Unified theory of magnetization dynamics with relativistic and nonrelativistic spin torques

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2018
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Berritta, Marco
Oppeneer, Peter M.
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Spin torques play a crucial role in operative properties of modern spintronic devices. To study current-driven magnetization dynamics, spin-torque terms providing the action of spin-polarized currents have previously often been added in a phenomenological way to the Landau-Lifshitz-Gilbert equation describing the local spin dynamics, yet without derivation from fundamental principles. Here, starting from the Dirac-Kohn-Sham theory and incorporating nonlocal spin transport we rigorously derive the various spin-torque terms that appear in current-driven magnetization dynamics. In particular we obtain an extended magnetization dynamics equation that precisely contains the nonrelativistic adiabatic and relativistic nonadiabatic spin-transfer torques of the Berger and Zhang-Li forms as well as relativistic spin-orbit torques. We derive in addition a previously unnoticed relativistic spin-torque term and moreover show that the various obtained spin-torque terms do not appear in the same mathematical form in both the Landau-Lifshitz and Landau-Lifshitz-Gilbert equations of spin dynamics.

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ISO 690MONDAL, Ritwik, Marco BERRITTA, Peter M. OPPENEER, 2018. Unified theory of magnetization dynamics with relativistic and nonrelativistic spin torques. In: Physical Review B. 2018, 98(21), 214429. ISSN 2469-9950. eISSN 2469-9969. Available under: doi: 10.1103/PhysRevB.98.214429
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@article{Mondal2018Unifi-46180,
  year={2018},
  doi={10.1103/PhysRevB.98.214429},
  title={Unified theory of magnetization dynamics with relativistic and nonrelativistic spin torques},
  number={21},
  volume={98},
  issn={2469-9950},
  journal={Physical Review B},
  author={Mondal, Ritwik and Berritta, Marco and Oppeneer, Peter M.},
  note={Article Number: 214429}
}
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    <dcterms:abstract xml:lang="eng">Spin torques play a crucial role in operative properties of modern spintronic devices. To study current-driven magnetization dynamics, spin-torque terms providing the action of spin-polarized currents have previously often been added in a phenomenological way to the Landau-Lifshitz-Gilbert equation describing the local spin dynamics, yet without derivation from fundamental principles. Here, starting from the Dirac-Kohn-Sham theory and incorporating nonlocal spin transport we rigorously derive the various spin-torque terms that appear in current-driven magnetization dynamics. In particular we obtain an extended magnetization dynamics equation that precisely contains the nonrelativistic adiabatic and relativistic nonadiabatic spin-transfer torques of the Berger and Zhang-Li forms as well as relativistic spin-orbit torques. We derive in addition a previously unnoticed relativistic spin-torque term and moreover show that the various obtained spin-torque terms do not appear in the same mathematical form in both the Landau-Lifshitz and Landau-Lifshitz-Gilbert equations of spin dynamics.</dcterms:abstract>
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