This repository contains the libraries and scripts to completely reproduce the simulations of the publication Nano-scale magnetic skyrmions and target states in confined geometries by D. Cortés-Ortuño, N. Romming, M. Beg, K. von Bergmann, A. Kubetzka, O. Hovorka, H. Fangohr and R. Wiesendanger.
These simulations are based on the Fidimag code [1] which can perform discrete spin simulations.
Images of the experimental data used in the simulations are located in the
Romming_data folder. These images are copyrighted and were obtained by the
group of R. Wiesendanger from the
University of Hamburg.
Simulation scripts are located in the simulation folder, where they are
separated in three categories:
-
relaxation: scripts that directly relax a given initial state for a particular geometry (the experimental island, hexagons or truncated triangles). Magnetic parameters can also be modified, see the
bashscripts for details. The library containing all the available options and initial states ishexagonal_fidimag.py, which usesargparse. The relaxation directory also contains the scripts to fully reproduce the phase diagrams shown in [1]. These simulations require substantial simulation time and disk space, thus it is recommended to start them with precaution. -
hysteresis: these scripts take the initial state from the relaxation simulations (specific paths to
npyfiles might require updating the final step number) and perform a sequential field sweep of the system, according to the specified options. Scripts are written ascfgPython config files and the main library with the options ishexagonal_hysteresis.py. -
NEBM: these scripts also rely on the simulations from the relaxation folder to specify the initial state. The main library in this case is
hexagonal_neb_fidimag.py, which uses the GNEBM implementation from Fidimag.
A library to create a mesh/simulation from an image is given in
sim_from_image.py. In our case we use the islands from experiments in the
Romming_data folder. A copy of the numpy array containing the spin data,
which was btained with this library for the island system, is stored in the
mu_s directory.
A library to create meshes with different geometries is given in the
mesh_geometries folder.
An interactive widget is provided in the simulation_widget_nb.ipynb notebook
which runs the simulation_widget.py library. This widget is a proof of
concept for the extensibility of Fidimag, in this case with the IPython widgets
library. The notebook shows a simulation for the island system reproduced from
experiments but further options are available in simulation_widget.py
Jupyter notebooks with the analysis of the data from the simulations are
provided in the notebooks directory. Notebooks can be viewed directly from
Github. In case you run the notebooks the paths to simulation files need to be
updated according to the simulation files produced in your machine (final time
steps might change) and the folders in your system (some notebooks might be
outdated). Notebooks with GNEBM results require the nebm_plot_tools library.
In this repository we provide 10 notebooks:
-
Hexagons NEBM skyrmion collapse.ipynb: GNEBM results for the skyrmion collapse transition in hexagonal islands of varying size, applied field and boundary condition. Results are based on the simulations located in
simulations/NEBM/nebm_2Dhex_hexagons_PdFe-Ir_sk-down-collapse_B-sweep_DT/andsimulations/NEBM/nebm_2Dhex_hexagons_PdFe-Ir_sk-down-collapse_B-sweep_pinned_boundary_DT/ -
Hexagons NEBM skyrmion escape.ipynb: GNEBM results for the skyrmion escape transition in hexagonal islands with free boundaries and varying size and applied field. Results are based on the simulations located in
simulations/NEBM/nebm_2Dhex_hexagons_PdFe-Ir_sk-down-escape_B-sweep_DT/ -
Hexagons NEBM tgt-state-up skyrmion-down collapse.ipynb: GNEBM results for the decay of a target state into a skyrmion in hexagonal islands of varying size, applied field and boundary condition. Results are based on the simulations located in
simulations/NEBM/nebm_2Dhex_hexagons_PdFe-Ir_tgt-st-up_sk-down_collapse_B-sweep_DT/andsimulations/NEBM/nebm_2Dhex_hexagons_PdFe-Ir_tgt-st-up_sk-down_B-sweep_pinned_boundary_DT/ -
Hexagons PdPdFe energies_positive_fields.ipynb: Notebook analysing the energy of ferromagnetic orderings, skyrmions and target states in hexagonal islands, as a function of island size, applied field and boundary condition. The notebook also shows snapshots of the relaxed configurations. Results are based on the simulations located in
simulations/relaxation/hexagons_size_variation_DT/andsimulations/relaxation/hexagons_size_variation_pinned_boundary_DT/ -
Hexagons_phase_diagram.ipynb: Phase diagram with the lowest energy configurations in hexagonal islands with free boundaries, as a function of island size and applied field. The phase diagram is shown both using the topological charge and the snapshots of the ground states. Results are based on the simulations located in
simulations/relaxation/hexagons_phase_diagram_B_L/ -
Hexagons_phase_diagram_pinned_bs.ipynb: Same than the previous phase diagram notebook but in islands with a ferromagnetic rim. Results are based on the simulations located in
simulations/relaxation/hexagons_phase_diagram_B_L_pinned_bs/ -
image_rotated NEBM target state-skyrmion.ipynb: GENBM results for the decay of target states into skyrmions in quasi-hexagonal islands fabricated experimentally. Results are shown as a function of the applied field. Simulation files are located in
simulations/NEBM/nebm_2Dhex_image-rotated_PdFe-Ir_tgt-st-up_sk-down_B-sweep_DT/andsimulations/NEBM/nebm_2Dhex_image-rotated_PdFe-Ir_tgt-st-3PI_tgt-st-2PI_B-sweep_DT/ -
image_rotated snapshots-positive_fields.ipynb: Results for the simulation of hysteresis-like field sweep processes in quasi-hexagonal islands fabricated experimentally. Results are shown for different initial states and the energy of the configurations found during the simulated sweep process are compared with the energy of magnetic configurations found during a field sweep experiment. Results are based on the files located in
simulations/hysteresis/image_rotated_DT/ -
image_rotated_energies_positive_fields.ipynb: Notebook analysing the energies and topological charge of different magnetic configurations in quasi-hexagonal islands fabricated experimentally. Results are compared with the energies of configurations observed during a field sweep experiment. In addition, the notebook provides details about the translation of the mesh from experiment into the simulations. Snapshots of different magnetic orderings are also shown along the notebook. Simulation files are located in
simulations/relaxation/image_rotated_B-sweep_DT/ -
image_rotated_relaxed_from_image.ipynb: Notebook showing the simulation of quasi-hexagonal islands fabricated experimentally. Simulations are directly compared with the experimental observations, which are based on SP-STM measurements. Simulation files are located in
simulations/relaxation/image_rotated_relax-from-image/. Experimental images are provided in theRomming_data/folder
If you find this material useful please cite us (you might need the LaTeX's
url package)
@Misc{Cortes2019,
author = {David Cort{\'e}s-Ortu{\~n}o and Niklas Romming and Marijan Beg and Kirsten von Bergmann and Andr{\'e} Kubetzka and Ondrej Hovorka and Hans Fangohr and Roland Wiesendanger},
title = {{Data set for: Nano-scale magnetic skyrmions and target states in confined geometries}},
howpublished = {Zenodo \url{doi:10.5281/zenodo.1438396}. Github: \url{https://github.com/davidcortesortuno/paper-2019_nanoscale_skyrmions_target_states_confined_geometries}},
year = {2019},
doi = {10.5281/zenodo.1438396},
url = {https://doi.org/10.5281/zenodo.1438396},
}
[1] Bisotti, M.-A., Cortés-Ortuño, D., Pepper, R., Wang, W., Beg, M., Kluyver, T., & Fangohr, H. (2018). Fidimag – A Finite Difference Atomistic and Micromagnetic Simulation Package. Journal of Open Research Software, 6(1), 22. DOI: http://doi.org/10.5334/jors.223