Stacking order in a 2D magnet produces Dirac magnons

Researchers in the UK, South Korea and the U.S recently discovered that the two-dimensional layered magnet chromium triiodide (CrI₃) acts as a topological magnon insulator in the absence of an external magnetic field. This result could have potential applications for so-called dissipationless spintronics in which electrons are used to transmit and store information in an ultra-fast and ultra-low power fashion.

Thanks to detailed neutron scattering measurements and fine analysis, the team has found that this phenomenon comes from the way in which the layers in the material are stacked together. That is, while a single layer of CrI₃ is ferromagnetic, two stacked layers are antiferromagnetic which counterintuitively is different from that in ferromagnetic bulk.

Two-dimensional (2D) materials are made up of atomically thin layers stacked on top of each other. These layers are held together by weak van der Waals forces and the electrons in these materials behave very differently to those in bulk materials. For example, the “Dirac” electrons in graphene, one of the most famous 2D materials, can move at almost relativistic speeds and behave as if they are massless.

Some 2D materials are also topological insulators – materials in which electrons flow freely along the edges of a 2D sheet, but cannot flow along the surface. This effect is related to the spin of the electrons, making these materials promising for spintronic devices, which store and process information using the electrons’ spin states.

Certain 2D magnetic materials are also predicted to be magnetic and topological insulators. In such materials, which are very rare, quasiparticles known as magnons would travel along the edges of a sheet, much like electrons in a conventional 2D topological insulator. Magnons are collective oscillations of the spin magnetic moments of a material and are expected to be massless too, meaning that they could travel over long distances without dissipating. This property would make them interesting for spintronics applications too.

Three years ago, Lebing Chen from Rice University and coworkers found such Dirac magnons in CrI₃, which has a honeycomb lattice structure similarly to graphene. They came to their conclusion by studying the material using inelastic neutron scattering at the Spallation Neutron Source at Oak Ridge National Laboratory. In this technique, neutrons, which have magnetic moments, create magnons when they scatter from a CrI₃ sheet. By measuring the energy lost by the neutrons during the scattering process, Chen and colleagues were able to calculate the properties of these magnons. They found that these magnons exhibit properties consistent with them being topological and having a dissipation-less edge mode.

In their new work, the scientists performed further neutron-scattering measurements at a much larger precision as well as resolution and have found that the magnons’s topological properties arise thanks to spin-orbit coupling – a relativistic interaction of an electron’s spin with its motion. This coupling induces asymmetric interactions between spin of electrons in the materials, explains Elton Santos of the School's Higgs Centre for Theoretical Physics, Jae-Ho Chung of Korea University’s Department of Physics and Pengcheng Dai of Rice University who led the new study. These interactions make the spin “feel” the magnetic field differently, affecting their topological excitations.

Elton commented: "Surprisingly the spins have some chirality like in a mirror where left and right can work differently. We observed that without such chiral interactions, or in more complicated terms Dzyaloshinskii-Moriya exchange, we can’t describe the data".

The result has an accompanying magnetic phenomenon: a stacking-dependent magnetic order in which a single layer of Cr_I3 is ferromagnetic but two stacked layers are antiferromagnetic. “The reason for this behavior is that the interaction between stacked layers in CrI₃ is a combination of ferromagnetic and antiferromagnetic exchanges - despite apparent ferromagnetic stacking,” explains team member Jae-Ho.

“Our new work also confirms the previously observed topological nature of the spin excitation based on the Dzyaloshinkii-Moriya exchange, and rules out the competing interpretation based on the Kitaev exchange,” comments Pengcheng Dai to Physics World. “The latter is known to be an important spin-spin interaction in more complex materials (i.e. spin liquids), but not for CrI3. This comes as a surprise to us.”