David Cortés-Ortuño^1,2, Marijan Beg^1,3, Martin Lang¹, Vanessa Nehruji^1,4, Ryan A. Pepper¹, and Hans Fangohr^1,5,6

¹ Faculty of Engineering and the Environment, University of Southampton, Southampton SO17 1BJ, United Kingdom
² Department of Earth Sciences, Utrecht University, 3584 CD Utrecht, The Netherlands
³ Department of Earth Science and Engineering, Imperial College London, London SW7 2AZ, United Kingdom
⁴ Department of Physics, University of Durham, Durham DH1 3LE, United Kingdom
⁵ Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
⁶ Center for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany

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DOI

Different Dzyaloshinskii-Moriya interaction forms can be written as different combinations of Lifshitz invariants depending on the crystallographic class of the magnetic material [1]. This mathematical formalism can also be applied to interfacial DMI systems [2], where the lack of inversion symmetry in the magnetic system is present due to the interfaces between different materials. It is usually referred to the C_nv DMI as interfacial DMI.

This module is a modification and extension of the OOMMF extension for interfacial systems [3] and the differences are:

1. Sign of the DMI constant,
2. This OOMMF extension supports periodic boundary conditions.

C_nv crystallographic class has the following energy density [1, 2]:

where is the DMI constant and is the normalised magnetisation field.

This OOMMF extension supports periodic boundary conditions. It works with both Oxs_RectangularMesh and Oxs_PeriodicRectangularMesh.

1. Copy DMI_Cnv_[xyz].cc and DMI_Cnv_[xyz].h files from the src directory in this repository into the app/oxs/local directory in the OOMMF main directory.
2. Recompile OOMMF, usually by running

$ tclsh oommf.tcl pimake distclean && tclsh oommf.tcl pimake upgrade && tclsh oommf.tcl pimake

We give examples in .mif files for the relaxation resulting in an isolated skyrmion state in a confined cuboid (with no periodic boundary conditions) and relaxation resulting in a skyrmion lattice in a unit cell of an infinite system (with periodic boundary conditions). Examples demonstrate the use of all three terms (with appropriately adjusted geometry).

DMI extensions for other crystallographic classes are D_2d and T(O).

If you require support, have questions, want to report a bug or suggest an improvement, please raise an issue in ubermag/help repository.

All contributions are welcome, however small they are. If you would like to contribute, please fork the repository and create a pull request. If you are unsure how to contribute, please contact us by raising an issue in ubermag/help repository, and we will help you get started and assist you on the way.

1. David Cortés-Ortuño et al. Proposal for a micromagnetic standard problem for materials with Dzyaloshinskii–Moriya interaction. New J. Phys. 20, 113015 (2018).

2. David Cortés-Ortuño, Marijan Beg, Martin Lang, Vanessa Nehruji, Ryan A. Pepper, and Hans Fangohr. OOMMF extension: Dzyaloshinskii-Moriya interaction for the crystallographic class Cnv. DOI: 10.5281/zenodo.1196417 (2018).

Licensed under the BSD 3-Clause "New" or "Revised" License. For details, please refer to the LICENSE file.

• OpenDreamKit – Horizon 2020 European Research Infrastructure project (676541)

• EPSRC Programme Grant on Skyrmionics (EP/N032128/1)

[1] A. Bogdanov and D. Yablonskii. Thermodynamically stable "vortices" in magnetically ordered crystals. The mixed state of magnets. Zh. Eksp. Teor. Fiz 95, 178 (1989).

[2] A. O. Leonov, T. L. Monchesky, N. Romming, A. Kubetzka, A. N. Bogdanov, and R. Wiesendanger. The properties of isolated chiral skyrmions in thin magnetic films. New J. of Phys. 18, 065003 (2015).

[3] S. Rohart and A. Thiaville. Skyrmion confinement in ultrathin film nanostructures in the presence of Dzyaloshinskii-Moriya interaction. Phys. Rev. B 88, 184422 (2013).