Gilbert damping in binary magnetic multilayers

We present quantum mechanical calculations of the Gilbert damping constant alpha in ultrathin L1(0) [Co/NM](N) superlattices and (001) fcc [Co/NM](N) magnetic multilayers built of cobalt and nonmagnetic metals NM = Cu, Ag, Pd, Pt, and Au. The calculations are performed within a realistic nine-orbital tight-binding model of the band structure including spin-orbit interaction. The dependence of a on the stacking number N, ferromagnetic and nonmagnetic layer thicknesses as well as the electron scattering rate is investigated. The damping constant is shown to be the sum of a constant term (bulklike) and a 1/N term (due to external surfaces) which arise from inter-and intraband electronic transitions, respectively. The calculated a is found to be enhanced in the considered multilayers in comparison with its values for bulk Co and their bilayer counterparts with the same total Co thickness. The origin of this enhancement and the variation of a with the geometric structure of the multilayers are further investigated by analyzing the damping contributions from individual atomic layers. The obtained theoretical results for the damping constant are shown to be in good agreement with previous experimental observations in magnetic multilayers. In particular, the experimentally observed linear dependence on the ratio of NM (Pd or Pt) and Co layer thicknesses is reproduced in the present calculations.