Relationship between Gilbert damping and magneto-crystalline anisotropy in a Ti-buffered Co/Ni multilayer system (original) (raw)
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Applied Physics Letters, 2013
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Higher-order perpendicular magnetic anisotropy and interfacial damping of Co/Ni multilayers
Physical Review B
We report on the experimental investigation of the perpendicular magnetic anisotropy in Pt/[Co/Ni] N /Ir multilayers. Broadband ferromagnetic resonance (FMR) and polar angle dependent FMR measurements reveal the presence of a strong fourth-order contribution to the perpendicular anisotropy. By numerically solving the Smit-Beljers relation, we are able to fit the polar angle dependence of the resonance field and extract both the second and fourth-order anisotropy constants. While this model provides a qualitative description for all samples, we note that, for samples near or in the easy cone state of the phase diagram, systematic deviations emerge in the polar angle dependent data. The exchange stiffness of the multilayers is found to be lower than the weighted average of the exchange stiffness reported for Co and Ni in the literature. We find that the effective Gilbert damping scales with the inverse multilayer thickness, indicating a significant interfacial contribution to the damping process.
Gilbert damping in magnetic layered systems
Physical Review B, 2014
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.
Gilbert damping in binary magnetic multilayers
Physical Review B, 2017
We present quantum mechanical calculations of the Gilbert damping constant α 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 α 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 interand intraband electronic transitions, respectively. The calculated α 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 α 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.
Calculation of Gilbert damping in ferromagnetic films
EPJ Web of Conferences, 2013
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.
Gilbert damping in magnetic multilayers
Physical Review B, 2003
We study the enhancement of the ferromagnetic relaxation rate in thin films due to the adjacent normal metal layers. Using linear response theory, we derive the dissipative torque produced by the s − d exchange interaction at the ferromagnet-normal metal interface. For a slow precession, the enhancement of Gilbert damping constant is proportional to the square of the s−d exchange constant times the zero-frequency limit of the frequency derivative of the local dynamic spin susceptibility of the normal metal at the interface. Electron-electron interactions increase the relaxation rate by the Stoner factor squared. We attribute the large anisotropic enhancements of the relaxation rate observed recently in multilayers containing palladium to this mechanism. For free electrons, the present theory compares favorably with recent spin-pumping result of Tserkovnyak et al. [Phys. Rev. Lett. 88,117601 (2002)].
Quantum mechanism of nonlocal Gilbert damping in magnetic trilayers
Physical Review B, 2015
A fully quantum-mechanical calculation of the Gilbert damping constant α in magnetic trilayers is done by employing the torque-correlation formula within a realistic tight-binding model. A remarkable enhancement of α in Co/NM 1 /NM 2 trilayers is obtained due to adding the caps NM 2 =Pd, Pt, and it decays with the thickness of the spacers NM 1 =Cu, Ag, Au in agreement with experiment. Nonlocal origin of the Gilbert damping is visualized with its atomic layer contributions. It is shown that magnetization in Co is damped remotely by strong spin-orbit coupling in NM 2 via quantum states with large amplitude in both Co and NM 2 .
Physical Review Letters, 2001
Unique features of the Gilbert damping in magnetic multilayers were investigated by ferromagnetic resonance (FMR) using magnetic single and double layer structures prepared by molecular beam epitaxy. The FMR linewidth for the Fe films in the double layer structures was larger than the FMR linewidth in the single Fe films having the same thickness. The additional FMR linewidth scaled inversely with the film thickness, and increased linearly with increasing microwave frequency. These results demonstrate that a transfer of electron angular momentum between the magnetic layers leads to additional relaxation torques.
Applied Physics Letters, 2014
We use broadband ferromagnetic resonance spectroscopy to systematically measure the Landau-Lifshitz damping parameter, perpendicular anisotropy, and the orbital moment asymmetry in Co 90 Fe 10 /Ni multilayers. No relationship is found between perpendicular magnetic anisotropy and the damping parameter in this material. However, inadequate accounting for inhomogeneous linewidth broadening, spin-pumping, and two-magnon scattering could give rise to an apparent relationship between anisotropy and damping. In contrast, the orbital-moment asymmetry and the perpendicular anisotropy are linearly proportional to each other. These results demonstrate a fundamental mechanism by which perpendicular anisotropy can be varied independently of the damping parameter. [