Calculation of Gilbert damping in ferromagnetic ﬁlms
Institute of Physical Chemistry of the Polish Academy of
Sciences, Warsaw, Poland
2 Department of Mathematics, Imperial College, London SW7 2BZ, UK
3 Department of Mathematics, Open University, Milton Keynes MK7 6AA, UK
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The Gilbert damping constant in the phenomenological Landau-Lifshitz-Gilbert equation which describes the dynamics of magnetization, is calculated for Fe, Co and Ni bulk ferromagnets, Co ﬁlms and Co/Pd bilayers within a nine-band tight-binding model with spin-orbit coupling included. The calculational effciency is remarkably improved by introducing ﬁnite temperature into the electronic occupation factors and subsequent summation over the Matsubara frequencies. The calculated dependence of Gilbert damping constant on scattering rate for bulk Fe, Co and Ni is in good agreement with the results of previous ab initio calculations. Calculations are reported for ferromagnetic Co metallic ﬁlms and Co/Pd bilayers. The dependence of the Gilbert damping constant on Co ﬁlm thickness, for various scattering rates, is studied and compared with recent experiments.
© Owned by the authors, published by EDP Sciences, 2013