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# On the origin of magnetic inertia : a rigorous relativistic Dirac theory derivation

Type of Publication: | Contribution to a conference |

Publication status: | Published |

Author: | Oppeneer, Peter M.; Nandy, Ashis K.; Berritta, Marco; Mondal, Ritwik |

Year of publication: | 2018 |

Conference: | SPIE Nanoscience + Engineering, 2018, Aug 19, 2018 - Aug 23, 2018, San Diego, California, USA |

Published in: | Spintronics XI / Drouhin, Henri-Jean; Wegrowe, Jean-Eric; Razeghi, Manijeh; Jaffrès, Henri (ed.). - Bellingham, Washington, USA : SPIE, 2018. - (Proceedings of SPIE ; 10732). - pp. 10732-10785. - ISSN 0277-786X. - eISSN 1996-756X. - ISBN 978-1-5106-2035-3 |

DOI (citable link): | https://dx.doi.org/10.1117/12.2323968 |

Summary: |
Inertia is a fundamental property of a particle that can be understood from Newtons laws of motion. In a similar way, any magnetized body must possess magnetic inertia by the virtue of its magnetization. The influence of possible magnetic inertia effects has recently drawn attention in ultrafast magnetization dynamics and switching. Magnetization dynamics at the inertial regime has been investigated using thermodynamic theories that predicted the magnetic inertia can become impactful at shorter timescales. However, at the fundamental level, the origin of magnetic inertial dynamics is still unknown.
Here, we derive rigorously a description of magnetic inertia in the extended Landau-Lifshitz-Gilbert (LLG) equation starting from a fundamental and relativistic Dirac-Kohn-Sham framework. We use a unitary transformation, the so called called Foldy-Wouthuysen transformation, up to the order of 1/c ^{4}. In this way, the particle and anti-particle in fully relativistic description become decoupled and a Hamiltonian describing only the particles is derived. This Hamiltonian involves the nonrelativistic Schrodinger-Pauli Hamiltonian together with the relativistic corrections of the order 1/c^{2 }and 1/c^{4}.With the thus-derived Hamiltonian, we calculate the corresponding spin dynamics leading to the LLG equation of motion. Our result exemplify that the relativistic correction terms of 1/c ^{2} are responsible for the Gilbert damping, however, the relativistic correction terms of 1/c4 are responsible for magnetic inertial dynamics. Therefore, we predict that the intrinsic magnetic inertia is a higher-order relativistic spin-orbit coupling effect and is expected to be prominent only on ultrashort timescales (subpicoseconds). We also show that the corresponding Gilbert damping and magnetic inertia parameters are related to one another through the imaginary and real parts of the magnetic susceptibility tensor, respectively. |

Subject (DDC): | 530 Physics |

Bibliography of Konstanz: | Yes |

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OPPENEER, Peter M., Ashis K. NANDY, Marco BERRITTA, Ritwik MONDAL, 2018. On the origin of magnetic inertia : a rigorous relativistic Dirac theory derivation. SPIE Nanoscience + Engineering, 2018. San Diego, California, USA, Aug 19, 2018 - Aug 23, 2018. In: DROUHIN, Henri-Jean, ed., Jean-Eric WEGROWE, ed., Manijeh RAZEGHI, ed., Henri JAFFRÈS, ed.. Spintronics XI. Bellingham, Washington, USA:SPIE, pp. 10732-10785. ISSN 0277-786X. eISSN 1996-756X. ISBN 978-1-5106-2035-3. Available under: doi: 10.1117/12.2323968

@inproceedings{Oppeneer2018origi-44480, title={On the origin of magnetic inertia : a rigorous relativistic Dirac theory derivation}, year={2018}, doi={10.1117/12.2323968}, number={10732}, isbn={978-1-5106-2035-3}, issn={0277-786X}, address={Bellingham, Washington, USA}, publisher={SPIE}, series={Proceedings of SPIE}, booktitle={Spintronics XI}, pages={10732--10785}, editor={Drouhin, Henri-Jean and Wegrowe, Jean-Eric and Razeghi, Manijeh and Jaffrès, Henri}, author={Oppeneer, Peter M. and Nandy, Ashis K. and Berritta, Marco and Mondal, Ritwik}, note={Article Number: 107322E} }