"Why the Spin-Currents?". A practical example with tungsten diselenide.

[boccunia]

Many people today are wondering: "What is a spin current?". While the question may seem legitimate, experts in the field might quip, "Well, of course, it's a current of spin, you dummy!" So, rather than focus on what a spin current is, I find it more interesting to ask: "Why is the spin current so important?"

This is precisely what we explored in our letter titled "Unveiling the Role of Spin Currents in the Giant Rashba Splitting of Single-Layer WSe2." WSe2 (tungsten diselenide) belongs to the class of transition metal dichalcogenides (TMDs). In their monolayer form, TMDs have attracted significant interest due to their exotic physical properties and potential applications in spintronics. For example, the combination of space inversion symmetry (SIS) breaking, time-reversal symmetry (TRS) preservation, and strong spin−orbit coupling (SOC) leads to a giant Rashba-type I spin splitting at the top of the valence band in single-layer TMDs—ranging from 150 to 500 meV at the K point.

Traditional Density Functional Theory (DFT) underestimates Rashba splitting due to the fact that the DFT Hamiltonian does not include SOC. Trying to incorporate SOC explicitly in the Hamiltonian leads to spin-current DFT (SCDFT), where the energy functionals E[n, Jx, Jy, Jz] (n, being the particle number density) depend on the noncollinear spin-current components Jx, Jy and Jz. In this letter we have tested two ways of extending DFT to SCDFT in order to properly capture the modifications to the electronic band structure of single-layer WSe2 due to SOC:

• An explicit inclusion with the meta-generalized-gradient approximation functional (MGGAs) J-r2SCAN;
• An implicit inclusion with the use of the hybrid PBE functional with a fraction of exact exchange.

Our findings reveal that the systematic underestimation of Rashba splitting in the valence band—by about 15%—can be attributed to the absence of spin currents in traditional DFT. Indeed, SCDFT increases the Rashba splitting by 18–20%, aligning well with experimental values of 513 ± 10 meV. Additionally, SCDFT improves the description of quasi-degenerate band gaps at KK and KQ, as well as the gap at GammaK.

In summary, we’ve demonstrated that spin currents are essential for accurately modeling SOC effects in 2D materials. SCDFT effectively resolves the Rashba splitting underestimation, positioning it as a superior alternative to standard DFT for spintronic materials. While hybrid functionals yield better band gap predictions, meta-GGA functionals that explicitly include spin currents enhance SOC accuracy. Future work will focus on combining the strengths of both SCDFT approaches.

If you’d like to read the full letter, you can find it here:
https://pubs.acs.org/doi/abs/10.1021/acs.jpclett.4c01607

All calculations were performed using the CRYSTAL software. If you’re curious about visualizing spin currents, you can explore their beautiful swirls using the dedicated class available in the CRYSTALClear python framework:
https://github.com/crystaldevs/CRYSTALClear

[Jacques]

Here is a nice paper for the SCF (spin-current fan) inside you!

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.96.076604