Abstract
The Gilbert damping constant in the phenomenological Landau-Lifshitz-Gilbert equation which de- scribes 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 e! ciency 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.
Highlights
The switching of magnetization in nanoscale magnetic elements is of importance for application in magnetoelectronic devices
The first of them originates from the spin-orbit (SO) interaction which couples the spins of electrons to the lattice, and leads to a torque exerted on the magnetisation as its direction varies with time. This torque is represented by the Gilbert damping term in the phenomenological LandauLifshitz-Gilbert (LLG) equation and it plays an important role in spin dynamics of ferromagnetic metallic systems
The oscillatory behavior of the damping constant originates mainly from interband term and it is attributed to quantum-well states (QWS) with energies close to the Fermi level F
Summary
The switching of magnetization in nanoscale magnetic elements is of importance for application in magnetoelectronic devices. The first of them originates from the spin-orbit (SO) interaction which couples the spins of electrons to the lattice, and leads to a torque exerted on the magnetisation as its direction varies with time This torque is represented by the Gilbert damping term in the phenomenological LandauLifshitz-Gilbert (LLG) equation and it plays an important role in spin dynamics of ferromagnetic metallic systems. Related to the SO coupling, is another important factor for DW structures and it can be large in multilayers, like Co/Pt or Co/Ni (see, e.g., [14, 15]) In this communication, we calculate the Gilbert damping constant within Kambersky’s spin-orbital torque correlation theory using a realistic nine-band tight binding (TB)
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