This is the supplementary source code for the paper Topological magnon band structure of emergent Landau levels in a skyrmion lattice.

The code contains a Takin plugin module and its helper tools. The module calculates the dispersion and the dynamical structure factor for the helimagnetic, the field-polarised, and the skyrmion phase of MnSi.

The development repository can be found here:

• https://code.ill.fr/scientific-software/takin/plugins/mnsi

This software depends on Takin, the tlibs libraries, Minuit2 and some basic libs. An archived copy of their source codes are included in the directory ext/. Furthermore, their repositories are available here:

• Stable releases: https://github.com/t-weber/takin2
• Development versions: https://code.ill.fr/scientific-software/takin
• Binary releases: https://wiki.mlz-garching.de/takin
• DOIs: Takin 2: 10.5281/zenodo.4117437, tlibs 2: 10.5281/zenodo.5717779, old Takin 1 and tlibs 1: 10.5281/zenodo.3961491.

• Set up the external dependencies: cd ext && ./setup_externals.sh && cd ...
• The ext/ directory should now contain the source code of the external libraries (Takin and tlibs).
• Build the module: make -j4.
• Copy the built plugin modules to Takin's plugin directory: mkdir -pv ~/.takin/plugins/ && cp -v lib/*.so ~/.takin/plugins/
• The helper tools can be found in the bin/ directory.

See the included Dockerfile for more compilation info. This can also be used to compile it in a dockerimage with docker build -t takin2-msni . if you have build problems.

This source code is based on theoretical magnon dispersion models and their Mathematica implementations by M. Garst and J. Waizner, see these references and our papers below:

• M. Garst and J. Waizner, Skyrmion linear spin-wave theory and Mathematica implementation, personal communications (2017-2020).
• M. Garst and J. Waizner, Helimagnon linear spin-wave model and Mathematica implementation, personal communications (2014-2019).
• M. Garst and J. Waizner, Field-polarised linear spin-wave model and Mathematica implementation, personal communications (2016-2019).
• M. Garst, J. Waizner, and D. Grundler, J. Phys. D: Appl. Phys. 50 293002, https://doi.org/10.1088/1361-6463/aa7573 (2017).
• J. Waizner, PhD thesis, Universität zu Köln, https://kups.ub.uni-koeln.de/7937/ (2017).

Furthermore, the present source code is based on optimised Python implementations by M. Kugler and G. Brandl of early versions of the theoretical models mentioned above; the present source code started as a translation of the following Python codes into C++:

• G. Brandl and M. Kugler, Helimagnon implementation in Python, personal communications (2015-2016).
• M. Kugler, G. Brandl, J. Waizner, M. Janoschek, R. Georgii, A. Bauer, K. Seemann, A. Rosch, C. Pfleiderer, P. Böni, and M. Garst, Phys. Rev. Lett. 115, 097203, https://doi.org/10.1103/PhysRevLett.115.097203 (2015).
• M. Kugler and G. Brandl, Skyrmion spin-wave implementation in Python, personal communication (2016).

The following alternate Python implementations of the skyrmion spin-wave model exist:

• D. Fobes, Implementation in Python, personal communication (2016).
• L. Beddrich, Implementation in Python, https://github.com/LukasBeddrich/skyrmion-model (2017).

The helimagnon and ferromagnetic parts of this code have been used in the following papers:

• T. Weber, J. Waizner, P. Steffens, A. Bauer, C. Pfleiderer, M. Garst, and P. Böni, Phys. Rev. B 100, 060404(R), https://doi.org/10.1103/PhysRevB.100.060404 (2019).
• T. Weber, J. Waizner, G. S. Tucker, R. Georgii, M. Kugler, A. Bauer, C. Pfleiderer, M. Garst, and P. Böni, Phys. Rev. B 97, 224403, https://doi.org/10.1103/PhysRevB.97.224403 (2018).
• T. Weber, J. Waizner, G. S. Tucker, L. Beddrich, M. Skoulatos, R. Georgii, A. Bauer, C. Pfleiderer, M. Garst, and P. Böni, AIP Advances 8, 101328, https://doi.org/10.1063/1.5041036 (2018).

The skyrmion part of this code has been used in the following paper:

• T. Weber, D. M. Fobes, J. Waizner, P. Steffens, G. S. Tucker, M. Böhm, L. Beddrich, C. Franz, H. Gabold, R. Bewley, D. Voneshen, M. Skoulatos, R. Georgii, G. Ehlers, A. Bauer, C. Pfleiderer, P. Böni, M. Janoschek, and M. Garst, Science 375(6584), pp. 1025-1030, https://doi.org/10.1126/science.abe4441 (2022).

Completion of dependencies and Docker build info: N. Garofil, Universiteit Antwerpen.