Source code supplement for "Topological magnon band structure of emergent Landau levels in a skyrmion lattice"

Skyrmion, conical, and field-polarised magnon dynamics in MnSi

Description

This is the supplementary source code to our paper, Topological magnon band structure of emergent Landau levels in a skyrmion lattice. (The complementary data supplement can be found here.)

The code contains a Takin plugin module and its helper tools. The module calculates the dispersion relations and the dynamical structure factor for the conical, 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.

Videos comparing the skyrmion and conical dispersion relations are available here:

• https://youtu.be/CuoA6sIM2oM,
• https://youtu.be/n3Pvjo7iNHE.

Dependencies

The Takin software and the tlibs libraries are needed for compilation. 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.

Setup

• Download the external dependencies: cd ext && ./setup_externals.sh && cd ...
• The ext/ directory should now contain the source code of the external libraries.
• 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.

References and Acknowledgements

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; it 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).