Fractional Landau-Lifshitz-Gilbert equation
The dynamics of a magnetic moment or spin are of high interest to applications in technology. Dissipation in these systems is therefore of importance for improvement of efficiency of devices, such as the ones proposed in spintronics. A large spin in a magnetic field is widely assumed to be described...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2023-08-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.5.033128 |
| _version_ | 1797210475675516928 |
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| author | R. C. Verstraten T. Ludwig R. A. Duine C. Morais Smith |
| author_facet | R. C. Verstraten T. Ludwig R. A. Duine C. Morais Smith |
| author_sort | R. C. Verstraten |
| collection | DOAJ |
| description | The dynamics of a magnetic moment or spin are of high interest to applications in technology. Dissipation in these systems is therefore of importance for improvement of efficiency of devices, such as the ones proposed in spintronics. A large spin in a magnetic field is widely assumed to be described by the Landau-Lifshitz-Gilbert (LLG) equation, which includes a phenomenological Gilbert damping. Here, we couple a large spin to a bath and derive a generic (non-)Ohmic damping term for the low-frequency range using a Caldeira-Leggett model. This leads to a fractional LLG equation, where the first-order derivative Gilbert damping is replaced by a fractional derivative of order s∈R_{≥0}. We show that the parameter s can be determined from a ferromagnetic resonance experiment, where the resonance frequency and linewidth no longer scale linearly with the effective field strength. |
| first_indexed | 2024-04-24T10:11:11Z |
| format | Article |
| id | doaj.art-ec2ab3c3fd124b5fab101fe3d750f387 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:11:11Z |
| publishDate | 2023-08-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-ec2ab3c3fd124b5fab101fe3d750f3872024-04-12T17:33:29ZengAmerican Physical SocietyPhysical Review Research2643-15642023-08-015303312810.1103/PhysRevResearch.5.033128Fractional Landau-Lifshitz-Gilbert equationR. C. VerstratenT. LudwigR. A. DuineC. Morais SmithThe dynamics of a magnetic moment or spin are of high interest to applications in technology. Dissipation in these systems is therefore of importance for improvement of efficiency of devices, such as the ones proposed in spintronics. A large spin in a magnetic field is widely assumed to be described by the Landau-Lifshitz-Gilbert (LLG) equation, which includes a phenomenological Gilbert damping. Here, we couple a large spin to a bath and derive a generic (non-)Ohmic damping term for the low-frequency range using a Caldeira-Leggett model. This leads to a fractional LLG equation, where the first-order derivative Gilbert damping is replaced by a fractional derivative of order s∈R_{≥0}. We show that the parameter s can be determined from a ferromagnetic resonance experiment, where the resonance frequency and linewidth no longer scale linearly with the effective field strength.http://doi.org/10.1103/PhysRevResearch.5.033128 |
| spellingShingle | R. C. Verstraten T. Ludwig R. A. Duine C. Morais Smith Fractional Landau-Lifshitz-Gilbert equation Physical Review Research |
| title | Fractional Landau-Lifshitz-Gilbert equation |
| title_full | Fractional Landau-Lifshitz-Gilbert equation |
| title_fullStr | Fractional Landau-Lifshitz-Gilbert equation |
| title_full_unstemmed | Fractional Landau-Lifshitz-Gilbert equation |
| title_short | Fractional Landau-Lifshitz-Gilbert equation |
| title_sort | fractional landau lifshitz gilbert equation |
| url | http://doi.org/10.1103/PhysRevResearch.5.033128 |
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