Spontaneous ferromagnetism in two-dimensional electron systems

Abstract

What is the ground state of an electron system when its density is very low? This question has perplexed scientists for nearly a century. At low densities, electrons interact strongly, and our familiar free-electron models fall short. In 1929, Bloch predicted that such interaction should lead to a spontaneous spin polarization when the exchange energy dominates the kinetic (Fermi) energy of the system. Albeit a topic of great interest, this phenomenon, the so-called Bloch ferromagnetism, eluded experiments because it requires high-quality and low-density simultaneously. In this Thesis, we experimentally realize this physics in two systems.

We first study a two-dimensional electron system, where at high densities, electrons occupy two spin states and two conduction-band valleys. As we apply gate voltage, and lower the density below a critical value corresponding to $r_s$ (the ratio of Coulomb to Fermi energies, which is inversely proportional to the square root of density) surpassing $\simeq 20$, all the electrons suddenly transfer to one valley, signaling a spontaneous valley polarization. When we lower the density even further, at $r_s \simeq 35$, electrons become spin polarized. We discuss our observations of spontaneous valley and spin polarization in light of Bloch ferromagnetism. Finally, at extremely low densities, when $r_s$ exceeds $38$, we find hints of Wigner solid, the ultimate fate of a low-density electron system.

Our second platform is a two-dimensional Fermi sea of composite fermions (quasiparticles composed of an electron and two flux quanta). Via direct measurements of the spin polarization, we observe a sudden transition from a partially-spin-polarized to a fully-spin-polarized ground state as we lower the density, signaling the Bloch ferromagnetism of composite fermions.

Access to this strongly correlated regime opens up lab-on-a-chip experiments to test different theories of many-body physics. Here we investigate the Luttinger theorem, which postulates that the Fermi sea and its area should not change with interaction. We confirm that the Luttinger theorem holds even when the inter-composite fermion interaction is strong enough to cause Bloch ferromagnetism. On the application front, our findings of gate-tunable spin and valley polarization should pave the way towards future memory and transistors based on electron's spin and valley degrees of freedom rather than its charge.