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Register a new userConductivity-Like Gilbert Damping due to Intraband Scattering in Epitaxial Iron
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Confirming the origin of Gilbert damping by experiment has remained a challenge for many decades, even for simple ferromagnetic metals. In this Letter, we experimentally identify Gilbert damping that increases with decreasing electronic scattering in epitaxial thin films of pure Fe. This observation of conductivity-like damping, which cannot be accounted for by classical eddy current loss, is in excellent quantitative agreement with theoretical predictions of Gilbert damping due to intraband scattering. Our results resolve the longstanding question about a fundamental damping mechanism and offer hints for engineering low-loss magnetic metals for cryogenic spintronics and quantum devices.
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Tailoring Gilbert damping of metallic ferromagnetic thin films is one of the central interests in spintronics applications. Here we report a giant Gilbert damping anisotropy in epitaxial Co$_{50}$Fe$_{50}$ thin film with a maximum-minimum damping ratio of 400 %, determined by broadband spin-torque as well as inductive ferromagnetic resonance. We conclude that the origin of this damping anisotropy is the variation of the spin orbit coupling for different magnetization orientations in the cubic lattice, which is further corroborate from the magnitude of the anisotropic magnetoresistance in Co$_{50}$Fe$_{50}$.
The magnetostatic mode (MSM) spectrum of a 300$mu$m diameter single crystalline sphere of yttrium iron garnet is investigated using broadband ferromagnetic resonance (FMR). The individual MSMs are identified via their characteristic dispersion relations and the corresponding mode number tuples $(nmr)$ are assigned. Taking FMR data over a broad frequency and magnetic field range allows to analyze both the Gilbert damping parameter~$alpha$ and the inhomogeneous line broadening contribution to the total linewidth of the MSMs separately. The linewidth analysis shows that all MSMs share the same Gilbert damping parameter $alpha=2.7(5) times 10^{-5}$ irrespective of their mode index. In contrast, the inhomogeneous line broadening shows a pronounced mode dependence. This observation is modeled in terms of two-magnon scattering processes of the MSMs into the spin-wave manifold, mediated by surface and volume defects.
The modification of the magnetization dissipation or Gilbert damping caused by an inhomogeneous magnetic structure and expressed in terms of a wave vector dependent tensor $underline{alpha}(vec{q})$ is investigated by means of linear response theory. A corresponding expression for $underline{alpha}(vec{q})$ in terms of the electronic Green function has been developed giving in particular the leading contributions to the Gilbert damping linear and quadratic in $q$. Numerical results for realistic systems are presented that have been obtained by implementing the scheme within the framework of the fully relativistic KKR (Korringa-Kohn-Rostoker) band structure method. Using the multilayered system (Cu/Fe$_{1-x}$Co$_x$/Pt)$_n$ as an example for systems without inversion symmetry we demonstrate the occurrence of non-vanishing linear contributions. For the alloy system bcc Fe$_{1-x}$Co$_x$ having inversion symmetry, on the other hand, only the quadratic contribution is non-zero. As it is shown, this quadratic contribution does not vanish even if the spin-orbit coupling is suppressed, i.e. it is a direct consequence of the non-collinear spin configuration.
A method with which to calculate the Gilbert damping parameter from a real-space electronic structure method is reported here. The anisotropy of the Gilbert damping with respect to the magnetic moment direction and local chemical environment is calculated for bulk and surfaces of Fe$_{50}$Co$_{50}$ alloys from first principles electronic structure in a real space formulation. The size of the damping anisotropy for Fe$_{50}$Co$_{50}$ alloys is demonstrated to be significant. Depending on details of the simulations, it reaches a maximum-minimum damping ratio as high as 200%. Several microscopic origins of the strongly enhanced Gilbert damping anisotropy have been examined, where in particular interface/surface effects stand out, as do local distortions of the crystal structure. Although theory does not reproduce the experimentally reported high ratio of 400% [Phys. Rev. Lett. 122, 117203 (2019)], it nevertheless identifies microscopic mechanisms that can lead to huge damping anisotropies.
Thin highly textured Fe$_{mathrm{1+x}}$Co$_{mathrm{2-x}}$Si ($0 leq$ x $leq 1$) films were prepared on MgO (001) substrates by magnetron co-sputtering. The magneto-optic Kerr effect (MOKE) and ferromagnetic resonance (FMR) measurements were used to investigate the composition dependence of the magnetization, the magnetic anisotropy, the gyromagnetic ratio and the relaxation of the films. The effective magnetization for the thin Fe$_{mathrm{1+x}}$Co$_{mathrm{2-x}}$Si films, determined by FMR measurements, are consistent with the Slater Pauling prediction. Both MOKE and FMR measurements reveal a pronounced fourfold anisotropy distribution for all films. In addition we found a strong influence of the stoichiometry on the anisotropy as the cubic anisotropy strongly increases with increasing Fe concentration. The gyromagnetic ratio is only weakly dependent on the composition. We find low Gilbert damping parameters for all films with values down to $0.0012pm0.00012$ for Fe$_{1.75}$Co$_{1.25}$Si. The effective damping parameter for Co$_2$FeSi is found to be $0.0018pm 0.0004$. We also find a pronounced anisotropic relaxation, which indicates significant contributions of two-magnon scattering processes that is strongest along the easy axes of the films. This makes thin Fe$_{mathrm{1+x}}$Co$_{mathrm{2-x}}$Si films ideal materials for the application in STT-MRAM devices.
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