Peer review of: Spin-phonon relaxation from a universal ab initio density-matrix approach (2020)


RR2
Reviewers' comments:
Reviewer #1 (Remarks to the Author):
  The revised version of the manuscript and new results make this work of very high interest. I think
 that with the additional (final!) suggestions I am making below, such a paper will become a milestone
 of the field of spin relaxation. So I encourage the authors to add the following
 1- For the case of Graphene, the simulations show two features which apparently seem to contradict
 each other. Indeed, the ratio between out-of-plane spin lifetime and in-plane is about 1⁄2, in full
 coincidence with the Dyakonov Perel regime for spin relaxation. The increase of the spin lifetime with
 decreasing Fermi level is also similar to what was found by Ertler et al Phys. Rev. B 80, 041405(R)
 (2009), using Monte carlo simulations of electron transport in presence of a static random spin-orbit
 coupling fields.
 However simultaneously, the spin lifetime computed here (Figure 2(c)) decays with increasing
 temperature, which would at first sight contradict the Dyakonov-Perel mechanism following the work
 mentioned above. However I think the main difference here is that the author ́s simulation frame
 entangles vibrational disorder with fluctuations of spin-orbit coupling terms, so that the higher the
 temperature, the stronger the fluctuations of the SOC field and thus the faster the spin relaxation.
 This to me seems a plausible interpretation, which should be of main interest!
 I thus encourage the authors to comment on that, but also to try to extract the inelastic scattering
 time (tau_in) versus temperature from their simulations so as to show a new curve of how the spin
 lifetime (tau_s) scales with inelastic scattering time?
 If the scenario is correct, the authors will find that tau_s = 1/tau_in, therefore manifesting the
 universality of Dyakonov-Perel and the absence of contradiction with works such as Ertler et al Phys.
 Rev. B 80, 041405(R) (2009).
 1- For the case of MoS2, the results and conclusion are also excellent....the authors find that the out-
 of-plane spin lifetime can be about 10 times the in-plane spin lifetimes as a results of internal SOC
 field. Actually the term at the origin of such effect is the Valley Zeeman coupling which could certainly
 be defined by some reparametrized tight-binding model of MoS2. The point is that such anisotropy
 corresponds perfectly to what has been widely discussed theoretically for graphene/TMD (transition
 metal dichalcogenide). In this case the TMD imprints SOC on graphene and a similar spin transport
 anisotropy was predicted (Physical Review Letters 119 (20), 206601 (2017)) and measured
 experimentally (Nature Physics 14 (3), 303-308 (2018)). The observation of such huge anisotropy
 however requires disorder so as to enter a similar “Dyakonov-Perel regime”, although not dominated
 anymore by a Rashba-type of SOC fields.
 I am strongly recommending to the authors to make such connection more explicit, since it gives
 further validation of their simulations and show the universalities of spin transport anisotropy with
 respect to SOC effects. Again the temperature dependence found in the simulations of Xu et al could
 be seen as contradicting the analogy, but the same argument as discussed for graphene is likely to
 apply, mainly that the change in temperature is concomitant with a varying strength of SOC fields
 active in the ab-initio calculations.
 I hope the authors will admit that if they revise the manuscript adding the ingredients above, their
 contribution will have an even larger impact in the field of spin transport in nanomaterials.
 Reviewer #2 (Remarks to the Author):
 The authors have submitted a revised manuscript, in which they have addressed the comments and
 concerns of the previous referee reports, and included a sizable amount of new results. The detailed
 
responses to the points raised in the previous reviews are convincing. The paper is now much stronger,
 and definitely suitable for publication in Nature Communications.