3D Spinwellen-transport auf gekrümmten Oberflächen
Zusammenfassung der Projektergebnisse
This project aims to theoretically explore the geometrical effects on spin waves, the fundamental low- energy excitations of ferromagnets, propagating in curved magnetic shells. Supported by an efficient numerical technique developed for this purpose, several aspects of curvilinear spinwave dynamics involving magnetic pseudo-charges, the topology of curved magnets, symmetrybreaking effects, and dynamics of spin textures have been studied. In recent years, geometrical and curvature effects on mesoscale ferromagnets have attracted the attention of fundamental and applied research. Exciting curvature-induced phenomena include chiral symmetry breaking, the stabilization of magnetic skyrmions on Gaussian bumps, or topologically induced domain walls in Möbius ribbons. Spin waves in vortex-state magnetic nanotubes exhibit a curvature-induced dispersion asymmetry due to geometric contributions to the magnetic volume pseudo-charges. However, previous theoretical studies were limited to simple and thin curved shells due to the complexity of analytical models and the time-consuming nature of existing numerical techniques. For a systematic study of spin-wave propagation in curved shells, we have been developing a numerical method to calculate spin-wave spectra in waveguides with arbitrarily shaped cross-sections efficiently. For this, a finite-element/boundary-element method to calculate dynamic dipolar fields, the Fredkin-Koehler method, was extended for propagating waves. The technique is implemented in the micromagnetic modeling package TetraX developed and made available as open source to the scientific community. Equipped with this method, the formulated objectives of the project have been studied. Thus we show that the geometric contributions to the magnetic charges leads to nonlocal chiral symmetry breaking. The theoretical study of curvilinear magnetism was extended to thick shells, uncovering a curvature-induced nonreciprocity in the spatial mode profiles of the spin waves. Consequently, nonreciprocal dipole-dipole hybridization between different modes leads to asymmetric level gaps enabling spin-wave diode behavior. Besides unidirectional transport, curvature modifies the weakly nonlinear spin-wave interactions. Furthermore, we show that a topological Berry phase of spin waves in helical-state nanotubes is also connected to a local curvature-induced chiral interaction, not only dipolar but also exchange origin. To understand the effects of achiral symmetry breaking, the second objective focuses on the deformation of symmetric shells, here, cylindrical nanotubes, to polygonal and elliptical (was not part of the original proposal) shapes. Lowering rotational symmetry leads to splitting spin-wave dispersions into singlet and doublets branches, which is explained using a simple group theory approach and is analogous to the electron band structure in crystals. Apart from mode splitting, this symmetry breaking allows hybridization between different spin-wave modes and modifies their microwave absorption. While this hybridization appears discretely in polygonal tubes, tuning the eccentricity of elliptical tubes allows controlling the level gaps appearing from hybridization. Finally, introducing the toroidal moment to spin-wave dynamics allows us to predict whether the symmetry breaking is present even in complicated systems with spatially inhomogeneous equilibria or corrugated shells with constant or gradient curvatures. We show that corrugated shells with gradient curvature show asymmetric dispersion as well as shells with inhomogeneous equilibria, as the Néel walls trapped in the highly curved section. Overall, I believe that the results of this proposal contributes to the fundamental understanding of spin-wave dynamics on the mesoscale but also advertises these for possible magnonic applications.
Projektbezogene Publikationen (Auswahl)
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Finite-element dynamic-matrix approach for spin-wave dispersions in magnonic waveguides with arbitrary cross section. AIP Advances, 11(9).
Körber, L.; Quasebarth, G.; Otto, A. & Kákay, A.
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Nonreciprocity of spin waves in magnetic nanotubes with helical equilibrium magnetization. Applied Physics Letters, 118(26).
Salazar-Cardona, M. M.; Körber, L.; Schultheiss, H.; Lenz, K.; Thomas, A.; Nielsch, K.; Kákay, A. & Otálora, J. A.
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Numerical reverse engineering of general spin-wave dispersions: Bridge between numerics and analytics using a dynamic-matrix approach. Physical Review B, 104(17).
Körber, L. & Kákay, A.
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Symmetry and curvature effects on spin waves in vortex-state hexagonal nanotubes. Physical Review B, 104(18).
Körber, Lukas; Zimmermann, Michael; Wintz, Sebastian; Finizio, Simone; Kronseder, Matthias; Bougeard, Dominique; Dirnberger, Florian; Weigand, Markus; Raabe, Jörg; Otálora, Jorge A.; Schultheiss, Helmut; Josten, Elisabeth; Lindner, Jürgen; Kézsmárki, István; Back, Christian H. & Kákay, Attila
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Curvilinear spin-wave dynamics beyond the thin-shell approximation: Magnetic nanotubes as a case study. Physical Review B, 106(1).
Körber, L.; Verba, R.; Otálora, Jorge A.; Kravchuk, V.; Lindner, J.; Fassbender, J. & Kákay, A.
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Finite-element dynamic-matrix approach for propagating spin waves: Extension to mono-and multi-layers of arbitrary spacing and thickness. AIP Advances, 12(11).
Körber, L.; Hempel, A.; Otto, A.; Gallardo, R. A.; Henry, Y.; Lindner, J. & Kákay, A.
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Mode splitting of spin waves in magnetic nanotubes with discrete symmetries. Physical Review B, 105(18).
Körber, Lukas; Kézsmárki, István & Kákay, Attila
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TetraX: Finite-Element Micromagnetic-Modeling Package”, RODARE (2022), software publication
Lukas Körber; Gwendolyn Quasebarth; Alexander Hempel; Friedrich Zahn;reas Otto; Elmar Westphal; Riccardo Hertel & Attila Kákay
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Spin waves in curved magnetic shells. Sachsische Landesbibliothek, Staats-und Universitatsbibliothek Dresden.
Körber, Lukas
