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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
Submission summary
| Authors (as registered SciPost users): | Banasree Sadhukhan |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202409_00026v1 (pdf) |
| Date submitted: | 2024-09-20 21:01 |
| 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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
0- The manuscript gives a detailed investigation of spin-lattice couplings (SLC) in a system where a skyrmion lattice can be induced by a magnetic field.
1- In principle, this could now be the starting point to check how structural modifications (due to anharmonic effects at finite temperature or at step-edges) change the stability of the skyrmion lattice.
2- Large SLC probably means also that the structure is modified by magnetic pattern. Maybe the authors can at some point estimate these changes for a skyrmion lattice of given size (2nd term in eq. B3).
Weaknesses
1- In the title, 'dynamical magnetic interactions' are mentioned, so I expected to see some impact of SLC on the spin-dynamics. Maybe 'magnetic interactions' would be more clear.
2- See list of requested changes below.
Report
1. The system Pd/Fe/Ir(111) was one of the first, where a skyrmion lattice could be induced via an external magnetic field. The stability depends sensitively on the stacking, and small structural changes can probably have a large effect on the exchange parameters. Here, the authors investigate the dependence of Heisenberg parameters (J) and the Dzyaloshinskii-Moriya interaction (DMI) on small displacements of the Fe positions, termed spin-lattice coupling (SLC). The parameters (up to 3rd nearest neighbors) are evaluated with density functional theory (DFT) and the stability of the skyrmion lattice checked with atomistic spin-dynamics simulations. Compared to systems investigated by some of the authors in other papers (CrI3 and bcc Fe), large valued of the SLC were found.
2. The manuscript is in most parts clearly written and addresses the topic in depth, there are, however, a few points that should be clarified (see below).
Requested changes
1- The interlayer distances given on page 3 are too large. In an fcc(111) film, the ratio between interlayer distance and in-plane lattice constant should be sqrt(2/3). For Pd/Fe and Fe/Ir one expects them to be even smaller (see ref.[15]).
2- The type of exchange-correlation functional should be specified. Probably there are many different LSDA's in the used DFT codes, e.g. Perdew-Zunger or Vosko-Wilk-Nussair.
3- Specifying the displacements, the authors use directions like [100] or [101]. Probably this does not correspond to the Ir lattice, please introduce the notation or use the bulk Ir directions as reference.
4- Related to that, looking at Fig.4, I did not figure out in which direction the Fe was displaced. Assuming that the shift in (b) and (e) is in y-direction, I had expected a (vertical) mirror symmetry in the panels. Maybe the authors can indicate the shift direction in the panels.
5- In the introduction, the authors write that 'A is the entire plane perpendicular to the propagation direction'. I don't know what propagates here.
6- On page 6 I read that 'due to thermal displacements' the Fe layer loses its 6-fold symmetry. What are thermal displacements in this connection? Anharmonic vibrations should mainly occur along the surface normal. In-plane, the layer lost it 6-fold symmetry already due to the substrate and overlayer.
7- In the references, please correct the capitalization in the titles (e.g. CrI3 instead of cri3).
Recommendation
Ask for major revision
Strengths
1- very original. The coupling between phonon and magnetic interactions is usually not studied because it very complex. Here the authors have used a combination of codes (VASP, Phonopy and home made second principle code) and techniques (MC, DFT) and are able to explain very well the outcome.
2- excellent bibliography. Pd/Fe/Ir(111) is a prototypical skyrmion ultra-thin film. There are a lot of work in this subject and it is sometimes difficult to navigate in all the references. The authors have done a great job in this respect.
3- clearly written
Weaknesses
1- the figures. Please put the article references on fig.1 and fig.2 Use thicker dashed lines in panel b like in panel a. Use also smaller symbols on panel a
2- the phonon spectra is not really useful here. It is mentioned that it is only here to check the stability of the ultra thin film however, the stability of PdFe/Ir(111) is not a key finding. It would be more interesting to study the substitution and intermixing. With the phonon band structure, one can do more that what is done in the paper i.e. establishing an elastic model for thermal phonon and coupling it to the extended Heisenberg. Since all phonon were calculated, the displacement can also be done along a specific phonon - also not done.
3- the coupling between u and J or D is also not mentioned - the model could be refined here.
4- some typos (appendix C - formaliism)
5- the effects of the displacement on the phase diagrams are not
Report
The article "Microscopic effect of spin-lattice couplings on dynamical magnetic interactions of a
skyrmion system PdFe/Ir(111)" by Sadhukhan et al reports on the effect of atomic displacement on the parametrization of an extended Heisenberg Hamiltonian. PdFe/Ir(111) is one of the protypical skyrmion system. This system has been studied extensively since the last ten years and is now a very good test case. It is now being used to explore the coupling between magnetism and phonon displacement. This is an interesting topic which could have implications in the future spintronics and skyrmionics where the stability of skyrmions with respect to temperature is a crucial quantity and is a directly link to thermal phonon.
The article is well written and the figure are appropriate but could be improved.
Appart from the comment above, I have a two requests.
- The effect of the phonon is explored but no table summarizes the Hamiltonian parameters is given in the paper. It would be interesting to have these quantities to explore the stability diagram depending on phonon displacement.
- the force constants obtained from the band structure should be published. As I said before the stability of this ultra thin film is not really interesting because it is obviously stable. The elastic parameters are more important. Even if the authors do not have access to a code with phonon and Heisenberg parameters, other people in the community might be interested by this quantity.
Requested changes
1- table with the different parameters of the extended Heisenberg
Recommendation
Ask for minor revision