Finite-element dynamic-matrix approach for propagating spin waves: Extension to mono- and multi-layers of arbitrary spacing and thickness
In our recent work [Körber et al., AIP Adv. 11, 095006 (2021)], we presented an efficient numerical method to compute dispersions and mode profiles of spin waves in waveguides with translationally invariant equilibrium magnetization. A finite-element method (FEM) allowed to model two-dimensional wav...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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AIP Publishing LLC
2022-11-01
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| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/5.0107457 |
| _version_ | 1828058355844775936 |
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| author | L. Körber A. Hempel A. Otto R. A. Gallardo Y. Henry J. Lindner A. Kákay |
| author_facet | L. Körber A. Hempel A. Otto R. A. Gallardo Y. Henry J. Lindner A. Kákay |
| author_sort | L. Körber |
| collection | DOAJ |
| description | In our recent work [Körber et al., AIP Adv. 11, 095006 (2021)], we presented an efficient numerical method to compute dispersions and mode profiles of spin waves in waveguides with translationally invariant equilibrium magnetization. A finite-element method (FEM) allowed to model two-dimensional waveguide cross sections of arbitrary shape but only finite size. Here, we extend our FEM propagating-wave dynamic-matrix approach from finite waveguides to the important cases of infinitely extended mono- and multi-layers of arbitrary spacing and thickness. To obtain the mode profiles and frequencies, the linearized equation of the motion of magnetization is solved as an eigenvalue problem on a one-dimensional line-trace mesh, defined along the normal direction of the layers. Being an important contribution to multi-layer systems, we introduce interlayer exchange into our FEM approach. With the calculation of dipolar fields being the main focus, we also extend the previously presented plane-wave Fredkin–Koehler method to calculate the dipolar potential of spin waves in infinite layers. The major benefit of this method is that it avoids the discretization of any non-magnetic material such as non-magnetic spacers in multilayers. Therefore, the computational effort becomes independent of the spacer thicknesses. Furthermore, it keeps the resulting eigenvalue problem sparse, which, therefore, inherits a comparably low arithmetic complexity. As a validation of our method (implemented into the open-source finite-element micromagnetic package TETRAX), we present results for various systems and compare them with theoretical predictions and with established finite-difference methods. We believe this method offers an efficient and versatile tool to calculate spin-wave dispersions in layered magnetic systems. |
| first_indexed | 2024-04-10T21:26:56Z |
| format | Article |
| id | doaj.art-42ebe42452bd4620850b7059855c267e |
| institution | Directory Open Access Journal |
| issn | 2158-3226 |
| language | English |
| last_indexed | 2024-04-10T21:26:56Z |
| publishDate | 2022-11-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | AIP Advances |
| spelling | doaj.art-42ebe42452bd4620850b7059855c267e2023-01-19T16:29:03ZengAIP Publishing LLCAIP Advances2158-32262022-11-011211115206115206-1310.1063/5.0107457Finite-element dynamic-matrix approach for propagating spin waves: Extension to mono- and multi-layers of arbitrary spacing and thicknessL. Körber0A. Hempel1A. Otto2R. A. Gallardo3Y. Henry4J. Lindner5A. Kákay6Helmholtz-Zentrum Dresden-Rossendorf, Institut für Ionenstrahlphysik und Materialforschung, D-01328 Dresden, GermanyHelmholtz-Zentrum Dresden-Rossendorf, Institut für Ionenstrahlphysik und Materialforschung, D-01328 Dresden, GermanyFakultät Physik, Technische Universität Dresden, D-01062 Dresden, GermanyDepartamento de Física, Universidad Técnica Federico Santa María, Avenida España 1680, Valparaíso, ChileUniversité de Strasbourg, CNRS, Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504, F-67000 Strasbourg, FranceHelmholtz-Zentrum Dresden-Rossendorf, Institut für Ionenstrahlphysik und Materialforschung, D-01328 Dresden, GermanyHelmholtz-Zentrum Dresden-Rossendorf, Institut für Ionenstrahlphysik und Materialforschung, D-01328 Dresden, GermanyIn our recent work [Körber et al., AIP Adv. 11, 095006 (2021)], we presented an efficient numerical method to compute dispersions and mode profiles of spin waves in waveguides with translationally invariant equilibrium magnetization. A finite-element method (FEM) allowed to model two-dimensional waveguide cross sections of arbitrary shape but only finite size. Here, we extend our FEM propagating-wave dynamic-matrix approach from finite waveguides to the important cases of infinitely extended mono- and multi-layers of arbitrary spacing and thickness. To obtain the mode profiles and frequencies, the linearized equation of the motion of magnetization is solved as an eigenvalue problem on a one-dimensional line-trace mesh, defined along the normal direction of the layers. Being an important contribution to multi-layer systems, we introduce interlayer exchange into our FEM approach. With the calculation of dipolar fields being the main focus, we also extend the previously presented plane-wave Fredkin–Koehler method to calculate the dipolar potential of spin waves in infinite layers. The major benefit of this method is that it avoids the discretization of any non-magnetic material such as non-magnetic spacers in multilayers. Therefore, the computational effort becomes independent of the spacer thicknesses. Furthermore, it keeps the resulting eigenvalue problem sparse, which, therefore, inherits a comparably low arithmetic complexity. As a validation of our method (implemented into the open-source finite-element micromagnetic package TETRAX), we present results for various systems and compare them with theoretical predictions and with established finite-difference methods. We believe this method offers an efficient and versatile tool to calculate spin-wave dispersions in layered magnetic systems.http://dx.doi.org/10.1063/5.0107457 |
| spellingShingle | L. Körber A. Hempel A. Otto R. A. Gallardo Y. Henry J. Lindner A. Kákay Finite-element dynamic-matrix approach for propagating spin waves: Extension to mono- and multi-layers of arbitrary spacing and thickness AIP Advances |
| title | Finite-element dynamic-matrix approach for propagating spin waves: Extension to mono- and multi-layers of arbitrary spacing and thickness |
| title_full | Finite-element dynamic-matrix approach for propagating spin waves: Extension to mono- and multi-layers of arbitrary spacing and thickness |
| title_fullStr | Finite-element dynamic-matrix approach for propagating spin waves: Extension to mono- and multi-layers of arbitrary spacing and thickness |
| title_full_unstemmed | Finite-element dynamic-matrix approach for propagating spin waves: Extension to mono- and multi-layers of arbitrary spacing and thickness |
| title_short | Finite-element dynamic-matrix approach for propagating spin waves: Extension to mono- and multi-layers of arbitrary spacing and thickness |
| title_sort | finite element dynamic matrix approach for propagating spin waves extension to mono and multi layers of arbitrary spacing and thickness |
| url | http://dx.doi.org/10.1063/5.0107457 |
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