Pith. sign in

REVIEW 3 major objections 4 minor 1 cited by

mumax+: extensible GPU-accelerated micromagnetics and beyond

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper presents mumax+, a GPU finite-difference solver that extends micromagnetics to antiferromagnets, non-collinear order, and magnetoelasticity, and demonstrates it on domain-wall, racetrack, and Mn3Sn simulations.

desk verdict Real software, real value, and one real hole in the advertised AFM DMI boundary conditions that the authors need to close. read the letter →

arxiv 2411.18194 v4 pith:PCD7OWRY submitted 2024-11-27 cond-mat.mes-hall

Lars Moreels , Ian Lateur , Diego De Gusem , Jeroen Mulkers , Jonathan Maes , Milorad V. Milošević , Jonathan Leliaert , Bartel Van Waeyenberge This is my paper · ORCID
classification cond-mat.mes-hall
keywords antiferromagnetismmicromagneticsfinite-differencemethodGPUaccelerationmagnetoelasticcouplingdomain-wallmotionnon-collinearantiferromagnetracetrackmemory
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper presents mumax+, a GPU-accelerated micromagnetic simulator with a Python interface, and argues that one finite-difference solver can handle ferromagnets, collinear and non-collinear antiferromagnets, and ferrimagnets by resolving multiple sublattices. Its main new physics is full magnetoelastic coupling for antiferromagnets, joining magnetization dynamics to an elastodynamic equation whose strain feeds back through the inverse magnetostrictive, or Villari, effect. To show this works, the authors simulate three current problems: current-driven domain-wall motion in a polycrystalline antiferromagnet, a strain-pulse-driven antiferromagnetic racetrack memory in NiO, and the stray-field patterns of Mn3Sn as seen by nitrogen-vacancy magnetometry. If correct, the package gives the community a common platform for testing spintronic and straintronic proposals in systems where ferromagnetic approximations fail.

What carries the argument

The machinery is the sublattice-resolved finite-difference treatment: exchange is split into intra-sublattice ferromagnetic exchange, inhomogeneous inter-sublattice exchange, and a homogeneous antiferromagnetic exchange proportional to $4A_0/(M_S a^2)$ acting on the other sublattice's magnetization, with Neumann boundary conditions, Eq. (5), that couple the two sublattices and the DMI at surfaces. Magnetoelasticity is added by solving the elastodynamic equation $\rho\,\partial_t^2\mathbf{u}=\mathbf{f}_{\mathrm{tot}}$ with the elastic force computed as the numerical divergence of stress, and by coupling each sublattice magnetization to the shared strain through its own magnetoelastic constants $B_1^{(s)}$ and $B_2^{(s)}$. Time integration uses embedded Runge-Kutta methods with adaptive stepping.

What would settle it

Send a single calibrated 8 GHz shear traction pulse through a NiO strip with notches at 300 nm and 600 nm: the model predicts each domain wall moves exactly one notch spacing, 150 nm, so if a single pulse moves the walls by zero or by more than one notch, the coupled magnetoelastic implementation is wrong.

Watch

Extended reading notes

Core claim

The central claim is that a finite-difference micromagnetics code that evolves each sublattice magnetization with the Landau-Lifshitz-Gilbert torque, spin-transfer torques, antiferromagnetic exchange, Dzyaloshinskii-Moriya interaction, and magnetostatic fields, while simultaneously solving the elastodynamic equation with magnetoelastic forces, produces the three demonstrated behaviors: grain-boundary-dependent domain-wall mobility consistent with a known analytical model, stepwise domain-wall transport in NiO under an 8 GHz shear traction pulse, and Mn3Sn stray-field images comparable to measured nitrogen-vacancy magnetometry scans.

Load-bearing premise

The load-bearing premise is that the finite-difference exchange field and Neumann boundary conditions of the antiferromagnetic model faithfully represent real antiferromagnets on a grid; in the Mn3Sn demonstration this premise includes material parameters that are presented without a cited source.

Editorial extensions

If this is right

  • The same solver can model collinear antiferromagnets, non-collinear antiferromagnets, and ferrimagnets, with each sublattice having its own anisotropy, DMI tensor, and magnetoelastic constants while sharing one elastic displacement field.
  • A strain pulse generated by boundary traction can move domain walls stepwise between notches, demonstrating the working principle of a traction-driven antiferromagnetic racetrack memory.
  • The simulated out-of-plane stray field 60 nm above a polycrystalline Mn3Sn film has the same patchwork character and order of magnitude as nitrogen-vacancy magnetometry scans.
  • Current-driven domain-wall velocity in a polycrystalline antiferromagnet decreases and pinning strengthens as the inter-grain exchange is reduced, with the zero-reduction case matching the analytical model.
  • Because the code is open-source and object-oriented, new physical terms can be added by users without rewriting the core solver.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same finite-difference machinery should extend to other non-collinear magnets, such as the wider Mn3X family, and to coupled elastic-magnetic wave devices like surface-acoustic-wave-driven domain-wall motion; the paper does not test those cases.
  • A direct sensitivity test would be to vary the exchange and DMI parameters used for the Mn3Sn simulation and check whether the patchwork stray-field pattern persists; if it changes drastically, the agreement with the measured image is parameter-fitted rather than predictive.
  • The magnetoelastic formulation with a shared elastic displacement but per-sublattice coupling constants could be used to study strain-induced spin reorientation transitions or magnetoacoustic resonance in antiferromagnets, phenomena not demonstrated in the paper.
  • The comparison with the nitrogen-vacancy images is qualitative; quantifying local stray-field statistics point by point would provide a stronger, more quantitative test of the model.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The manuscript presents mumax+, an open-source GPU-accelerated finite-difference micromagnetics package with a Python interface, positioned as an extensible successor to mumax3. The reported advances are the ability to simulate antiferromagnets and ferrimagnets with multiple sublattices, a generalized DMI description, and coupled elastodynamics with magnetoelasticity. Three demonstrations are used to support these claims: current-driven domain-wall mobility in a polycrystalline antiferromagnet, a strain-driven domain-wall racetrack in NiO, and stray-field images of non-collinear Mn3Sn compared with NV magnetometry. The Methods section defines the LLG equation, exchange fields, magnetostatic fields, DMI energy and boundary conditions, elastic wave equation, and magnetoelastic couplings.

Significance. If the implementation is correct, mumax+ would be a valuable community resource: it is open-source, GPU-accelerated, and Python-based, and the paper explicitly ships a repository with tests. The paper contains some genuine external anchors: the 0% grain-boundary mobility curve agrees with the analytical model of Ref. [31], and the Mn3Sn calculation is compared to published NV images. However, the correctness of the advertised general DMI capability is called into question by the boundary condition in Eq. (5), and the Mn3Sn demonstration uses parameters whose provenance and sensitivity are not documented. These issues do not necessarily invalidate the three demonstrations, but they do weaken the broad claim that mumax+ is a general solver for non-collinear antiferromagnets with DMI.

major comments (3)
  1. [3.1.3, Eq. (5)] Equation (5) contains only the intrasublattice DMI boundary term D^(s) · (n ⊗ m^(s)). Varying the general DMI energy of Eq. (4) with respect to m^(s) produces, after integration by parts, surface terms n_i D_{ijk}^{(s,s')} m_j^(s') δm_k^(s) summed over partner sublattices s'. For s' ≠ s these terms are proportional to the partner magnetization and are absent from Eq. (5). Thus the advertised 'third DMI tensor' for intersublattice interactions does not enter the boundary-value problem as written, and the code does not solve the general DMI+exchange variational problem for antiferromagnets. The three demonstrations use intralattice/interfacial and homogeneous DMI only, so they do not expose the omission. The paper should either derive and implement the full boundary condition, or explicitly restrict the DMI capability claim to intrasublattice and homogeneous DMI.
  2. [Fig. 3 caption and Section 2.3] The exchange constants (10, -15, -25 pJ/m) and the homogeneous DMI (10 MJ/m^3) in the Mn3Sn simulation are presented without citation, and the agreement with Fig. 3(b) is only visual. The claim to 'reproduce experimentally observed domain structures' therefore needs a statement of whether these parameters are literature values or were adjusted, together with a sensitivity check (e.g., how much the pattern changes when the intergrain exchange reduction or the DMI strength is varied). Without this, the apparent agreement could be a consequence of parameter choice rather than a validated prediction of the model.
  3. [Section 2 and Section 4] The paper asserts that all capabilities have been thoroughly tested against the standard micromagnetic problems, mumax3, and analytical results, but no test outcomes are reported and the validation is deferred to an external repository. Since the central claim of the paper is that the solver is correct, the manuscript should include at least a concise summary of the verification tests (which problems were run, what error metrics were used, and the outcomes), even if the full test scripts remain online.
minor comments (4)
  1. [Table 1 and Eq. (7)] There are small typographical errors: 'magnetoelatic' should be 'magnetoelastic' in Table 1, and Eq. (7) reads 'andftot' with a missing space.
  2. [References] Several references are incomplete or lack journal names, e.g., Refs. [26], [42], [43], [44], [45], [46], [47], and [48] have volume/page or DOI information but no journal title; please restore the full bibliographic metadata.
  3. [Section 3.1.3] After Eq. (6), the phrase 'The latter lies parallel to the principal axis of the material' is ambiguous; it would be clearer to state that the implemented homogeneous DMI vector is restricted to that direction or that an arbitrary d-vector can be set in the input.
  4. [Section 2.2 caption to Table 1] The sentence in Table 1 that the interfacial DMI 'is chosen to stabilize the domain wall' is honest but it would help to state whether the two domain walls are static and pinned in the absence of strain over the simulated time; this would establish that the motion is caused by the elastic pulse rather than by spontaneous relaxation.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the demonstrations are anchored to external standard problems, an external analytical model, and experimental NV images, with the authors' prior work used only for implementation details.

full rationale

The paper does not claim a derivation of its physics from first principles; it presents a solver and three demonstration simulations. The polycrystalline antiferromagnet domain-wall mobility is compared with the analytical model of Sánchez-Tejerina et al. (external Ref. [31]) and with the group's earlier permalloy studies, but the external analytical curve is the quantitative check. The NiO racetrack simulation uses material parameters from external Refs. [38-41] and is a proof-of-principle demonstration rather than a fitted prediction. The Mn3Sn stray-field reproduction is compared with the experimental NV image of Li et al. (external Ref. [47]); although some exchange and DMI parameters in the Fig. 3 caption are not individually cited, the paper does not describe a fitting procedure, so there is no demonstrated reduction of the prediction to a fitted value. Eq. (3) and Eq. (5) are explicitly attributed to external Refs. [31] and [60]. Self-citations to mumax3 [5], defect simulations [28,30,32], and the magnetoelastic extension [66] supply numerical techniques and prior software, not the central validation. The possible omission of intersublattice DMI surface terms in Eq. (5) is a physics-support/correctness concern, not a circularity, because the target outputs are not used to define the equations. No load-bearing self-citation chain or definitional equivalence was found.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

The presentation rests on standard micromagnetism and continuum elasticity. The main load-bearing inputs are the antiferromagnetic exchange field and boundary conditions (Eqs. 3, 5) from Refs. [31, 60], the elastodynamic equation with Rayleigh damping (Eq. 7) from Refs. [64, 65, 72], and the antiferromagnetic magnetoelastic model (Eqs. 8-9) from Ref. [73]. The demonstrations add hand-set inputs: interfacial DMI and Rayleigh damping in the NiO simulation (Table 1), unsourced exchange and DMI constants for Mn3Sn (Fig. 3 caption), and the Voronoi grain-boundary model from Ref. [30]. No new physical entities are postulated.

free parameters (4)
  • Interfacial DMI in NiO racetrack simulation = 0.7 mJ/m2
    Table 1 states the DMI is 'chosen to stabilize the domain wall', i.e., not from experiment; the racetrack moving-wall result depends on it.
  • Rayleigh damping stiffness coefficient = 0.1 ps
    Table 1: chosen to yield a damping ratio of about 5% for shear waves with 24 nm wavelength; the elastic pulse dynamics depend on this choice.
  • Mn3Sn exchange constants and homogeneous DMI = 10 pJ/m; -15 pJ/m; -25 pJ/m; 10 MJ/m3
    Fig. 3 caption lists these values without citation; they determine the simulated domain structure and stray-field pattern, so the claimed reproduction could rely on them.
  • Intergrain exchange reduction in Mn3Sn simulation = 90% reduction (10% of intragrain value)
    Fig. 3 caption: 'the exchange coupling between neighboring grains is reduced to 10% of the intragrain value'; chosen by hand, not cited.
assumptions (7)
  • domain assumption The Landau-Lifshitz-Gilbert equation with summed field terms (Eqs. 1-2) is the correct dynamical model for the magnetization in all simulated systems.
    Standard micromagnetism; invoked in Section 3.1 as the core of the solver.
  • domain assumption The antiferromagnetic exchange field form and Neumann boundary conditions of Eqs. (3) and (5), taken from Refs. [31, 60], with homogeneous exchange 4 A0/(MS a^2) m(s'), correctly describe collinear and non-collinear antiferromagnets on a finite-difference grid.
    Load-bearing for all three demonstrations; the paper does not re-derive this model.
  • domain assumption The elastodynamic equation (7) with cubic-symmetry stiffness, fourth-order central differences, and Rayleigh-type viscous damping correctly captures elastic wave propagation in NiO at 8 GHz.
    Section 3.2; the racetrack demonstration depends on the strain pulse behavior, with damping chosen by hand.
  • domain assumption The antiferromagnetic magnetoelastic coupling model (shared displacement, per-sublattice coupling constants, Eqs. 8-9) following Ref. [73] is valid for NiO and Mn3Sn.
    Section 3.3; the NiO racetrack uses the Villari effect via this coupling.
  • domain assumption Voronoi-tessellated grains with reduced intergrain exchange represent polycrystalline disorder faithfully enough to reproduce observed domain-wall pinning and mobility trends.
    Used in Sections 2.1 and 2.3 following Ref. [30]; the mobility and domain-pattern results depend on this representation.
  • standard math OOMMF-style magnetostatic field computation (analytical near field, asymptotic far field, spin sum per cell) yields accurate stray fields for thin films with net moments.
    Section 3.1.2; used for the Mn3Sn stray-field image.
  • domain assumption The embedded Runge-Kutta integrators (Table 2) are applied within their stability and accuracy limits for the coupled magnetoelastic system.
    Section 3.1 and Section 4; the paper notes that adaptive time stepping appropriate for magnetoelastic simulations is future work, so the current coupling lacks specialized error control.

how reviews work

0 comments
Cite this review

Pith. "Pith review of mumax+: extensible GPU-accelerated micromagnetics and beyond." pith.science (2026). https://pith.science/paper/PCD7OWRY

@misc{pith2026241118194,
  author       = {Pith},
  title        = {Pith review of: mumax+: extensible GPU-accelerated micromagnetics and beyond},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PCD7OWRY}},
  note         = {Machine review of arXiv:2411.18194}
}
read the original abstract

We present mumax+, an extensible GPU-accelerated micromagnetic simulator with a Python user interface, to address the challenges posed by current magnetism research into systems with complex magnetic ordering and interfaces. It is a general solver for the space- and time-dependent evolution of the magnetization and related vector quantities, using finite difference discretization. Here, we present its application and design and discuss features not available in \mumaxthree{}, such as the modeling of antiferromagnets with magnetoelastic coupling. As an illustration of its capabilities, we use \mumaxp{} to simulate state of the art magnetic systems. Specifically, we demonstrate the current induced domain wall motion in a polycrystalline antiferromagnet, we simulate the working principle of a strain-driven antiferromagnetic racetrack memory and we reproduce experimentally observed domain structures in a non-collinear antiferromagnet.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Modeling Magnetoelastic Wave Interactions in Magnetic Films and Heterostructures: A finite-difference approach

    physics.comp-ph 2025-09 conditional novelty 6.0 of 10

    A finite-difference simulation scheme for coupled magnetic and elastic wave dynamics was implemented, including interface jump conditions for stress and strain in magnetic heterostructures.

Reference graph

Works this paper leans on

72 extracted references · 44 canonical work pages · cited by 1 Pith paper

  1. [31]

    S´ anchez-Tejerina, L., Puliafito, V., Khalili Amiri, P., Carpentieri, M., Finocchio, G.: Dynamics of domain-wall motion driven by spin-orbit torque in antiferromag- nets. Phys. Rev. B 101, 014433 (2020) https://doi.org/10.1103/PhysRevB.101. 014433

    doi:10.1103/physrevb.101 2020

  2. [1]

    - 6376, National Institute of Standards and Technology, Gaithersburg, MD (1999)

    Donahue, M.: OOMMF User’s Guide, Version 1.0. - 6376, National Institute of Standards and Technology, Gaithersburg, MD (1999). https://doi.org/10.6028/ NIST.IR.6376

    work page 1999

  3. [2]

    Journal of Magnetism and Magnetic Materials323(21), 2585–2591 (2011) https://doi.org/10.1016/j.jmmm.2011.05.037

    Vansteenkiste, A., Van de Wiele, B.: MuMax: A new high-performance micro- magnetic simulation tool. Journal of Magnetism and Magnetic Materials323(21), 2585–2591 (2011) https://doi.org/10.1016/j.jmmm.2011.05.037

    doi:10.1016/j.jmmm.2011.05.037 2011

  4. [3]

    https://github.com/mumax/2 11

    Vansteenkiste, A., Van de Wiele, B., Dvornik, M., Lassalle-Balier, R., Rowlands, G.: mumax2 (2012). https://github.com/mumax/2 11

    work page 2012

  5. [4]

    Com- putational Materials Science 28(2), 366–383 (2003) https://doi.org/10.1016/ S0927-0256(03)00119-8

    Scholz, W., Fidler, J., Schrefl, T., Suess, D., Dittrich, R., Forster, H., Tsiantos, V.: Scalable parallel micromagnetic solvers for magnetic nanostructures. Com- putational Materials Science 28(2), 366–383 (2003) https://doi.org/10.1016/ S0927-0256(03)00119-8 . Proceedings of the Symposium on Software Development for Process and Materials Design

    work page 2003

  6. [5]

    AIP Advances 4(10), 107133 (2014) https://doi.org/10.1063/1.4899186

    Vansteenkiste, A., Leliaert, J., Dvornik, M., Helsen, M., Garcia-Sanchez, F., Van Waeyenberge, B.: The design and verification of MuMax3. AIP Advances 4(10), 107133 (2014) https://doi.org/10.1063/1.4899186

    doi:10.1063/1.4899186 2014

  7. [6]

    IEEE Transactions on Magnetics 43(6), 2896–2898 (2007) https://doi

    Fischbacher, T., Franchin, M., Bordignon, G., Fangohr, H.: A systematic approach to multiphysics extensions of finite-element-based micromagnetic simulations: Nmag. IEEE Transactions on Magnetics 43(6), 2896–2898 (2007) https://doi. org/10.1109/TMAG.2007.893843

    work page arXiv 2007

  8. [7]

    https://github.com/micromagnetics/magnum.fe

    MicroMagnetics Team: Magnum.FE: Finite-Element Micromagnetic Simulation. https://github.com/micromagnetics/magnum.fe. Accessed: 2024-12-04 (2024)

    work page 2024

Show all 72 references
  1. [8]

    Journal of Applied Physics 109(7), 07–358 (2011) https://doi.org/10.1063/1.3563081

    Chang, R., Li, S., Lubarda, M.V., Livshitz, B., Lomakin, V.: FastMag: Fast micro- magnetic simulator for complex magnetic structures (invited). Journal of Applied Physics 109(7), 07–358 (2011) https://doi.org/10.1063/1.3563081

    2011 doi

  2. [9]

    IEEE Transactions on Magnetics 46(6), 2303– 2306 (2010) https://doi.org/10.1109/TMAG.2010.2048016

    Kakay, A., Westphal, E., Hertel, R.: Speedup of FEM Micromagnetic Simulations With Graphical Processing Units. IEEE Transactions on Magnetics 46(6), 2303– 2306 (2010) https://doi.org/10.1109/TMAG.2010.2048016

    2010

  3. [10]

    Journal of Applied Physics 128(24), 243902 (2020) https://doi.org/10.1063/5.0024382

    Lepadatu, S.: Boris computational spintronics—High performance multi-mesh magnetic and spin transport modeling software. Journal of Applied Physics 128(24), 243902 (2020) https://doi.org/10.1063/5.0024382

    2020 doi

  4. [11]

    https://github.com/MicroMagnum/ MicroMagnum

    Drews, A., Selke, G., Krueger, B., Abert, C., Gerhardt, T.: MicroMag- num: Micromagnetic Simulation Framework. https://github.com/MicroMagnum/ MicroMagnum. Accessed: 2024-12-04 (2024)

    2024

  5. [12]

    https://github.com/micromagnetics/magnum.fd

    MicroMagnum Team: Magnum.FD: Finite-Difference Micromagnetic Simulation. https://github.com/micromagnetics/magnum.fd. Forked from MicroMagnum, Accessed: 2024-12-04 (2024)

    2024

  6. [13]

    Baltz, V., Manchon, A., Tsoi, M., Moriyama, T., Ono, T., Tserkovnyak, Y.: Anti- ferromagnetic spintronics. Rev. Mod. Phys. 90, 015005 (2018) https://doi.org/ 10.1103/RevModPhys.90.015005

    2018 doi

  7. [14]

    Nature 499(7459), 419–425 (2013) https://doi.org/10.1038/nature12385

    Geim, A.K., Grigorieva, I.V.: Van der Waals heterostructures. Nature 499(7459), 419–425 (2013) https://doi.org/10.1038/nature12385 . Publisher: Nature Pub- lishing Group. Accessed 2024-12-02 12

    2013 doi

  8. [15]

    npj Spintronics 2(1), 1–15 (2024) https://doi

    Bandyopadhyay, S.: Perspective: There is plenty of room for magnetic strain- tronics in the analog domain. npj Spintronics 2(1), 1–15 (2024) https://doi. org/10.1038/s44306-024-00018-3 . Publisher: Nature Publishing Group. Accessed 2024-12-02

    2024 doi

  9. [16]

    Applied Physics Reviews 8(4), 041323 (2021) https: //doi.org/10.1063/5.0062993

    Bandyopadhyay, S., Atulasimha, J., Barman, A.: Magnetic straintronics: Manip- ulating the magnetization of magnetostrictive nanomagnets with strain for energy-efficient applications. Applied Physics Reviews 8(4), 041323 (2021) https: //doi.org/10.1063/5.0062993 . Accessed 2024-12-05

    2021 doi

  10. [17]

    CreateSpace, Scotts Valley, CA (2009)

    Van Rossum, G., Drake, F.L.: Python 3 Reference Manual. CreateSpace, Scotts Valley, CA (2009)

    2009

  11. [18]

    Nature 585(7825), 357–362 (2020) https://doi.org/10.1038/s41586-020-2649-2

    Harris, C.R., Millman, K.J., Walt, S.J., Gommers, R., Virtanen, P., Cournapeau, D., Wieser, E., Taylor, J., Berg, S., Smith, N.J., Kern, R., Picus, M., Hoyer, S., Kerkwijk, M.H., Brett, M., Haldane, A., R ´ ıo, J.F., Wiebe, M., Peterson, P., G´ erard-Marchant, P., Sheppard, K....

    2020 doi

  12. [19]

    Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/ s41592-019-0686-2

    Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Courna- peau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Po...

    2020

  13. [20]

    Computing in Science & Engineering 9(3), 90–95 (2007) https://doi.org/10.1109/MCSE.2007.55

    Hunter, J.D.: Matplotlib: A 2d graphics environment. Computing in Science & Engineering 9(3), 90–95 (2007) https://doi.org/10.1109/MCSE.2007.55

    2007 doi

  14. [21]

    ISO/IEC Standard (2020)

    ISO/IEC: ISO/IEC 14882:2024 - Programming Languages – C++. ISO/IEC Standard (2020). https://www.iso.org/standard/83626.html

    2020

  15. [22]

    Version 12.6 (2024)

    NVIDIA Corporation: NVIDIA CUDA C Programming Guide. Version 12.6 (2024)

    2024

  16. [23]

    https://www.ctcms.nist.gov/∼rdm/mumag.org.html Accessed 2024-11-25

    µMAG organization: µMAG Micromagnetic Modeling Activity Group (2021). https://www.ctcms.nist.gov/∼rdm/mumag.org.html Accessed 2024-11-25

    2021

  17. [24]

    Journal of Applied Physics 134(17) (2023)

    Joos, J.J., Bassirian, P., Gypens, P., Mulkers, J., Litzius, K., Van Waeyen- berge, B., Leliaert, J.: Tutorial: Simulating modern magnetic material systems in mumax3. Journal of Applied Physics 134(17) (2023)

    2023

  18. [25]

    Science 309(5741), 1688–1692 (2005) https://doi.org/10.1126/science.1108813 https://www.science.org/doi/pdf/10.1126/science.1108813

    Allwood, D.A., Xiong, G., Faulkner, C.C., Atkinson, D., 13 Petit, D., Cowburn, R.P.: Magnetic domain-wall logic. Science 309(5741), 1688–1692 (2005) https://doi.org/10.1126/science.1108813 https://www.science.org/doi/pdf/10.1126/science.1108813

    2005 doi

  19. [26]

    90.015005

    Baltz, V., Manchon, A., Tsoi, M., Moriyama, T., Ono, T., Tserkovnyak, Y.: Anti- ferromagnetic spintronics 90(1), 015005 https://doi.org/10.1103/RevModPhys. 90.015005 . Publisher: American Physical Society. Accessed 2025-05-19

    2025 doi

  20. [27]

    Accessed 2025-05-14

    Nomoto, T., Arita, R.: Cluster multipole dynamics in noncollinear antiferromag- nets 2(1), 012045 https://doi.org/10.1103/PhysRevResearch.2.012045 . Accessed 2025-05-14

    2025 doi

  21. [28]

    Leliaert, J., Wiele, B., Vansteenkiste, A., Laurson, L., Durin, G., Dupr´ e, L., Van Waeyenberge, B.: Influence of material defects on current-driven vortex domain wall mobility. Phys. Rev. B 89, 064419 (2014) https://doi.org/10.1103/ PhysRevB.89.064419

    2014

  22. [29]

    Journal of Magnetism and Magnetic Materials 159(1), 1–7 (1996) https://doi.org/10.1016/ 0304-8853(96)00062-5

    Slonczewski, J.C.: Current-driven excitation of magnetic multilayers. Journal of Magnetism and Magnetic Materials 159(1), 1–7 (1996) https://doi.org/10.1016/ 0304-8853(96)00062-5

    1996

  23. [30]

    Journal of Applied Physics 115(23), 233903 (2014) https://doi.org/10.1063/1.4883297 https://pubs.aip.org/aip/jap/article- pdf/doi/10.1063/1.4883297/15138111/233903 1 online.pdf

    Leliaert, J., Wiele, B., Vansteenkiste, A., Laurson, L., Durin, G., Dupr´ e, L., Van Waeyenberge, B.: Current-driven domain wall mobility in polycrystalline permalloy nanowires: A numer- ical study. Journal of Applied Physics 115(23), 233903 (2014) https://doi.org/10.1063/1.48...

    2014 doi

  24. [32]

    Journal of Applied Physics115(17), 17–102 (2014) https://doi.org/10.1063/1.4854956 https://pubs.aip.org/aip/jap/article- pdf/doi/10.1063/1.4854956/15135090/17d102 1 online.pdf

    Leliaert, J., Wiele, B., Vansteenkiste, A., Laurson, L., Durin, G., Dupr´ e, L., Van Waeyenberge, B.: A numerical approach to incorporate intrinsic material defects in micromagnetic simulations. Journal of Applied Physics115(17), 17–102 (2014) https://doi.org/10.1063/1.4854956...

    2014 doi

  25. [34]

    Journal of Magnetism and Magnetic Materials 552, 169229 14 (2022) https://doi.org/10.1016/j.jmmm.2022.169229

    Yu, G., Shi, S., Peng, R., Guo, R., Qiu, Y., Wu, G., Li, Y., Zhu, M., Zhou, H.: Strain-driven magnetic domain wall dynamics controlled by voltage in multifer- roic heterostructures. Journal of Magnetism and Magnetic Materials 552, 169229 14 (2022) https://doi.org/10.1016/j.jmm...

    2022

  26. [35]

    AIP Advances 12(3), 035036 (2022) https: //doi.org/10.1063/9.0000279 https://pubs.aip.org/aip/adv/article- pdf/doi/10.1063/9.0000279/16461111/035036 1 online.pdf

    Yu, G., He, X., Qiu, Y., Wu, G., Guo, R., Zhu, M., Zhou, H.: Dynamics of domain wall induced by voltage-controlled strain-field gradient. AIP Advances 12(3), 035036 (2022) https: //doi.org/10.1063/9.0000279 https://pubs.aip.org/aip/adv/article- pdf/doi/10.1063/9.0000279/164611...

    2022 doi

  27. [36]

    International Series of Monographs on Physics

    Chikazumi, S.: Physics of Ferromagnetism. International Series of Monographs on Physics. OUP Oxford, Oxford (2009)

    2009

  28. [37]

    Science (New York, N.Y.) 320, 190–4 (2008) https://doi.org/10.1126/science

    Parkin, S., Hayashi, M., Thomas, L.: Magnetic domain-wall racetrack memory. Science (New York, N.Y.) 320, 190–4 (2008) https://doi.org/10.1126/science. 1145799

    2008 doi

  29. [38]

    K¨ odderitzsch, D., Hergert, W., Temmerman, W.M., Szotek, Z., Ernst, A., Winter, H.: Exchange interactions in nio and at the nio(100) surface. Phys. Rev. B 66, 064434 (2002) https://doi.org/10.1103/PhysRevB.66.064434

    2002 doi

  30. [39]

    Chen, F., Ge, X., Luo, W., Xing, R., Liang, S., Yang, X., You, L., Xiong, R., Otani, Y., Zhang, Y.: Strain-induced megahertz oscillation and stable velocity of an antiferromagnetic domain wall. Phys. Rev. Appl. 15, 014030 (2021) https: //doi.org/10.1103/PhysRevApplied.15.014030

    2021 doi

  31. [40]

    Nature Photonics 5(1), 31–34 (2010) https: //doi.org/10.1038/nphoton.2010.259

    Kampfrath, T., Sell, A., Klatt, G., Pashkin, A., M¨ ahrlein, S., Dekorsy, T., Wolf, M., Fiebig, M., Leitenstorfer, A., Huber, R.: Coherent terahertz control of antiferromagnetic spin waves. Nature Photonics 5(1), 31–34 (2010) https: //doi.org/10.1038/nphoton.2010.259

    2010 doi

  32. [41]

    Azovtsev, A.V., Pertsev, N.A.: Thz and sub-thz antiferromagnetic magnons via magnetoacoustic resonances excited by picosecond strain pulses in nio. Phys. Rev. Mater. 8, 044404 (2024) https://doi.org/10.1103/PhysRevMaterials.8.044404

    2024 doi

  33. [42]

    Accessed 2025-05-20

    Wang, X., Yan, H., Zhou, X., Chen, H., Feng, Z., Qin, P., Meng, Z., Liu, L., Liu, Z.: Noncollinear mn3sn for antiferromagnetic spintronics 28, 100878 https: //doi.org/10.1016/j.mtphys.2022.100878 . Accessed 2025-05-20

    2022

  34. [43]

    Accessed 2025-05-14

    Lee, W.-B., Hwang, S., Ko, H.-W., Park, B.-G., Lee, K.-J., Choi, G.-M.: Spin-torque-driven gigahertz magnetization dynamics in the non-collinear anti- ferromagnet mn3sn 20(4), 487–493 https://doi.org/10.1038/s41565-025-01859-7 . Accessed 2025-05-14

    doi

  35. [44]

    Accessed 2025-06-10 15

    Park, P., Oh, J., Uhl ´ ıˇ rov´ a, K., Jackson, J., De´ ak, A., Szunyogh, L., Lee, K.H., Cho, H., Kim, H.-L., Walker, H.C., Adroja, D., Sechovsk´ y, V., Park, J.-G.: Magnetic excitations in non-collinear antiferromagnetic weyl semimetal mn3sn 3(1), 1–8 https://doi.org/10.1038/...

    doi

  36. [45]

    org/10.1038/nature15723

    Nakatsuji, S., Kiyohara, N., Higo, T.: Large anomalous hall effect in a non- collinear antiferromagnet at room temperature 527(7577), 212–215 https://doi. org/10.1038/nature15723 . Accessed 2025-05-13

    2025 doi

  37. [46]

    Accessed 2025-05-12

    Reichlova, H., Janda, T., Godinho, J., Markou, A., Kriegner, D., Schlitz, R., Zelezny, J., Soban, Z., Bejarano, M., Schultheiss, H., Nemec, P., Jungwirth, T., Felser, C., Wunderlich, J., Goennenwein, S.T.B.: Imaging and writing magnetic domains in the non-collinear antiferroma...

    doi

  38. [47]

    Accessed 2025-06-10

    Li, S., Huang, M., Lu, H., McLaughlin, N.J., Xiao, Y., Zhou, J., Fullerton, E.E., Chen, H., Wang, H., Du, C.R.: Nanoscale magnetic domains in polycrystalline mn3sn films imaged by a scanning single-spin magnetometer 23(11), 5326–5333 https://doi.org/10.1021/acs.nanolett.3c0152...

    doi

  39. [48]

    Accessed 2025-06-24

    Higo, T., Man, H., Gopman, D.B., Wu, L., Koretsune, T., Erve, O.M.J., Kabanov, Y.P., Rees, D., Li, Y., Suzuki, M.-T., Patankar, S., Ikhlas, M., Chien, C.L., Arita, R., Shull, R.D., Orenstein, J., Nakatsuji, S.: Large magneto-optical kerr effect and imaging of magnetic octupole...

    doi

  40. [49]

    reproduced in collected papers of ld landau

    Landau, L., Lifshitz, E.: On the theory of the dispersion of magnetic permeability in ferromagnetic bodies. reproduced in collected papers of ld landau. Pergamon, New York (1935)

    1935

  41. [50]

    Zhang, S., Li, Z.: Roles of Nonequilibrium Conduction Electrons on the Magne- tization Dynamics of Ferromagnets. Phys. Rev. Lett. 93, 127204 (2004) https: //doi.org/10.1103/PhysRevLett.93.127204

    2004 doi

  42. [51]

    Pearson Addison Wesley, Edinburgh (2004)

    Leader, J.J.: Numerical Analysis and Scientific Computation. Pearson Addison Wesley, Edinburgh (2004)

    2004

  43. [52]

    Applied Math- ematics Letters 2(4), 321–325 (1989) https://doi.org/10.1016/0893-9659(89) 90079-7

    Bogacki, P., Shampine, L.F.: A 3(2) pair of runge - kutta formulas. Applied Math- ematics Letters 2(4), 321–325 (1989) https://doi.org/10.1016/0893-9659(89) 90079-7

    1989 doi

  44. [53]

    ACM Trans

    Cash, J.R., Karp, A.H.: A variable order runge-kutta method for initial value problems with rapidly varying right-hand sides. ACM Trans. Math. Softw. 16(3), 201–222 (1990) https://doi.org/10.1145/79505.79507

    1990

  45. [54]

    NASA technical report

    Fehlberg, E., Center, G.C.M.S.F.: Low-order Classical Runge-Kutta Formulas with Stepsize Control and Their Application to Some Heat Transfer Prob- lems. NASA technical report. National Aeronautics and Space Administration, Washington (1969)

    1969

  46. [55]

    Journal of Computational and Applied Mathematics 6(1), 19–26 (1980) https://doi.org/ 16 10.1016/0771-050X(80)90013-3

    Dormand, J.R., Prince, P.J.: A family of embedded runge-kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980) https://doi.org/ 16 10.1016/0771-050X(80)90013-3

    1980 doi

  47. [56]

    Gilbert, T.L.: A Lagrangian formulation of the gyromagnetic equation of the magnetization field. Phys. Rev. 100, 1243 (1955)

    1955

  48. [57]

    AIP Advances 7(12), 125010 (2017) https://doi.org/10.1063/1.5003957

    Leliaert, J., Mulkers, J., De Clercq, J., Coene, A., Dvornik, M., Van Waeyenberge, B.: Adaptively time stepping the stochastic Landau-Lifshitz-Gilbert equation at nonzero temperature: Implementation and validation in MuMax3. AIP Advances 7(12), 125010 (2017) https://doi.org/10...

    2017 doi

  49. [58]

    Journal of Geophysical Research: Solid Earth 98(B6), 9551–9555 (1993) https://doi.org/10.1029/93JB00694

    Newell, A.J., Williams, W., Dunlop, D.J.: A generalization of the demagnetiz- ing tensor for nonuniform magnetization. Journal of Geophysical Research: Solid Earth 98(B6), 9551–9555 (1993) https://doi.org/10.1029/93JB00694

    1993 doi

  50. [59]

    6th Interna- tional Symposium on Hysteresis Modeling and Micromagnetics (2007)

    Donahue, M.J.: Accurate computation of the demagnetization tensor. 6th Interna- tional Symposium on Hysteresis Modeling and Micromagnetics (2007). Accessed 2024-11-25

    2007

  51. [60]

    Hals, K.M.D., Everschor-Sitte, K.: New Boundary-Driven Twist States in Systems with Broken Spatial Inversion Symmetry. Phys. Rev. Lett. 119, 127203 (2017) https://doi.org/10.1103/PhysRevLett.119.127203

    2017 doi

  52. [61]

    Mahfouzi, F., Kioussis, N.: Bulk generalized Dzyaloshinskii-Moriya interaction in PT -symmetric antiferromagnets. Phys. Rev. B 106, 220404 (2022) https://doi. org/10.1103/PhysRevB.106.L220404

    2022 doi

  53. [62]

    Journal of Magnetism and Magnetic Materials 507, 166800 (2020) https://doi.org/10.1016/j.jmmm.2020.166800

    Gorobets, O.Y., Gorobets, Y.I.: 3d analytical model of skyrmion-like structures in an antiferromagnet with dmi. Journal of Magnetism and Magnetic Materials 507, 166800 (2020) https://doi.org/10.1016/j.jmmm.2020.166800

    2020

  54. [63]

    Khoshlahni, R., Qaiumzadeh, A., Bergman, A., Brataas, A.: Ultrafast generation and dynamics of isolated skyrmions in antiferromagnetic insulators. Phys. Rev. B 99, 054423 (2019) https://doi.org/10.1103/PhysRevB.99.054423

    2019 doi

  55. [64]

    Graff, K.F.: Wave Motion in Elastic Solids. (1975)

    1975

  56. [65]

    North-Holland Publishing Company/American Elsevier, Amsterdam (1973)

    Achenbach, J.D.: Wave Propagation in Elastic Solids. North-Holland Publishing Company/American Elsevier, Amsterdam (1973)

    1973

  57. [66]

    Open Research Europe 1(35) (2021) https://doi.org/10

    Vanderveken, F., Mulkers, J., Leliaert, J., Van Waeyenberge, B., Sor´ ee, B., Zografos, O., Zografos, O., Ciubotaru, F., Adelmann, C.: Finite difference mag- netoelastic simulator. Open Research Europe 1(35) (2021) https://doi.org/10. 12688/openreseurope.13302.1

    2021

  58. [67]

    Solid Mechanics and Its Applications

    Barber, J.R.: Elasticity. Solid Mechanics and Its Applications. Springer, Dor- drecht (2012)

    2012

  59. [68]

    Always learning

    Sauer, T., Sauer, T.: Numerical Analysis. Always learning. Pearson, London 17 (2012)

    2012

  60. [69]

    Cambridge university press, Cambridge (2000)

    Wineman, A.S., Rajagopal, K.R.: Mechanical Response of Polymers: an Intro- duction. Cambridge university press, Cambridge (2000)

    2000

  61. [70]

    Mechanics Research Communications 36(2), 232–235 (2009) https://doi

    Rajagopal, K.R.: A note on a reappraisal and generalization of the kelvin–voigt model. Mechanics Research Communications 36(2), 232–235 (2009) https://doi. org/10.1016/j.mechrescom.2008.09.005

    2009 doi

  62. [71]

    Materials Today 12(3), 44 (2009) https://doi.org/10.1016/S1369-7021(09)70086-0

    Stachurski, Z.H.: Mechanical behavior of materials. Materials Today 12(3), 44 (2009) https://doi.org/10.1016/S1369-7021(09)70086-0

    2009 doi

  63. [72]

    Journal of Sound and Vibration 206(5), 741–744 (1997) https://doi.org/10.1006/jsvi.1997.1067

    Semblat, J.F.: Rheological interpretation of rayleigh damping. Journal of Sound and Vibration 206(5), 741–744 (1997) https://doi.org/10.1006/jsvi.1997.1067

    1997

  64. [73]

    Barra, A., Domann, J., Kim, K.W., Carman, G.: Voltage Control of Antiferromag- netic Phases at Near-Terahertz Frequencies. Phys. Rev. Appl. 9, 034017 (2018) https://doi.org/10.1103/PhysRevApplied.9.034017 18

    2018 doi

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.