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(4) 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(5).

2024

Parametric magnon transduction to spin qubits

Bejarano, M.(6); Goncalves, F. J. T.; Hache, T.; Hollenbach, M.; Heins, C.; Hula, T.; Körber, L.(7); Heinze, J.; Berencen, Y.(8); Helm, M.; Faßbender, J.(9); Astakhov, G.(10); Schultheiß, H.(11)

Related publications


Coherent Magnons with Giant Nonreciprocity at Nanoscale Wavelengths

Gallardo, R. A.; Weigand, M.; Schultheiß, K.(14); Kakay, A.(15); Mattheis, R.; Raabe, J.; Schütz, G.; Deac, A. M.; Lindner, J.(16); Wintz, S.

Related publications


2023

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

Iurchuk, V.(19); Sorokin, S.; Lindner, J.; Faßbender, J.(20); Kakay, A.(21)

Related publications

Downloads


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

Uzunova, V.; Körber, L.(25); Kavvadia, A.; Quasebarth, G.; Schultheiß, H.(26); Kakay, A.(27); Ivanov, B.

Downloads


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

Hache, T.; Körber, L.(29); Hula, T.; Lenz, K.(30); Kakay, A.(31); Hellwig, O.(32); Lindner, J.; Faßbender, J.(33); Schultheiß, H.(34)

Related publications

Downloads


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

Pablo-Navarro, J.; Klingner, N.(37); Hlawacek, G.(38); Kakay, A.(39); Bischoff, L.(40); Narkovic, R.; Mazarov, P.; Hübner, R.(41); Meyer, F.; Pilz, W.; Lindner, J.; Lenz, K.(42)

Related publications

Downloads

  • Secondary publication expected from 26.10.2024

Chirality coupling in topological magnetic textures with multiple magnetochiral parameters

Volkov, O.(45); Wolf, D.; Pylypovskyi, O.(46); Kakay, A.(47); Sheka, D. D.; Büchner, B.; Faßbender, J.(48); Lubk, A.; Makarov, D.(49)


Modification of three-magnon splitting in a flexed magnetic vortex

Körber, L.(51); Heins, C.; Soldatov, I.; Schäfer, R.; Kakay, A.(52); Schultheiß, H.(53); Schultheiß, K.(54)

Related publications

Downloads


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

Salikhov, R.(57); Ilyakov, I.(58); Körber, L.(59); Kakay, A.(60); Gallardo, R. A.; Ponomaryov, O.(61); Deinert, J.-C.(62); de Oliveira, T.(63); Lenz, K.(64); Faßbender, J.(65); Bonetti, S.; Hellwig, O.(66); Lindner, J.; Kovalev, S.(67)

Related publications


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

Iurchuk, V.(70); Pablo-Navarro, J.; Hula, T.(71); Narkovic, R.; Hlawacek, G.(72); Körber, L.(73); Kakay, A.(74); Schultheiß, H.(75); Faßbender, J.(76); Lenz, K.(77); Lindner, J.

Related publications


Pattern recognition in reciprocal space with a magnon-scattering reservoir

Körber, L.(83); Heins, C.; Hula, T.(84); Kim, J.-V.; Thlang, S.; Schultheiß, H.(85); Faßbender, J.(86); Schultheiß, K.(87)

Related publications


2022

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

Körber, L.(91); Hempel, A.; Otto, A.; Gallardo, R. A.; Henry, Y.; Lindner, J.; Kakay, A.(92)

Related publications


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

Körber, L.(95); Verba, R.; Otálora, J. A.; Kravchuk, V.; Lindner, J.; Faßbender, J.(96); Kakay, A.(97)

Related publications

Downloads


Mode splitting of spin waves in magnetic nanotubes with discrete symmetries

Körber, L.(100); Kézsmárki, I.; Kakay, A.(101)

Related publications

Downloads


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

Yershov, K.(104); Kakay, A.(105); Kravchuk, V. P.(106)

Downloads


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

Makarov, D.(108); Volkov, O.(109); Kakay, A.(110); Pylypovskyi, O.(111); Budinska, B.; Dobrovolskiy, O.

Related publications


Spin-wave frequency combs

Hula, T.(114); Schultheiß, K.(115); Trindade Goncalves, F. J.(116); Körber, L.(117); Bejarano, M.(118); Copus, M.; Flacke, L.(119); Liensberger, L.; Buzdakov, A.; Kakay, A.(120); Weiler, M.(121); Camley, R.; Faßbender, J.(122); Schultheiß, H.

Related publications

Downloads


2021

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

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

Downloads

  • Secondary publication expected

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

Flacke, L.; Ahrens, V.; Mendisch, S.; Körber, L.(127); Böttcher, T.; Meidinger, E.; Yaqoob, M.; Müller, M.; Liensberger, L.; Kakay, A.(128); Becherer, M.; Pirro, P.; Althammer, M.; Geprägs, S.; Huebl, H.; Gross, R.; Weiler, M.

Downloads


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

Körber, L.(130); 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.(131)

Related publications

Downloads


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

Körber, L.(134); Kakay, A.(135)

Downloads


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

Iurchuk, V.(137); Körber, L.(138); Deac, A. M.; Faßbender, J.(139); Lindner, J.; Kakay, A.(140)


Nonreciprocity of spin waves in magnetic nanotubes with helical equilibrium magnetization

Salazar-Cardona, M. M.; Körber, L.(142); Schultheiß, H.; Lenz, K.(143); Thomas, A.; Nielsch, K.; Kakay, A.(144); Otálora, J. A.

Downloads


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

Gospodarič, P.; Młyńczak, E.; Soldatov, I.; Kakay, A.(146); Bürgler, D. E.; Plucinski, L.; Schäfer, R.; Faßbender, J.(147); Schneider, C. M.


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

Körber, L.(149); Quasebarth, G.(150); Otto, A.; Kakay, A.(151)

Related publications


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

Verba, R.(154); Körber, L.(155); Schultheiß, K.(156); Schultheiß, H.(157); Tiberkevich, V.(158); Slavin, A.

Related publications

Downloads


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

Saha, S.; Zhou, J.; Hofhuis, K.; Kakay, A.(161); Scagnoli, V.; Heyderman, L. J.; Gliga, S.

Related publications

Downloads


Time refraction of spin waves

Schultheiß, K.(165); Sato, N.; Matthies, P.; Körber, L.(166); Wagner, K.; Hula, T.(167); Gladii, O.; Pearson, J. E.; Hoffmann, A.; Helm, M.; Faßbender, J.(168); Schultheiß, H.(169)

Downloads


Numerical ferromagnetic resonance experiments in nanosized elements

Wagner, K.; Körber, L.(171); Stienen, S.; Lindner, J.; Farle, M.; Kakay, A.(172)

Related publications

Downloads


Self-stabilizing exchange-mediated spin transport

Schneider, T.; Hill, D.; Kakay, A.(175); Lenz, K.(176); Lindner, J.; Faßbender, J.(177); Upadhyaya, P.; Liu, Y.; Wang, K.; Tserkovnyak, Y.; Krivorotov, I. N.; Barsukov, I.

Related publications

Downloads


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.(180); Fowley, C.; Lindner, J.; Fassbender, J.; Deac, A. M.

Downloads


Propagation of spin waves through a Néel domain wall

Wojewoda, O.(182); Hula, T.(183); Flajšman, L.(184); Vaňatka, M.; Gloss, J.(185); Holobrádek, J.; Staňo, M.(186); Stienen, S.; Körber, L.(187); Schultheiß, K.(188); Schmid, M.(189); Schultheiß, H.(190); Urbánek, M.(191)


Effect of curvature on the eigenstates of magnetic skyrmions

Korniienko, A.; Kakay, A.(193); Sheka, D. D.(194); Kravchuk, V. P.(195)

Downloads


Nonlocal stimulation of three-magnon splitting in a magnetic vortex

Körber, L.(197); Schultheiß, K.(198); Hula, T.(199); Verba, R.(200); Faßbender, J.(201); Kakay, A.(202); Schultheiß, H.(203)

Related publications

Downloads


Nonlinear losses in magnon transport due to four-magnon scattering

Hula, T.(206); Schultheiß, K.(207); Buzdakov, A.; Körber, L.(208); Bejarano, M.(209); Flacke, L.; Liensberger, L.; Weiler, M.; Shaw, J. M.; Nembach, H. T.; Faßbender, J.(210); Schultheiß, H.(211)

Related publications

Downloads


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

Llandro, J.; Love, D. M.; Kovács, A.; Caron, J.; Vyas, K. N.; Kakay, A.(214); Salikhov, R.; Lenz, K.(215); Faßbender, J.(216); Scherer, M. R. J.; Cimorra, C.; Steiner, U.; Barnes, C. H. W.; Dunin-Borkowski, R. E.; Fukami, S.; Ohno, H.

Downloads


Tunable magnetic vortex dynamics in ion-implanted permalloy disks

Ramasubramanian, L.; Kákay, A.; Fowley, C.(218); Yildirim, O.; Matthes, P.; Sorokin, S.(219); Titova, A.; Hilliard, D.; Böttger, R.; Hübner, R.(220); Gemming, S.; Schulz, S. E.; Kronast, F.; Makarov, D.(221); Faßbender, J.(222); Deac, A. M.

Related publications

Downloads


Nonlocal chiral symmetry breaking in curvilinear magnetic shells

Sheka, D. D.(225); Pylypovskyi, O.(226); Landeros, P.; Gaididei, Y.; Kakay, A.; Makarov, D.(227)


Domain wall-based spin-Hall nano-oscillators

Sato, N.; Schultheiß, K.(229); Körber, L.(230); Puwenberg, N.; Mühl, T.; Awad, A. A.; Arekapudi, S. S. P. K.; Hellwig, O.(231); Faßbender, J.(232); Schultheiß, H.(233)

Related publications

Downloads


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.(236); Makarov, D.(237)

Related publications

Downloads

  • Secondary publication expected

Strain Anisotropy and Magnetic Domains in Embedded Nanomagnets

Nord, M.; Semisalova, A.; Kákay, A.; Hlawacek, G.(240); Maclaren, I.; Liersch, V.; Volkov, O.; Makarov, D.; Paterson, G. W.; Potzger, K.; Lindner, J.; Faßbender, J.(241); Mcgrouther, D.; Bali, R.

Related publications


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

Rastei, M. V.; Pierron-Bohnes, V.; Toulemon, D.; Bouillet, C.; Kákay, A.(244); Hertel, R.; Tetsi, E.; Begin-Colin, S.; Pichon, B. P.

Downloads


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

Lenz, K.(246); 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.

Related publications


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

Kowalska, E.(249); Kákay, A.(250); Fowley, C.; Sluka, V.; Lindner, J.; Fassbender, J.(251); Deac, A. M.

Related publications

Downloads


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.

Related publications

  • Open Access Logo Physical Review Letters 122(2019), 097202(255)
    Cited 55 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

Downloads


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.

Related publications


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.(260); Weigand, M.; Warnatz, T.; Mattheis, R.; Roldan-Molina, A.; Landeros, P.; Tiberkevich, V.; Slavin, A.; Schütz, G.; Erbe, A.(261); Deac, A. M.; Lindner, J.; Faßbender, J.(262); Raabe, J.; Wintz, S.

Related publications

Downloads


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.

Downloads


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.

Downloads


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.

Downloads


URL of this article
https://www.hzdr.de/db/Cms?pOid=55944


Contact

Dr. Attila Kakay

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


Links of the content

(1) https://www.hzdr.de/db/Cms?pOid=60954
(2) https://www.hzdr.de/db/Cms?pOid=62797
(3) https://www.hzdr.de/db/Cms?pOid=63416
(4) https://tetrax.readthedocs.io
(5) https://www.hzdr.de/db/Cms?pOid=60954
(6) https://orcid.org/0000-0001-5970-0384
(7) https://orcid.org/0000-0001-8332-9669
(8) https://orcid.org/0000-0003-3529-0207
(9) https://orcid.org/0000-0003-3893-9630
(10) https://orcid.org/0000-0003-1807-3534
(11) https://orcid.org/0000-0002-6727-5098
(12) https://doi.org/10.17815/jlsrf-3-159
(13) https://doi.org/10.1126/sciadv.adi2042
(14) https://orcid.org/0000-0002-3382-5442
(15) https://orcid.org/0000-0002-3195-219X
(16) https://orcid.org/0000-0002-4955-515X
(17) https://doi.org/10.17815/jlsrf-3-159
(18) https://doi.org/10.1021/acsnano.3c08390
(19) https://orcid.org/0000-0002-8553-7004
(20) https://orcid.org/0000-0003-3893-9630
(21) https://orcid.org/0000-0002-3195-219X
(22) https://www.hzdr.de/publications/Publ-37978
(23) https://doi.org/10.14278/rodare.2584
(24) https://doi.org/10.1103/PhysRevApplied.20.024080
(25) https://orcid.org/0000-0001-8332-9669
(26) https://orcid.org/0000-0002-6727-5098
(27) https://orcid.org/0000-0002-3195-219X
(28) https://doi.org/10.1103/PhysRevB.108.174445
(29) https://orcid.org/0000-0001-8332-9669
(30) https://orcid.org/0000-0001-5528-5080
(31) https://orcid.org/0000-0002-3195-219X
(32) https://orcid.org/0000-0002-1351-5623
(33) https://orcid.org/0000-0003-3893-9630
(34) https://orcid.org/0000-0002-6727-5098
(35) https://www.hzdr.de/publications/Publ-37640
(36) https://doi.org/10.1103/PhysRevApplied.20.014062
(37) https://orcid.org/0000-0001-9539-5874
(38) https://orcid.org/0000-0001-7192-716X
(39) https://orcid.org/0000-0002-3195-219X
(40) https://orcid.org/0000-0003-3968-7498
(41) https://orcid.org/0000-0002-5200-6928
(42) https://orcid.org/0000-0001-5528-5080
(43) https://doi.org/10.17815/jlsrf-3-159
(44) https://doi.org/10.1103/PhysRevApplied.20.044068
(45) https://orcid.org/0000-0001-7246-4099
(46) https://orcid.org/0000-0002-5947-9760
(47) https://orcid.org/0000-0002-3195-219X
(48) https://orcid.org/0000-0003-3893-9630
(49) https://orcid.org/0000-0002-7177-4308
(50) https://doi.org/10.1038/s41467-023-37081-z
(51) https://orcid.org/0000-0001-8332-9669
(52) https://orcid.org/0000-0002-3195-219X
(53) https://orcid.org/0000-0002-6727-5098
(54) https://orcid.org/0000-0002-3382-5442
(55) https://www.hzdr.de/publications/Publ-36141
(56) https://doi.org/10.1063/5.0135573
(57) https://orcid.org/0000-0001-8461-0743
(58) https://orcid.org/0000-0002-5928-7996
(59) https://orcid.org/0000-0001-8332-9669
(60) https://orcid.org/0000-0002-3195-219X
(61) https://orcid.org/0000-0003-1200-2866
(62) https://orcid.org/0000-0001-6211-0158
(63) https://orcid.org/0000-0002-4886-0654
(64) https://orcid.org/0000-0001-5528-5080
(65) https://orcid.org/0000-0003-3893-9630
(66) https://orcid.org/0000-0002-1351-5623
(67) https://orcid.org/0000-0002-2290-1016
(68) https://doi.org/10.17815/jlsrf-2-58
(69) https://doi.org/10.1038/s41567-022-01908-1
(70) https://orcid.org/0000-0002-8553-7004
(71) https://orcid.org/0000-0002-1811-8862
(72) https://orcid.org/0000-0001-7192-716X
(73) https://orcid.org/0000-0001-8332-9669
(74) https://orcid.org/0000-0002-3195-219X
(75) https://orcid.org/0000-0002-6727-5098
(76) https://orcid.org/0000-0003-3893-9630
(77) https://orcid.org/0000-0001-5528-5080
(78) https://doi.org/10.17815/jlsrf-3-159
(79) https://www.hzdr.de/publications/Publ-36217
(80) https://doi.org/10.14278/rodare.2070
(81) https://arxiv.org/abs/2209.13180
(82) https://doi.org/10.1038/s41598-022-27249-w
(83) https://orcid.org/0000-0001-8332-9669
(84) https://orcid.org/0000-0002-1811-8862
(85) https://orcid.org/0000-0002-6727-5098
(86) https://orcid.org/0000-0003-3893-9630
(87) https://orcid.org/0000-0002-3382-5442
(88) https://www.hzdr.de/publications/Publ-37152
(89) https://doi.org/10.14278/rodare.2345
(90) https://doi.org/10.1038/s41467-023-39452-y
(91) https://orcid.org/0000-0001-8332-9669
(92) https://orcid.org/0000-0002-3195-219X
(93) https://www.hzdr.de/publications/Publ-35296
(94) https://doi.org/10.1063/5.0107457
(95) https://orcid.org/0000-0001-8332-9669
(96) https://orcid.org/0000-0003-3893-9630
(97) https://orcid.org/0000-0002-3195-219X
(98) https://www.hzdr.de/publications/Publ-34826
(99) https://doi.org/10.1103/PhysRevB.106.014405
(100) https://orcid.org/0000-0001-8332-9669
(101) https://orcid.org/0000-0002-3195-219X
(102) https://www.hzdr.de/publications/Publ-34728
(103) https://doi.org/10.1103/PhysRevB.105.184435
(104) https://orcid.org/0000-0003-2731-2808
(105) https://orcid.org/0000-0002-3195-219X
(106) https://orcid.org/0000-0003-4567-9929
(107) https://doi.org/10.1103/PhysRevB.105.054425
(108) https://orcid.org/0000-0002-7177-4308
(109) https://orcid.org/0000-0001-7246-4099
(110) https://orcid.org/0000-0002-3195-219X
(111) https://orcid.org/0000-0002-5947-9760
(112) https://doi.org/10.17815/jlsrf-3-159
(113) https://doi.org/10.1002/adma.202101758
(114) https://orcid.org/0000-0002-1811-8862
(115) https://orcid.org/0000-0002-3382-5442
(116) https://orcid.org/0000-0002-1671-437X
(117) https://orcid.org/0000-0001-8332-9669
(118) https://orcid.org/0000-0001-5970-0384
(119) https://orcid.org/0000-0002-6536-8653
(120) https://orcid.org/0000-0002-3195-219X
(121) https://orcid.org/0000-0003-0537-9251
(122) https://orcid.org/0000-0003-3893-9630
(123) https://www.hzdr.de/publications/Publ-34210
(124) https://arxiv.org/abs/2104.11491v1
(125) https://doi.org/10.1063/5.0090033
(126) https://doi.org/10.1103/PhysRevB.104.174417
(127) https://orcid.org/0000-0001-8332-9669
(128) https://orcid.org/0000-0002-3195-219X
(129) https://doi.org/10.1103/PhysRevB.104.L100417
(130) https://orcid.org/0000-0001-8332-9669
(131) https://orcid.org/0000-0002-3195-219X
(132) https://www.hzdr.de/publications/Publ-33475
(133) https://doi.org/10.1103/PhysRevB.104.184429
(134) https://orcid.org/0000-0001-8332-9669
(135) https://orcid.org/0000-0002-3195-219X
(136) https://doi.org/10.1103/PhysRevB.104.174414
(137) https://orcid.org/0000-0002-8553-7004
(138) https://orcid.org/0000-0001-8332-9669
(139) https://orcid.org/0000-0003-3893-9630
(140) https://orcid.org/0000-0002-3195-219X
(141) https://doi.org/10.1088/1361-6463/ac2333
(142) https://orcid.org/0000-0001-8332-9669
(143) https://orcid.org/0000-0001-5528-5080
(144) https://orcid.org/0000-0002-3195-219X
(145) https://doi.org/10.1063/5.0048692
(146) https://orcid.org/0000-0002-3195-219X
(147) https://orcid.org/0000-0003-3893-9630
(148) https://doi.org/10.1103/PhysRevResearch.3.023089
(149) https://orcid.org/0000-0001-8332-9669
(150) https://orcid.org/0000-0001-8097-0880
(151) https://orcid.org/0000-0002-3195-219X
(152) https://www.hzdr.de/publications/Publ-32562
(153) https://doi.org/10.1063/5.0054169
(154) https://orcid.org/0000-0001-8811-6232
(155) https://orcid.org/0000-0001-8332-9669
(156) https://orcid.org/0000-0002-3382-5442
(157) https://orcid.org/0000-0002-6727-5098
(158) https://orcid.org/0000-0002-8374-2565
(159) https://www.hzdr.de/publications/Publ-32057
(160) https://doi.org/10.1103/PhysRevB.103.014413
(161) https://orcid.org/0000-0002-3195-219X
(162) https://www.hzdr.de/publications/Publ-32277
(163) https://doi.org/10.1021/acs.nanolett.0c04294
(164) https://arxiv.org/abs/2011.04505
(165) https://orcid.org/0000-0002-3382-5442
(166) https://orcid.org/0000-0001-8332-9669
(167) https://orcid.org/0000-0002-1811-8862
(168) https://orcid.org/0000-0003-3893-9630
(169) https://orcid.org/0000-0002-6727-5098
(170) https://doi.org/10.1103/PhysRevLett.126.137201
(171) https://orcid.org/0000-0001-8332-9669
(172) https://orcid.org/0000-0002-3195-219X
(173) https://www.hzdr.de/publications/Publ-31884
(174) https://doi.org/10.1109/LMAG.2021.3055447
(175) https://orcid.org/0000-0002-3195-219X
(176) https://orcid.org/0000-0001-5528-5080
(177) https://orcid.org/0000-0003-3893-9630
(178) https://doi.org/10.17815/jlsrf-3-159
(179) https://doi.org/10.1103/PhysRevB.103.144412
(180) https://orcid.org/0000-0002-3195-219X
(181) https://doi.org/10.1103/PhysRevB.101.024430
(182) https://orcid.org/0000-0002-4276-520X
(183) https://orcid.org/0000-0002-1811-8862
(184) https://orcid.org/0000-0003-4411-0589
(185) https://orcid.org/0000-0002-0572-6287
(186) https://orcid.org/0000-0002-7440-7191
(187) https://orcid.org/0000-0001-8332-9669
(188) https://orcid.org/0000-0002-3382-5442
(189) https://orcid.org/0000-0003-3373-9357
(190) https://orcid.org/0000-0002-6727-5098
(191) https://orcid.org/0000-0003-0072-2073
(192) https://doi.org/10.1063/5.0013692
(193) https://orcid.org/0000-0002-3195-219X
(194) https://orcid.org/0000-0001-7311-0639
(195) https://orcid.org/0000-0003-4567-9929
(196) https://doi.org/10.1103/PhysRevB.102.014432
(197) https://orcid.org/0000-0001-8332-9669
(198) https://orcid.org/0000-0002-3382-5442
(199) https://orcid.org/0000-0002-1811-8862
(200) https://orcid.org/0000-0001-8811-6232
(201) https://orcid.org/0000-0003-3893-9630
(202) https://orcid.org/0000-0002-3195-219X
(203) https://orcid.org/0000-0002-6727-5098
(204) https://www.hzdr.de/publications/Publ-31137
(205) https://doi.org/10.1103/PhysRevLett.125.207203
(206) https://orcid.org/0000-0002-1811-8862
(207) https://orcid.org/0000-0002-3382-5442
(208) https://orcid.org/0000-0001-8332-9669
(209) https://orcid.org/0000-0001-5970-0384
(210) https://orcid.org/0000-0003-3893-9630
(211) https://orcid.org/0000-0002-6727-5098
(212) https://www.hzdr.de/publications/Publ-31718
(213) https://doi.org/10.1063/5.0015269
(214) https://orcid.org/0000-0002-3195-219X
(215) https://orcid.org/0000-0001-5528-5080
(216) https://orcid.org/0000-0003-3893-9630
(217) https://doi.org/10.1021/acs.nanolett.0c00578
(218) https://orcid.org/0000-0002-3025-4883
(219) https://orcid.org/0000-0002-7557-0345
(220) https://orcid.org/0000-0002-5200-6928
(221) https://orcid.org/0000-0002-7177-4308
(222) https://orcid.org/0000-0003-3893-9630
(223) https://doi.org/10.17815/jlsrf-3-159
(224) https://doi.org/10.1021/acsami.0c08024
(225) https://orcid.org/0000-0001-7311-0639
(226) https://orcid.org/0000-0002-5947-9760
(227) https://orcid.org/0000-0002-7177-4308
(228) https://doi.org/10.1038/s42005-020-0387-2
(229) https://orcid.org/0000-0002-3382-5442
(230) https://orcid.org/0000-0001-8332-9669
(231) https://orcid.org/0000-0002-1351-5623
(232) https://orcid.org/0000-0003-3893-9630
(233) https://orcid.org/0000-0002-6727-5098
(234) https://doi.org/10.17815/jlsrf-3-159
(235) https://doi.org/10.1103/PhysRevLett.123.057204
(236) https://orcid.org/0000-0003-3893-9630
(237) https://orcid.org/0000-0002-7177-4308
(238) https://doi.org/10.17815/jlsrf-3-159
(239) https://doi.org/10.1103/PhysRevLett.123.077201
(240) https://orcid.org/0000-0001-7192-716X
(241) https://orcid.org/0000-0003-3893-9630
(242) https://doi.org/10.17815/jlsrf-3-159
(243) https://doi.org/10.1002/smll.201904738
(244) https://orcid.org/0000-0002-3195-219X
(245) https://doi.org/10.1002/adfm.201903927
(246) https://orcid.org/0000-0001-5528-5080
(247) https://doi.org/10.17815/jlsrf-3-159
(248) https://doi.org/10.1002/smll.201904315
(249) https://orcid.org/0000-0002-1269-0577
(250) https://orcid.org/0000-0002-3195-219X
(251) https://orcid.org/0000-0003-3893-9630
(252) https://www.hzdr.de/publications/Publ-27885
(253) https://doi.org/10.1063/1.5081036
(254) https://doi.org/10.17815/jlsrf-3-159
(255) https://doi.org/10.1103/PhysRevLett.122.097202
(256) https://doi.org/10.17815/jlsrf-3-159
(257) https://doi.org/10.1002/pssr.201800309
(258) https://www.hzdr.de/publications/Publ-28927
(259) https://doi.org/10.1038/s41598-019-45984-5
(260) https://orcid.org/0000-0002-3195-219X
(261) https://orcid.org/0000-0001-6368-8728
(262) https://orcid.org/0000-0003-3893-9630
(263) https://doi.org/10.17815/jlsrf-3-159
(264) https://doi.org/10.1038/s41565-019-0383-4
(265) https://doi.org/10.1103/PhysRevB.98.014403
(266) https://doi.org/10.1021/acs.nanolett.7b05222
(267) https://doi.org/10.1103/PhysRevLett.120.067201