Generalisation of Gilbert damping and magnetic inertia parameter as a series of higher-order relativistic terms

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2018
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Berritta, Marco
Oppeneer, Peter M.
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Journal of Physics : Condensed Matter. 2018, 30(26), 265801. ISSN 0953-8984. eISSN 1361-648X. Available under: doi: 10.1088/1361-648X/aac5a2
Zusammenfassung

The phenomenological Landau–Lifshitz–Gilbert (LLG) equation of motion remains as the cornerstone of contemporary magnetisation dynamics studies, wherein the Gilbert damping parameter has been attributed to first-order relativistic effects. To include magnetic inertial effects the LLG equation has previously been extended with a supplemental inertia term; the arising inertial dynamics has been related to second-order relativistic effects. Here we start from the relativistic Dirac equation and, performing a Foldy–Wouthuysen transformation, derive a generalised Pauli spin Hamiltonian that contains relativistic correction terms to any higher order. Using the Heisenberg equation of spin motion we derive general relativistic expressions for the tensorial Gilbert damping and magnetic inertia parameters, and show that these tensors can be expressed as series of higher-order relativistic correction terms. We further show that, in the case of a harmonic external driving field, these series can be summed and we provide closed analytical expressions for the Gilbert and inertial parameters that are functions of the frequency of the driving field.

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ISO 690MONDAL, Ritwik, Marco BERRITTA, Peter M. OPPENEER, 2018. Generalisation of Gilbert damping and magnetic inertia parameter as a series of higher-order relativistic terms. In: Journal of Physics : Condensed Matter. 2018, 30(26), 265801. ISSN 0953-8984. eISSN 1361-648X. Available under: doi: 10.1088/1361-648X/aac5a2
BibTex
@article{Mondal2018-07-04Gener-42821,
  year={2018},
  doi={10.1088/1361-648X/aac5a2},
  title={Generalisation of Gilbert damping and magnetic inertia parameter as a series of higher-order relativistic terms},
  number={26},
  volume={30},
  issn={0953-8984},
  journal={Journal of Physics : Condensed Matter},
  author={Mondal, Ritwik and Berritta, Marco and Oppeneer, Peter M.},
  note={Article Number: 265801}
}
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