Researchers have found that electrons organize themselves into a new kind of ferromagnet in twisted bilayer graphene (TBG). In this system, which forms when two sheets of graphene are stacked on top of one another with a small twist angle between them, it is the orbital motion of electrons, rather than their spins, that aligns. Such behaviour could produce emergent topological states that might be exploited in applications such as low-power magnetic memory in the future.

Graphene is a flat crystal of carbon just one atom thick. When two sheets of the material are placed on top of each other and misaligned by rotating them relative to each other, they form a moiré pattern. Last year, researchers at the Massachusetts Institute of Technology (MIT) found that at a “magic” twist angle of 1.1°, the material becomes a superconductor (that is, it can carry currents with no losses) at 1.7 K. This effect, which occurs thanks to miniband flattening at this angle that strongly enhances interactions between electrons in the material, disappears at slightly larger or smaller angle twists.

A team of researchers led by David Goldhaber-Gordon of Stanford University has now found unambiguous evidence of ferromagnetism – as the giant anomalous Hall (AH) effect – in TBG when its flat conduction miniband is three-quarters filled.

Three-quarter filling with a difference

The crystal structure of a single layer of graphene can be described as a simple repetition of carbon atoms, which is known as its unit cell. A normal electronic band can accommodate two electrons (one of each spin) per unit cell. This miniband can accommodate four electrons (each of two spins, each of two orbital states) per moiré cell.

“Three-quarter filling would naively mean that each of the four nearly-degenerate bands (spin up, orbital 1; spin down, orbital 1; spin up, orbital 2; and spin down, orbital 2) would be three-quarters filled,” explains Goldhaber-Gordon. “But, what if the electrons organized themselves to completely fill three of these bands instead, leaving the other one empty?”

In this case, the electrons would be polarized in both spin and orbital states with the orbital polarization giving rise to the giant AH effect, he says. And this is exactly what the researchers have observed in measurements of the voltage drops in a Hall bar device made from the material. Indeed, they measured an AH effect as large as 10.4 kΩ.

“Incipient” Chern insulator

The presence of a giant AH effect in an apparent insulator is reminiscent of a ferromagnetic topological insulator approaching a Chern insulator state, says Goldhaber-Gordon. Such a state is one whose bands are all either filled or empty (as described above) and whose filled bands have a net total Berry curvature or Chern number. Such a system should have zero longitudinal conductance and quantized Hall conductance.

“We instead see a minimum in longitudinal conductance at three-quarter filling (but not zero longitudinal conductance) and a large Hall conductance (that is not fully quantized),” he tells Physics World. “This suggests the presence of a parallel conduction mechanism.”

And that is not all: the researchers also found that they can, surprisingly, reverse the magnetization of the sample by applying a small DC current. This could possibly have implications for low-power magnetic memory applications in the future given the orders-of-magnitude smaller critical current density required for flipping the magnetization compared to previous such devices.

Measurements on a Hall bar device

Goldhaber-Gordon and colleagues performed their measurements on a Hall bar device made from TBG with a target twist angle of 1.17°. They sandwiched the graphene between two hexagonal boron nitride (hBN) cladding layers to protect the graphene channel from disorder and to act as dielectrics for electrostatic gating. By then adding a silicon back gate and Ti/Au top gate, they were able to independently tune the charge density in the TBG and an electric field applied perpendicular to the graphene sheets.

They measured the longitudinal and Hall resistances using standard “lock-in” techniques with an AC bias current.

The team, reporting its work in Science, is now studying the properties of the magnetic states at three-quarter and other band fillings using a mix of techniques, including transport measurements and optical probes. Understanding the magnetic order and topological character of the correlated insulating states will be crucial to unravelling the rich phase diagram of TBG, says Goldhaber-Gordon.