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Microscopic effect of spin-lattice couplings on dynamical magnetic interactions of a skyrmion system PdFe/Ir(111)
by Banasree Sadhukhan, Anders Bergman, Johan Hellsvik, Patrik Thunstr{\"o}m, Anna Delin
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Banasree Sadhukhan |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202409_00026v2 (pdf) |
| Date submitted: | 2024-12-03 19:32 |
| Submitted by: | Sadhukhan, Banasree |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
PdFe/Ir(111) has attracted tremendous attention for next-generation spintronics devices due to existence of magnetic skyrmions with the external magnetic field. Our density functional theoretical calculations in combination with spin dynamics simulation suggest that the spin spiral phase in fcc stacked PdFe/Ir(111) flips into the skyrmion lattice phase around B$_{ext} \sim$ 6 T. This leads to the microscopic understanding of the thermodynamic and kinetic behaviours affected by the intrinsic spin-lattice couplings (SLCs) in this skyrmion material for magneto-mechanical properties. Here we calculate fully relativistic SLC parameters from first principle computations and investigate the effect of SLC on dynamical magnetic interactions in skyrmion multilayers PdFe/Ir(111). The exchange interactions arising from next nearest-neighbors (NN) in this material are highly frustrated and responsible for enhancing skyrmion stability. We report the larger spin-lattice effect on both dynamical Heisenberg exchanges and Dzyaloshinskii-Moriya interactions for next NN compared to NN which is in contrast with recently observed spin-lattice effect in bulk bcc Fe and CrI$_3$ monolayer. Based on our analysis, we find that the effective measures of SLCs in fcc (hcp) stacking of PdFe/Ir(111) are $\sim 2.71 ( \sim 2.36)$ and $\sim 14.71 ( \sim21.89)$ times stronger for NN and next NN respectively, compared to bcc Fe. The linear regime of displacement for SLC parameters is $\leq$ 0.02 Å which is 0.72\% of the lattice constant for PdFe/Ir(111). The microscopic understanding of SLCs provided by our current study could help in designing spintronic devices based on thermodynamic properties of skyrmion multilayers.
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Reports on this Submission
Report
The authors partially modified the manuscript according to the referee reports, however there are a few open points (see below).
Requested changes
1- On page 2, they call "u" now a "thermal displacement". This displacement might be due to thermal motion, but it could also result from other sources, e.g., an electric field. At the moment, it is just a displacement and should be called so.
2- New table I: since J^xx = J^yy = J^zz and J^xy=-J^yx etc. only four out of nine tensor components need to be shown (or J and D_x, D_y, D_z).
3- A force constant is given in Appendix E, but it's not clear for which atoms and why the xx, yy, and zz components are identical in a multilayer film.
4- About the title: In an experiment at finite temperatures, magnetic interactions are naturally modified by the dynamics of the system, sure. What is calculated here (eq.2) is the effect of a displacement on a magnetic interaction at T=0, therefore, I don't think that "spin-lattice couplings on dynamical magnetic interactions" is a good description of the content.
5 - About the interlayer distances: since the system is stable and the exchange interactions agree also with other references, I think the results are OK, but maybe the authors give interatomic distances instead of interlayer distances.
6 - A reference for the Perdew-Zunger LSDA is missing.
7- About fig.4: Indeed, panels (b) and (c) show mirror symmetry, but along a plane 60 degrees tilted from the y-axis (for both panels). How does this match with the (in both panels, different) displacement directions?
8- About the 6-fold symmetry: of course, a free monolayer has C_6 symmetry, but the "monolayer of Fe in PdFe/Ir(111)" has not, irrespective of thermal displacements.
Recommendation
Ask for minor revision
Author: Banasree Sadhukhan on 2025-01-16 [id 5125]
(in reply to Report 1 on 2025-01-03)Please find the attachment.
Attachment:
Response-Second.pdf