Finite-element dynamic-matrix approach for propagating spin waves: Extension to mono- and multilayers of arbitrary spacing and thickness
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arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
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2022
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| _version_ | 1866914831443951616 |
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| author | Körber, Lukas Hempel, Alexander Otto, Andreas Gallardo, Rodolfo Henry, Yves Lindner, Jürgen Kákay, Attila |
| author_facet | Körber, Lukas Hempel, Alexander Otto, Andreas Gallardo, Rodolfo Henry, Yves Lindner, Jürgen Kákay, Attila |
| contents | In our recent work [AIP Adv. 11, 095006], we presented an efficient numerical method to compute dispersions and spatial mode profiles of spin waves propagating in waveguides with translationally invariant equilibrium magnetization. Using 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 practical cases of infinitely-extended mono- and multilayers of arbitrary spacing and thickness. To obtain the mode profiles and frequencies, the linearized equation of motion of magnetization is solved as an eigenvalue problem only on a one-dimensional line-trace mesh, defined along the normal direction of the layers. Being an important contribution in multilayer systems, we introduce interlayer-exchange interaction into our FEM approach. With the calculation of dynamic dipolar fields being the main focus of this paper, 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 completely independent on the spacer thicknesses. Furthermore, it keeps the resulting discretized 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 as well as with established finite-difference numerical methods. We believe this method offers an efficient and versatile tool to calculate spin-wave dispersions in layered magnetic systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2207_01519 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Finite-element dynamic-matrix approach for propagating spin waves: Extension to mono- and multilayers of arbitrary spacing and thickness Körber, Lukas Hempel, Alexander Otto, Andreas Gallardo, Rodolfo Henry, Yves Lindner, Jürgen Kákay, Attila Mesoscale and Nanoscale Physics Materials Science In our recent work [AIP Adv. 11, 095006], we presented an efficient numerical method to compute dispersions and spatial mode profiles of spin waves propagating in waveguides with translationally invariant equilibrium magnetization. Using 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 practical cases of infinitely-extended mono- and multilayers of arbitrary spacing and thickness. To obtain the mode profiles and frequencies, the linearized equation of motion of magnetization is solved as an eigenvalue problem only on a one-dimensional line-trace mesh, defined along the normal direction of the layers. Being an important contribution in multilayer systems, we introduce interlayer-exchange interaction into our FEM approach. With the calculation of dynamic dipolar fields being the main focus of this paper, 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 completely independent on the spacer thicknesses. Furthermore, it keeps the resulting discretized 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 as well as with established finite-difference numerical methods. We believe this method offers an efficient and versatile tool to calculate spin-wave dispersions in layered magnetic systems. |
| title | Finite-element dynamic-matrix approach for propagating spin waves: Extension to mono- and multilayers of arbitrary spacing and thickness |
| topic | Mesoscale and Nanoscale Physics Materials Science |
| url | https://arxiv.org/abs/2207.01519 |