Spontaneous ferromagnetism in a semiconductor

The magnetic properties of a dilute 2D electron system have long been a topic of theoretical speculation and controversy because physics here is governed by strong electron-electron interaction. It all started with Felix Bloch back in 1929. He predicted that as the electron density is lowered, exchange energy should eventually surpass the kinetic energy of the system, which leads to a ferromagnetic state. However, such a ferromagnet eluded experimental realization for nearly a century partly because of the absence of a material platform that supports both high-quality and low-density in the same sample. If the sample quality is not sufficiently high, electrons localize because of the impurities that are inevitably present in the sample. In our recent work, we finally report the first experimental observation of the elusive interaction-driven ferromagnetism in the absence of a magnetic field in a 2D electron system with exceptionally high quality, manifesting strong electron-electron interaction at very low densities.

Fantastic phases of low-density 2D electrons

Electron-electron interaction can be quantified using the parameter ‘rs’ which is the ratio of Coulomb energy to the Fermi energy, and is inversely proportional to the square root of the electron density. It is convenient to use ‘rs ’because it is independent of material systems and is directly proportional to the inter-electron interaction strength in the sample.

Now let us focus on the experimental results. We change the density and measure the magnetizing field, i.e, the magnetic field required to spin polarize the electrons. As we lower the electron density, near rs = 35, we observe a vanishing magnetizing field. Notably, the magnetizing field becomes zero at rs = 35. This means that the electrons already become fully spin polarized at rs = 35, signaling a transition to a ferromagnet.

This transition to a ferromagnet is accompanied by hysteresis in the transport coefficients. This is expected from a ferromagnet because domains of different spins form when the sign of the magnetization is switched. to elaborate, when the up-spin electrons are forced to be down-spin electrons, they do not change their spin all at the same time. Instead, the change from up-spin to down-spin occurs domain by domain. The signature of the domain formation is seen from the hysteresis in the resistances.

Our results demonstrate gate-tunable spin polarization of electrons in a semiconductor. Furthermore, we show a remarkable control over the ferromagnetic transition via tuning the valley polarization of the 2D electron system. Note that, our 2D electron system also has a valley degree of freedom, because the electrons occupy two conduction band valleys that are of the same energy. I will describe the valleys in detail in my next post. The Combination of the gate-tunable spin polarization and the interplay between the spin and valley degrees of freedom has exciting prospects for integrating spintronics and valleytronics in the same device.

Before closing, I want to mention that our system shows even more surprises. In particular, we observe two other phase transitions as we tune the electron density. The first one is a metal to insulator transition that happens at rs ~ 27, at a slightly higher density compared to the ferromagnetic transition. The next transition occurs at an extremely low density, at rs above 38, where we see a phase with strong non-linearities in differential resistance at small DC bias. This strong non-linearity hints at the formation of a pinned Wigner solid, a crystalline phase of electrons that is expected to occur at very low densities and very low temperatures.

Observations of all these phase transitions enable us to construct the full phase diagram of the 2D electrons as a function of the strength of electron-electron interaction. The presence of such a rich phase diagram of the ground state of the 2D electron system invites novel applications.

It is tempting to say that our observation of spontaneous ferromagnetism is a manifestation of what Felix Bloch predicted nearly a century ago. However, there is one important difference. The ferromagnetic transition in our sample occurs when the system is insulating. By contrast, Bloch transition is expected to occur in a metallic system. Further theoretical work is required to understand the connection between our observation and the Bloch transition.

Our article has been published in PNAS. Here is the link to the article: https://www.pnas.org/content/early/2020/12/02/2018248117

The link to the preprint: https://arxiv.org/abs/2011.01335

A PhD candidate pursuing research on experimental condensed matter physics. In this blog, I will discuss some of my research efforts and current physics topics.