Spin-orbit torques in low-symmetry materials

Last Friday, I joined a seminar by Cheng Song on OSSS. While most of the time I just watch recorded talks from the OSSS because the usual schedule is from 3 pm ET, which is 9 pm CET and a bit late for me (especially for Friday evenings). But this time, since the speaker was from Beijing, the talk started at 4 pm CET, almost at the end of the week for me. The seminar was mainly about using AFMs to generate “non-trivial” components of the SOT, whose directions are different from the usual spin Hall or Rashba torque directions. For example, Song and his colleagues demonstrated this in Mn2Au/Py. Such non-equilibrium spin accumulation is called “antiferromagnetic spin Hall effect” in the paper. We discussed a lot on the microscopic mechanisms after the talk, such as whether how the surface termination of Mn2Au at the Py interface affects the SOT or whether the mechanism is indeed from the bulk Mn2Au or from the interface.

Regardless, I think it’s a recurring theme in spin-orbitronics community that people seek for low-symmetry materials to generate non-trivial components of the SOT. Not only from fundamental aspect, but also technologically this is important to achieve field-free switching of the magnetization. Usually, switching of PMA magnets by the SOT requires an external magnetic field that breaks the degeneracy between +z and -z magnetization configurations. The community has tried many different ways in order to achieve the field-free switching. For example, in 2014, a UCLA group achieved a symmetry breaking in a latral direction by inhomogeneous oxygen contents in a wedge structure. Also, a KAIST group demonstrated the field-free switching in IrMn/CoFeB/MgO structures by using the exchange bias between the antiferromagnetic IrMn and ferromagnetic CoFeB.

Since then, many different clever ways are being proposed. I think there are two differnet directions overall: (1) Using nonmagnetic materials which breaks a in-plane mirror symmety by the crystal structure, (2) Using magnetic materials where the mirror symmetry is broken by the magnetization direction.

Typical examples of (1) are 2D materials. Many 2D materials have C3v symmetry. It means that, if the crystal is symmetric with respect to mirror operation x -> -x, it does not have a mirror symmetry for y -> -y. Thus, at the magnetic interface, it can generate additional component of the SOT as well as the conventional damping-like and field-like torques. This was experimentally demonstrated in WTe2/Py structure. A microscopic theory can be found in this paper. From a similar motivation, the field-free switching was also achieved in L1_1 ordered CuPt/CoPt interface. Also, a recent theory paper proposed a SOT in a single-layer FGT, where the SOT also originates from the C3v symmetry.

The symmetry can also be broken by magnetic layers. For instance, soon after the theoretical proposal of “interface-generated” spin currents an experiment was performed in magnetic trilayer structures. Meanwhile, the spin current induced by the magnetic order is often called “magnetic” spin Hall effect to distinghiush from the “usual” spin Hall effect that is even under the time-reversal. The magnetic spin Hall effect was also found in Mn3Sb, one of the non-collinear antiferromagnets in the Kagome lattice. In this sense, the antiferromagnetic spin Hall effect is also somewhat similar.

My impression on this direction of works is that there’s a consensus on the phenomenology and the symmetry requirements, far more investigations seem to be required for microscopic understanding of the mechanism, e.g. how is it correlated with the wave function in the bulk or interfacial states, etc. Anyway, I have no doubt that these are quite interesting pieces of physics and worth investigating further.

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