Micromagnetic Modeling

Recent progress in material science has enabled the first experimental studies concerning the static magnetization characterization of samples with tubular geometry, such as rolled-up structures, nanowires and nanotubes. The bending of a flat thin-film to a curved surface introduces a break of the local inversion symmetry and can lead to surprising phenomena which do not unfold in flat geometries. As an example, domain walls in nanotubes  show a chiral symmetry breaking regarding their propagation and moreover can propagate so fast that can trigger a  Cherenkov-type spin-wave radiation. A further example is that this lack of inversion symmetry leads to an asymmetric dispersion relation for the spin waves regarding the sign of the propagation vector. This is a purely curvature induced effect with its origin in the classical dipole-dipole interaction. 

Using finite element micromagnetic simulations with our in-house developed program TetraMag (originally developed by Dr. Riccardo Hertel), we study the effect of the surface curvature on the statics and dynamics of typical spin textures as well as on the spin-wave propagation. The usual spin textures are domain walls, vorticies, Bloch points and Skyrmions formed in ferromagnetic nanowires and nanotubes. Although investigating spin-wave and domain-wall dynamics is still a challenge from experimental point of view, a combined effort of the experimental groups in our devision helps to confirm the results predicted by simulations.

Besides the basic research we develop GPU accelerated micromagnetic codes used in our studies for the finite discretisation as well as for the finite element methods and all related programs required for the analysis of the simulations. 

Research Topics

  • Spin textures in curved geometries
  • Spin-wave propagation in curved nano-membranes
  • GPU accelerated micromagnetic code development

Research Projects

  • DFG: 3D transport of spin waves in curved nano-membranes
  • DACH: Curvature-induced effects in magnetic nanostructures, in collaboration with:
    • Prof. M. Huth, Goethe Universität, Frankfurth am Main
    • Dr. Denys Makarov, HZDR
    • Dr. Oleksandr Dobrovolskiy, Universotät Wien
  • DAAD: Influence of curvature and topology on spin-wave transport
    • Bilateral Exchange of Academics with Chile, Dr. J. A. Otálora from Universidad Católica del Norte 


We are grateful to Henrik Schulz and Jens Lasch for their continuous support of our computational infrastructure.

Recent publications

Full list availabe here.


Nonreciprocity of spin waves in magnetic nanotubes with helical equilibrium magnetization

Salazar-Cardona, M. M.; Körber, L.; Schultheiß, H.; Lenz, K.; Thomas, A.; Nielsch, K.; Kakay, A.; Otálora, J. A.


  • Secondary publication expected from 30.06.2022

Multistate current-induced magnetization switching in Au/Fe/MgO(001) epitaxial heterostructures

Gospodarič, P.; Młyńczak, E.; Soldatov, I.; Kakay, A.; Bürgler, D. E.; Plucinski, L.; Schäfer, R.; Faßbender, J.; Schneider, C. M.

Finite-element dynamic-matrix approach for spin-wave dispersions in magnonic waveguides with arbitrary cross section

Körber, L.; Quasebarth, G.; Otto, A.; Kakay, A.

Related publications

Theory of three-magnon interaction in a vortex-state magnetic nanodot

Verba, R.; Körber, L.; Schultheiß, K.; Schultheiß, H.; Tiberkevich, V.; Slavin, A.

Related publications


Spin-wave dynamics and symmetry breaking in an artificial spin ice

Saha, S.; Zhou, J.; Hofhuis, K.; Kakay, A.; Scagnoli, V.; Heyderman, L. J.; Gliga, S.

Related publications


  • Secondary publication expected from 09.03.2022

Time refraction of spin waves

Schultheiß, K.; Sato, N.; Matthies, P.; Körber, L.; Wagner, K.; Hula, T.; Gladii, O.; Pearson, J. E.; Hoffmann, A.; Helm, M.; Faßbender, J.; Schultheiß, H.


Numerical ferromagnetic resonance experiments in nanosized elements

Wagner, K.; Körber, L.; Stienen, S.; Lindner, J.; Farle, M.; Kakay, A.

Related publications


  • Secondary publication expected from 29.01.2022

Self-stabilizing exchange-mediated spin transport

Schneider, T.; Hill, D.; Kakay, A.; Lenz, K.; Lindner, J.; Faßbender, J.; Upadhyaya, P.; Liu, Y.; Wang, K.; Tserkovnyak, Y.; Krivorotov, I. N.; Barsukov, I.



Spin-transfer dynamics in MgO-based magnetic tunnel junctions with an out-of-plane magnetized free layer and an in-plane polarizer

Kowalska, E.; Sluka, V.; Kakay, A.; Fowley, C.; Lindner, J.; Fassbender, J.; Deac, A. M.


Propagation of spin waves through a Néel domain wall

Wojewoda, O.; Hula, T.; Flajšman, L.; Vaňatka, M.; Gloss, J.; Holobrádek, J.; Staňo, M.; Stienen, S.; Körber, L.; Schultheiß, K.; Schmid, M.; Schultheiß, H.; Urbánek, M.

Effect of curvature on the eigenstates of magnetic skyrmions

Korniienko, A.; Kakay, A.; Sheka, D. D.; Kravchuk, V. P.


Nonlocal stimulation of three-magnon splitting in a magnetic vortex

Körber, L.; Schultheiß, K.; Hula, T.; Verba, R.; Faßbender, J.; Kakay, A.; Schultheiß, H.

Related publications


Nonlinear losses in magnon transport due to four-magnon scattering

Hula, T.; Schultheiß, K.; Buzdakov, A.; Körber, L.; Bejarano, M.; Flacke, L.; Liensberger, L.; Weiler, M.; Shaw, J. M.; Nembach, H. T.; Faßbender, J.; Schultheiß, H.

Related publications


Visualizing Magnetic Structure in 3D Nanoscale Ni–Fe Gyroid Networks

Llandro, J.; Love, D. M.; Kovács, A.; Caron, J.; Vyas, K. N.; Kakay, A.; Salikhov, R.; Lenz, K.; Faßbender, J.; Scherer, M. R. J.; Cimorra, C.; Steiner, U.; Barnes, C. H. W.; Dunin-Borkowski, R. E.; Fukami, S.; Ohno, H.


  • Secondary publication expected

Tunable magnetic vortex dynamics in ion-implanted permalloy disks

Ramasubramanian, L.; Kákay, A.; Fowley, C.; Yildirim, O.; Matthes, P.; Sorokin, S.; Titova, A.; Hilliard, D.; Böttger, R.; Hübner, R.; Gemming, S.; Schulz, S. E.; Kronast, F.; Makarov, D.; Faßbender, J.; Deac, A. M.

Nonlocal chiral symmetry breaking in curvilinear magnetic shells

Sheka, D. D.; Pylypovskyi, O.; Landeros, P.; Gaididei, Y.; Kakay, A.; Makarov, D.

Domain wall-based spin-Hall nano-oscillators

Sato, N.; Schultheiß, K.; Körber, L.; Puwenberg, N.; Mühl, T.; Awad, A. A.; Arekapudi, S. S. P. K.; Hellwig, O.; Faßbender, J.; Schultheiß, H.



Experimental Observation of Exchange-Driven Chiral Effects in Curvilinear Magnetism

Volkov, O.; Kakay, A.; Florian, K.; Mönch, J. I.; Mohamad-Assaad, M.; Faßbender, J.; Makarov, D.


Strain Anisotropy and Magnetic Domains in Embedded Nanomagnets

Nord, M.; Semisalova, A.; Kákay, A.; Hlawacek, G.; Maclaren, I.; Liersch, V.; Volkov, O.; Makarov, D.; Paterson, G. W.; Potzger, K.; Lindner, J.; Faßbender, J.; Mcgrouther, D.; Bali, R.

Defect-Driven Magnetization Configuration of Isolated Linear Assemblies of Iron Oxide Nanoparticles

Rastei, M. V.; Pierron-Bohnes, V.; Toulemon, D.; Bouillet, C.; Kákay, A.; Hertel, R.; Tetsi, E.; Begin-Colin, S.; Pichon, B. P.


Magnetization Dynamics of an Individual Single-Crystalline Fe-Filled Carbon Nanotube

Lenz, K.; Narkowicz, R.; Wagner, K.; Reiche, C. F.; Körner, J.; Schneider, T.; Kákay, A.; Schultheiss, H.; Suter, D.; Büchner, B.; Fassbender, J.; Mühl, T.; Lindner, J.

Zero-field dynamics stabilized by in-plane shape anisotropy in MgO-based spin-torque oscillators

Kowalska, E.; Kákay, A.; Fowley, C.; Sluka, V.; Lindner, J.; Fassbender, J.; Deac, A. M.

Related publications


Excitation of whispering gallery magnons in a magnetic vortex

Schultheiss, K.; Verba, R.; Wehrmann, F.; Wagner, K.; Körber, L.; Hula, T.; Hache, T.; Kákay, A.; Awad, A. A.; Tiberkevich, V.; Slavin, A. N.; Fassbender, J.; Schultheiss, H.

  • Open Access Logo Physical Review Letters 122(2019), 097202
  • Invited lecture (Conferences)
    International Conference on Magnetism, 19.07.2018, San Francisco, USA
  • Invited lecture (Conferences)
    APS March Meeting, 04.03.2019, Boston, USA
  • Poster
    Wilhelm und Else Heraeus-Seminar “Spin Based Information Processing”, 08.01.2019, Bad Honnef, Deutschland
  • Lecture (Conference)
    Joint European Magnetic Symposia (JEMS), 04.09.2018, Mainz, Deutschland
  • Poster
    Magnonics 2019, 28.07.2019, Carovigno, Italien
  • Invited lecture (Conferences)
    Magnetics and Optics Research International Symposium, 24.06.2019, Prague, Czech Republic
  • Invited lecture (Conferences)
    Conference on Magnetism and Magnetic Materials (MMM), 06.11.2019, Las Vegas, USA


Experimental and Theoretical Study of Curvature Effects in Parabolic Nanostripes

Volkov, O. M.; Kronast, F.; Mönch, I.; Mawass, M.-A.; Kákay, A.; Fassbender, J.; Makarov, D.

Tunnel magnetoresistance angular and bias dependence enabling tuneable wireless communication

Kowalska, E.; Fukushima, A.; Sluka, V.; Fowley, C.; Kákay, A.; Aleksandrov, Y.; Lindner, J.; Fassbender, J.; Yuasa, S.; Deac, A. M.

Related publications

Emission and Propagation of Multi-Dimensional Spin Waves in Anisotropic Spin Textures

Sluka, V.; Schneider, T.; Gallardo, R. A.; Kakay, A.; Weigand, M.; Warnatz, T.; Mattheis, R.; Roldan-Molina, A.; Landeros, P.; Tiberkevich, V.; Slavin, A.; Schütz, G.; Erbe, A.; Deac, A. M.; Lindner, J.; Faßbender, J.; Raabe, J.; Wintz, S.



Frequency linewidth and decay length of spin waves in curved magnetic membranes

Otalora, J. A.; Kákay, A.; Lindner, J.; Schultheiss, H.; Thomas, A.; Fassbender, J.; Nielsch, K.


Origin and Manipulation of Stable Vortex Ground States in Permalloy Nanotubes

Zimmermann, M.; Gerhard-Meier, T. N.; Dirnberger, F.; Kákay, A.; Decker, M.; Wintz, S.; Finizio, S.; Josten, E.; Raabe, J.; Kronseder, M.; Bougeard, D.; Lindner, J.; Back, C. H.


Multiplet of skyrmion states on a curvilinear defect: Reconfigurable skyrmion lattices

Kravchuk, V. P.; Sheka, D. D.; Kákay, A.; Volkov, O. M.; Rößler, U. K.; van den Brink, J.; Makarov, D.; Gaididei, Y.



Dr. Attila Kakay

Micromagnetic Modeling group leader
Micromagnetic Simulations
Phone: +49 351 260 3410