The Gilbert damping constant present in the phenomenological Landau-Lifshitz-Gilbert equation describing the dynamics of magnetization is calculated for ferromagnetic metallic films as well as Co/nonmagnet (NM) bilayers. The calculations are done within a realistic nine-orbital tight-binding model including spin-orbit coupling. The convergence of the damping constant expressed as a sum over the Brillouin zone is remarkably improved by introducing finite temperature into the electronic occupation factors and subsequent summation over the Matsubara frequencies. We investigate how the Gilbert damping constant depends on the ferromagnetic film thickness as well as on the thickness of the nonmagnetic cap in Co/NM bilayers (NM = Cu, Pd, Ag, Pt, and Au). The obtained theoretical dependence of the damping constant on the electron-scattering rate, describing the average lifetime of electronic states, varies substantially with the ferromagnetic film thickness and it differs significantly from the dependence for bulk ferromagnetic metals. The presence of nonmagnetic caps is found to largely enhance the magnetic damping in Co/NM bilayers in accordance with experimental data. Unlike Cu, Ag, and Au a particularly strong enhancement is obtained for Pd and Pt caps. This is attributed to the combined effect of the large spin-orbit couplings of Pd and Pt and the simultaneous presence of d states at the Fermi level in these two metals. The calculated Gilbert damping constant also shows an oscillatory dependence on the thicknesses of both ferromagnetic and nonmagnetic parts of the investigated systems which is attributed to quantum-well states. Finally, the expression for contributions to the damping constant from individual atomic layers is derived. The obtained distribution of layer contributions in Co/Pt and Co/Pd bilayers proves that the enhanced damping which affects the dynamics of the magnetization in the Co film originates mainly from a region within the nonmagnetic part of the bilayer. Such a nonlocal damping mechanism, related to spin pumping, is almost absent in other investigated bilayers: Co/Cu, Co/Ag, and Co/Au.

Following the prescription of Ref. [1] in which perfect state transference (PST) of a qubit over distance regular spin networks was discussed, in this paper PST of an arbitrary d-level quantum state (qudit) over antipodes of more general networks called pseudo distance-regular networks, is investigated. In fact, the spectral analysis techniques used in the previous work [1], and algebraic structures of pseudo distance-regular graphs are employed to give an explicit formula for suitable coupling constants in the Hamiltonians so that the state of a particular qudit initially encoded on one site will evolve freely to the opposite site without any dynamical control, i.e., we show that how to derive the parameters of the system so that PST can be achieved.

Abstract. 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 efficiency 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.