2018/04/03 by Ritwik Mondal, Marco Berritta, Peter M. Oppeneer · 1 citation
Physics and Astronomy · #cond-mat.other #cond-mat.mes-hall
paper · pdf · doi:10.1088/1361-648x/aac5a2
published as J. Phys.: Condens. Matter 30, 165801 (2018) · 18 pages, 1 figure
arxiv created 2018/04/03 · arxiv updated 2018/06/28
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 and 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.