Composite fermions exhibit Bloch ferromagnetism
The magnetic properties of the ground state of a low-density, two-dimensional (2D) electron system have been a topic of intense theoretical speculation and controversy. This is because the physics here is governed by strong correlations, where the conventional free-electron models hopelessly fall short. It started with Felix Bloch back in 1929. He predicted that a system of interacting electrons will undergo a transition to a ferromagnetic ground state when the density is sufficiently lowered. Such a transition is expected to occur at very low densities when the gain in exchange energy by aligning the spins surpasses the enhancement in the kinetic (Fermi) energy. However, such a ferromagnetic state has eluded experimental realization for the last nine decades. In our latest work published in Nature Physics, we show an experimental realization of the elusive interaction-driven spin polarization in a system of unusual suspects, namely composite fermions.
The realization of Bloch ferromagnetism has been challenging because of the requirement of very low electron densities. In our work, we attain such a condition in composite fermions.
Composite fermions are exotic quasiparticles, each composed of an electron and two flux quanta, formed in the half-filled Landau level of a 2D electron system. Note that the Landau levels are the quantized energy levels of 2D electrons in the presence of a perpendicular magnetic field.
We determine the spin-polarization of these composite fermions through geometric resonance measurements, which provide a direct and quantitative measure of the Fermi wave vector and spin polarization of composite fermions, free of fitting parameters. Note that the geometric resonance occurs when the diameter of the cyclotron orbit (in the presence of a Lorentz force) of the composite fermions becomes commensurate with the period of a potential modulation that we impose on the system.
We find that at high densities, the composite fermions are fully spin-polarized, consistent with previous experiments. As we lower the electron density (to nc2 = 4.2 x 10¹⁰ 1/cm² ), the composite fermions lose their full spin-polarization, also as expected because of the lowering of the Zeeman energy at low densities. Remarkably, however, as the density is further reduced (to nc1 = 3.51 x 10¹⁰ 1/cm²), the composite fermions make a sudden transition and become fully spin-polarized. This is rather unexpected because, at such densities, the Zeeman energy of the composite fermions should be even smaller. However, somehow, the interaction between the composite fermions manages to produce a ferromagnetic state.
The full spin-polarization sets in at very low densities when the composite fermion system is very dilute and the exchange interaction between the composite fermions becomes very strong. This spontaneous magnetization of composite fermions, triggered by lowering of the density, closely resembles the Bloch ferromagnetism.
Motivated by the experimental results, we also performed theoretical calculations that provide a semi-quantitative understanding of the phenomenon. The calculations demonstrate that as the mixing between the Landau levels is enhanced when the density is lowered, the inter-composite fermion interaction gets stronger. Such an interaction leads to the Bloch ferromagnetism of composite fermions at sufficiently low densities.
Our findings finally confirm the existence of Bloch ferromagnetism and point to a new route towards electrical control of spin polarization via tuning the density.
Here is the link to our paper: https://www.nature.com/articles/s41567-020-1000-z
This is the link to the arXiv version: https://arxiv.org/abs/2008.11630
