phase with strongly nonlinear current-voltage characteristics, suggestive of a pinned Wigner solid, when $r_s$ exceeds $\simeq 38$. However, our sample makes a transition to an insulating state at $r_s\simeq 27$, preceding the onset of the spontaneous ferromagnetism, implying that besides interaction, the role of disorder must also be taken into account in understanding the different phases of a realistic dilute electron system. Significance Ground states of low-disorder, interacting, dilute electron systems are of fundamental interest in understanding electron–electron interaction phenomena. Our experimental data on a clean two-dimensional electron system reveal a sequence of transitions as the density is lowered. Starting from high densities, we observe a transition from a metallic state to an exotic insulating phase that is stabilized by disorder and interaction. As we further lower the density, we observe signs of a spontaneous transition to a ferromagnetic ground state and then to a strongly insulating state whose characteristics suggest that it is a pinned solid phase, possibly a (ferromagnetic) Wigner solid. We also find that the onset of ferromagnetism can be controlled by tuning the electrons’ valley degree of freedom.

We report measurements and calculations of the spin polarization, induced by a parallel magnetic field, of interacting, dilute, two-dimensional electron systems confined to GaAs/AlGaAs heterostructures. The results reveal the crucial role the non-zero electron layer thickness plays: it causes a deformation of the energy surface in the presence of a parallel field, leading to enhanced values for the effective mass and g factor, and a nonlinear spin polarization with field.