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Contact
Porträt Dr. Kakay, Attila; FWIN-C
Dr. Attila Kakay

Head
Micro­magnetic Modeling group leader
a.kakayAthzdr.de
Phone: +49 351 260 3410

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.

To study the effect of curvature on the magnetization dynamics often requires the knowledge about the spin-wave eigenmode spectrum. This is usually obtained by micromagnetic simulations solving the equation of motion of magnetization. Despite their flexibility, the classical time-domain micromagnetic simulations can be time-consuming, rely on high-performance GPUs, and need extensive post-processing. Thus, they are not suited to study magnons in complex systems.

During the last year we developed a finite-element method to rapidly obtain the spin-wave spectra in waveguides with arbitrarily-shaped cross-sections without any post-processing. This reduced the computational time from several days to minutes. Part of this endeavor was developing a novel finite-element/boundary-element method to compute long-range fields generated by propagating magnons [L. Körber, et al., AIP Adv. 11, 095006 (2021)]. Due to its flexibility and usefulness for the study of spin waves, the method was made available to the scientific community in the open-source package TetraX. 

 

TetraX is a package for finite-element-method (FEM) micromagnetic modeling with the aim to provide user friendly and versatile micromagnetic workflows. Apart from energy minimizers and an LLG solver, it aims to provide implementations of several FEM dynamic-matrix approaches to numerically calculate the normal modes and associated frequencies for magnetic specimen of different geometries such as confined samples, infinitely long waveguides, or infinitely extended multilayers. Apart from ferromagnets, the package also supports antiferromagnets as an experimental feature.

Research Topics

  • Spin textures in curved geometries
  • Spin-wave propagation in curved nano-membranes
  • Development of micromagnetic codes and numerical methods

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 

Acknowledgments

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

Recent publications

Full list availabe here.

2026

Self-induced Floquet magnons in magnetic vortices

Heins, C.; Körber, L.; Kim, J.-V.; Devolder, T.; Mentink, J. H.; Kakay, A.; Faßbender, J.; Schultheiß, K.; Schultheiß, H.

Involved research facilities

Related publications

  • Open Access Logo Science 391(2026)6781, 190-194
  • Open Access Logo Invited lecture (Conferences)
    820. WE-Heraeus-Seminar: Hybrid Angular Momentum Transport and Dynamics, 29.10.2024, Bad Honnef, Deutschland
  • Open Access Logo Invited lecture (Conferences)
    Workshop on Magnetic Neuromorphic Computing 2024, 17.06.2024, Trondheim, Norwegen
  • Open Access Logo Lecture (Conference)
    25th International Colloquium on Magnetic Films and Surfaces (ICMFS 2024), 07.-12.07.2024, Perugia, Italien
  • Open Access Logo Invited lecture (Conferences)
    Magnetics and Optics Research International Symposium (MORIS 2024), 27.-31.05.2024, York, Vereinigtes Königreich
  • Open Access Logo Invited lecture (Conferences)
    DPG-Frühjahrstagung 2024, 17.-22.03.2024, Berlin, Deutschland

Downloads

Permalink: https://www.hzdr.de/publications/Publ-39542

2025

Impact of layer count and thickness on spin wave modes in multilayer synthetic antiferromagnets

Jiménez-Bustamante, J.; Vidal-Silva, N.; Kakay, A.; Wintz, S.; Gallardo, R. A.

Permalink: https://www.hzdr.de/publications/Publ-42492

Toroidal moments in confined nanomagnets and their impact on magnonics

Brevis, F.; Körber, L.; Mimica-Figari, B.; Gallardo, R.; Kakay, A.; Landeros, P.

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  • Secondary publication expected from 25.08.2026

Permalink: https://www.hzdr.de/publications/Publ-42490

Nonreciprocal spin-wave dispersion in magnetic bilayers

Heins, C.; Iurchuk, V.; Gladii, O.; Körber, L.; Kakay, A.; Faßbender, J.; Schultheiß, K.; Schultheiß, H.

Involved research facilities

Related publications

Permalink: https://www.hzdr.de/publications/Publ-40197

2024

Curvature-induced parity loss and hybridization of magnons: Exploring the connection of flat and tubular magnetic shells

Brevis, F.; Landeros, P.; Lindner, J.; Kakay, A.; Körber, L.

Related publications

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Permalink: https://www.hzdr.de/publications/Publ-39818

Collective out-of-plane magnetization reversal in tilted stripe domain systems via a single point of irreversibility

Heinig, P.; Salikhov, R.; Samad, F.; Fallarino, L.; Patel, G. I.; Kakay, A.; Kiselev, N. S.; Hellwig, O.

Involved research facilities

Related publications

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  • Secondary publication expected

Permalink: https://www.hzdr.de/publications/Publ-39312

Excitation of the Gyrotropic Mode in a Magnetic Vortex by Time-Varying Strain

Iurchuk, V.; Lindner, J.; Faßbender, J.; Kakay, A.

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Permalink: https://www.hzdr.de/publications/Publ-38561

Coherent Magnons with Giant Nonreciprocity at Nanoscale Wavelengths

Gallardo, R. A.; Weigand, M.; Schultheiß, K.; Kakay, A.; Mattheis, R.; Raabe, J.; Schütz, G.; Deac, A. M.; Lindner, J.; Wintz, S.

Involved research facilities

Related publications

Permalink: https://www.hzdr.de/publications/Publ-38354

Three-dimensional magnetic nanotextures with high-order vorticity in soft magnetic wireframes

Volkov, O.; Pylypovskyi, O.; Porrati, F.; Kronast, F.; Fernandez Roldan, J. A.; Kakay, A.; Kuprava, A.; Barth, S.; Rybakov, F. N.; Eriksson, O.; Lamb-Camarena, S.; Makushko, P.; Mawass, M.-A.; Shakeel, S.; Dobrovolskiy, O. V.; Huth, M.; Makarov, D.

Involved research facilities

  • Data Center

Permalink: https://www.hzdr.de/publications/Publ-37958

2023

Piezostrain as a Local Handle to Control Gyrotropic Dynamics of Magnetic Vortices

Iurchuk, V.; Sorokin, S.; Lindner, J.; Faßbender, J.; Kakay, A.

Related publications

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Permalink: https://www.hzdr.de/publications/Publ-37975

Nontrivial Aharonov-Bohm effect and alternating dispersion of magnons in cone-state ferromagnetic rings

Uzunova, V.; Körber, L.; Kavvadia, A.; Quasebarth, G.; Schultheiß, H.; Kakay, A.; Ivanov, B.

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Permalink: https://www.hzdr.de/publications/Publ-37849

Control of Four-Magnon Scattering by Pure Spin Current in a Magnonic Waveguide

Hache, T.; Körber, L.; Hula, T.; Lenz, K.; Kakay, A.; Hellwig, O.; Lindner, J.; Faßbender, J.; Schultheiß, H.

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Permalink: https://www.hzdr.de/publications/Publ-37519

Direct magnetic manipulation of a permalloy nanostructure by a focused cobalt ion beam

Pablo-Navarro, J.; Klingner, N.; Hlawacek, G.; Kakay, A.; Bischoff, L.; Narkovic, R.; Mazarov, P.; Hübner, R.; Meyer, F.; Pilz, W.; Lindner, J.; Lenz, K.

Involved research facilities

Related publications

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  • Secondary publication expected

Permalink: https://www.hzdr.de/publications/Publ-36822

Chirality coupling in topological magnetic textures with multiple magnetochiral parameters

Volkov, O.; Wolf, D.; Pylypovskyi, O.; Kakay, A.; Sheka, D. D.; Büchner, B.; Faßbender, J.; Lubk, A.; Makarov, D.

Permalink: https://www.hzdr.de/publications/Publ-36672

Modification of three-magnon splitting in a flexed magnetic vortex

Körber, L.; Heins, C.; Soldatov, I.; Schäfer, R.; Kakay, A.; Schultheiß, H.; Schultheiß, K.

Related publications

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Permalink: https://www.hzdr.de/publications/Publ-35559

Coupling of terahertz light with nanometre-wavelength magnon modes via spin–orbit torque

Salikhov, R.; Ilyakov, I.; Körber, L.; Kakay, A.; Gallardo, R. A.; Ponomaryov, O.; Deinert, J.-C.; de Oliveira, T.; Lenz, K.; Faßbender, J.; Bonetti, S.; Hellwig, O.; Lindner, J.; Kovalev, S.

Involved research facilities

Related publications

Permalink: https://www.hzdr.de/publications/Publ-35382

Tailoring crosstalk between localized 1D spin-wave nanochannels using focused ion beams

Iurchuk, V.; Pablo-Navarro, J.; Hula, T.; Narkovic, R.; Hlawacek, G.; Körber, L.; Kakay, A.; Schultheiß, H.; Faßbender, J.; Lenz, K.; Lindner, J.

Involved research facilities

Related publications

Permalink: https://www.hzdr.de/publications/Publ-35208

2022

Finite-element dynamic-matrix approach for propagating spin waves: Extension to mono- and multilayers of arbitrary spacing and thickness

Körber, L.; Hempel, A.; Otto, A.; Gallardo, R. A.; Henry, Y.; Lindner, J.; Kakay, A.

Related publications

Permalink: https://www.hzdr.de/publications/Publ-35295

Curvilinear spin-wave dynamics beyond the thin-shell approximation: Magnetic nanotubes as a case study

Körber, L.; Verba, R.; Otálora, J. A.; Kravchuk, V.; Lindner, J.; Faßbender, J.; Kakay, A.

Related publications

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Permalink: https://www.hzdr.de/publications/Publ-34720

Mode splitting of spin waves in magnetic nanotubes with discrete symmetries

Körber, L.; Kézsmárki, I.; Kakay, A.

Related publications

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Permalink: https://www.hzdr.de/publications/Publ-34719

Curvature-induced drift and deformation of magnetic skyrmions: Comparison of the ferromagnetic and antiferromagnetic cases

Yershov, K.; Kakay, A.; Kravchuk, V. P.

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Permalink: https://www.hzdr.de/publications/Publ-33408

New dimension in magnetism and superconductivity: 3D and curvilinear nano-architectures

Makarov, D.; Volkov, O.; Kakay, A.; Pylypovskyi, O.; Budinska, B.; Dobrovolskiy, O.

Involved research facilities

Related publications

Permalink: https://www.hzdr.de/publications/Publ-32689

Spin-wave frequency combs

Hula, T.; Schultheiß, K.; Trindade Goncalves, F. J.; Körber, L.; Bejarano, M.; Copus, M.; Flacke, L.; Liensberger, L.; Buzdakov, A.; Kakay, A.; Weiler, M.; Camley, R.; Faßbender, J.; Schultheiß, H.

Related publications

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Permalink: https://www.hzdr.de/publications/Publ-32565

2021

Spin-wave focusing induced by dipole-dipole interaction in synthetic antiferromagnets

Gallardo, R. A.; Alvarado-Seguel, P.; Kákay, A.; Lindner, J.; Landeros, P.

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  • Secondary publication expected

Permalink: https://www.hzdr.de/publications/Publ-33489

Robust formation of nanoscale magnetic skyrmions in easy-plane anisotropy thin film multilayers with low damping

Flacke, L.; Ahrens, V.; Mendisch, S.; Körber, L.; Böttcher, T.; Meidinger, E.; Yaqoob, M.; Müller, M.; Liensberger, L.; Kakay, A.; Becherer, M.; Pirro, P.; Althammer, M.; Geprägs, S.; Huebl, H.; Gross, R.; Weiler, M.

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Permalink: https://www.hzdr.de/publications/Publ-33420

Symmetry and curvature effects on spin waves in vortex-state hexagonal nanotubes

Körber, L.; Zimmermann, M.; Wintz, S.; Finizio, S.; Kronseder, M.; Bougeard, D.; Dirnberger, F.; Weigand, M.; Raabe, J.; Otálora, J. A.; Schultheiß, H.; Josten, E.; Lindner, J.; Kézsmárki, I.; Back, C. H.; Kakay, A.

Related publications

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Permalink: https://www.hzdr.de/publications/Publ-33367

Numerical reverse engineering of general spin-wave dispersions: Bridge between numerics and analytics using a dynamic-matrix approach

Körber, L.; Kakay, A.

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Permalink: https://www.hzdr.de/publications/Publ-33366

Stress-induced modification of gyration dynamics in stacked double-vortex structures studied by micromagnetic simulations

Iurchuk, V.; Körber, L.; Deac, A. M.; Faßbender, J.; Lindner, J.; Kakay, A.

Permalink: https://www.hzdr.de/publications/Publ-33127

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.

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Permalink: https://www.hzdr.de/publications/Publ-32767

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.

Permalink: https://www.hzdr.de/publications/Publ-32616

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

Permalink: https://www.hzdr.de/publications/Publ-32561

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

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Permalink: https://www.hzdr.de/publications/Publ-31644

Numerical ferromagnetic resonance experiments in nanosized elements

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

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Permalink: https://www.hzdr.de/publications/Publ-31456

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.

Involved research facilities

Related publications

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Permalink: https://www.hzdr.de/publications/Publ-28374

2020

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.

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Permalink: https://www.hzdr.de/publications/Publ-32055

Effect of curvature on the eigenstates of magnetic skyrmions

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

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Permalink: https://www.hzdr.de/publications/Publ-31080

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

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Permalink: https://www.hzdr.de/publications/Publ-31058

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.

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Permalink: https://www.hzdr.de/publications/Publ-31026

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.

Involved research facilities

Related publications

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Permalink: https://www.hzdr.de/publications/Publ-30380

Nonlocal chiral symmetry breaking in curvilinear magnetic shells

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

Permalink: https://www.hzdr.de/publications/Publ-30272

2019

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.

Involved research facilities

Related publications

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  • Secondary publication expected

Permalink: https://www.hzdr.de/publications/Publ-30285

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.

Involved research facilities

Related publications

Permalink: https://www.hzdr.de/publications/Publ-29690

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.

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Permalink: https://www.hzdr.de/publications/Publ-29642

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.

Involved research facilities

Related publications

Permalink: https://www.hzdr.de/publications/Publ-29540

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.

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Permalink: https://www.hzdr.de/publications/Publ-28927

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.

Involved research facilities

Related publications

  • Open Access Logo Physical Review Letters 122(2019), 097202
    Cited 73 times in Scopus
  • 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

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Permalink: https://www.hzdr.de/publications/Publ-28116

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.

Involved research facilities

Related publications

Permalink: https://www.hzdr.de/publications/Publ-27940

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

Permalink: https://www.hzdr.de/publications/Publ-27885

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.

Involved research facilities

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Permalink: https://www.hzdr.de/publications/Publ-27662

2018

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.

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Permalink: https://www.hzdr.de/publications/Publ-27753

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.

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Permalink: https://www.hzdr.de/publications/Publ-27435

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.

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Permalink: https://www.hzdr.de/publications/Publ-27139