Differnet confusing names of spin-orbit torques

If you’re new to spin-orbitronics, you must be very confused for many different terminologies that seem to specify the same effect but from slightly different contexts. Honestely, this is really confusing and was terrible, especially when I had to study this field of research from the scratch in the beginning of my PhD. Just to name some of them, I easily find that these terms appear in many different papers: field-like torque, damping-like torque, antidamping-like torque, spin Hall torque, Rashba torque, Edelstein effect, even/odd torque, inverse spin Galvanic effect, intrinsic spin-orbit torque, interfacial torque, etc. This came out of discussion with my colleagues today and I came to think about it. In this article, I want to explain you a bit of motivations behind those terminologies and what they (usually) mean the same thing or not.

In thin film heterostructures such as Pt/Co, W/Py, etc. we usually find two independent components of the SOT. For instance, when an electric field is applied along the X direction, we have SOTs proportional to M x Y and (M x Y) x M. For instance, heterostructures with C4v symmetry ((001) stacks of bcc/fcc) and C6v symmetry (111 stacks of fcc(111) or hcp(0001)) have these two SOTs, as well as poly-crystalline samples (C-infinite-v symmetry). Although there exists higher-order terms that involve more M’s, M x Y and (M x Y) x M are the two leading terms. Phenomenologically, because M x Y torque is analogous to a situation with a magnetic field pointing along Y, M x Y torque is called field-like torque. By adding one more cross product with M, (M x Y) x M points toward the direction of the Gilbert damping, so it’s called damping-like torque. But since the direction of the torque can change if one flips the direction of the electric current, it can also cancels with the Gilbert daming. In this context, people call it “anti-damping”-like torque.

Around 2010, the whole community was debating over possible mechanisms for the SOT. While the SOT was “intuitively” understood as the spin Hall effect arising in the nonmagnetic substrate and the spin-transfer torque exerted by the spin current passing through the interface between the nonmagnet and ferromagnet, another mechanism based on the interfacial Rashba-type state was also proposed and many evidences that shows that the Rashba effect causes the SOT have been found. At the end, strictly speaking, both the SHE and Rashba mechanisms predict coexistence of the field-like and damping-like SOTs. In the SHE mechanism, the damping-like torque is direct consequence of the STT with the spin polarization direction Y, and the field-like torque is a secondary effect in the presence of the damping. On the other hand, the Rashba effect explains the field-like torque more naturally. There’s an effect called Rashba-Edelstein effect. The key idea for this effect is that shift of the Fermi surface by the current (Boltzmann-like) leads to finite spin density at the interface. On the other hand, although the damping-like torque emerges from the Rashba effect, it involves Berry phase physics and more complicated theoretical concepts. Though I’m not fully sure, but my suspicion is that many experimenatlists who were not familiar with the Berry phase physics didn’t buy the Rashba mechainsm for the damping-like torque because it doesn’t really come with most people’s “intuition”. Same thing might have happened for the field-like torque arising from the SHE mechanism. So, many people started to use spin Hall torque for the damping-like torque and Rashba torque for the field-like torque, if they want to emphasize microscopic mechanisms in their papers. Some people also called the Rashba torque by Edelstein effect. Because the Rashba effect is mostly present at the interface, it is also called interfacial torque.

Quite interesting fact is that although physical principles do not exclude either of the damping-like torque and field-like torque for both Rashba and SHE mechanisms, several DFT calculations showed that the damping-like torque is indeed dominated by the SHE while the field-like torque is mainly due to the Rashba effect. In the meantime, several theory papers were also publisehd by that time, showing that the Berry phase effect explains the damping-like torque from the Rashba effect. But these papers used specifically invese spin Galvanic effect, thus still people use invese spin Galvanic effect in order to specify the damping-like torque arising from the Rashba effect from the Berry phase mechanism. But because of the intrinsic mechanism involved in the Berry phase mechanism, it is also called intrinsic spin-orbit torque. By the way, since M x Y torque invovles only “one” M, which is odd with respect to the time-reversal, so it is called odd torque. Likewise, (M x Y) x M torque is called even torque.

In summary, (anti)damping-like torque, spin Hall torque, inverse spin Galvanic effect, even torque mostly mean the same term ~ (M x y) x M, and people use field-like torque, Rashba torque, Edelstein effect, Rashba torque, interfacial torque, odd torque to specify the term ~ M x Y.

Final remark: These terminologies were coined with poly-crystalline heterostructures in mind, or at least C6v or C4v symmetries. So, they don’t really make sense to apply to other low-symmetry materials. Recently, 2D materials such as FGT or TMD were found and the SOT are being actively discussed. Many 2D materials have C3v symmetry and the properties are very different from other crystals. For example, there’s a new SOT term which acts like an electric-field-induced magnetic anisotropy in a single-layer FGT. So phenomenologically, it acts like an effective anisotropy field, but the torque is even in M. Another example is a SOT in TMD/FM. Although many people discuss interface mechanisms here, which is believed to be the main contribution, there are cases that an interfacial contribution does not exactly correspond to the SOT arising from the Rashba effect in metallic thin films. I hope that the community uses vocabularies more carefully rather than extrapolating what we knew in metallic thin films and try to set up right terms to call new components of the torques that are being discovered in new materials.

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