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Register a new userMicroscopic theory of Gilbert damping in metallic ferromagnets
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We present a microscopic theory for magnetization relaxation in metallic ferromagnets of nanoscopic dimensions that is based on the dynamic spin response matrix in the presence of spin-orbit coupling. Our approach allows the calculation of the spin excitation damping rate even for perfectly crystalline systems, where existing microscopic approaches fail. We demonstrate that the relaxation properties are not completely determined by the transverse susceptibility alone, and that the damping rate has a non-negligible frequency dependence in experimentally relevant situations. Our results indicate that the standard Landau-Lifshitz-Gilbert phenomenology is not always appropriate to describe spin dynamics of metallic nanostructure in the presence of strong spin-orbit coupling.
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Magnetic damping is a key metric for emerging technologies based on magnetic nanoparticles, such as spin torque memory and high-resolution biomagnetic imaging. Despite its importance, understanding of magnetic dissipation in nanoscale ferromagnets remains elusive, and the damping is often treated as a phenomenological constant. Here we report the discovery of a giant frequency-dependent nonlinear damping that strongly alters the response of a nanoscale ferromagnet to spin torque and microwave magnetic field. This novel damping mechanism originates from three-magnon scattering that is strongly enhanced by geometric confinement of magnons in the nanomagnet. We show that the giant nonlinear damping can invert the effect of spin torque on a nanomagnet leading to a surprising current-induced enhancement of damping by an antidamping torque. Our work advances understanding of magnetic dynamics in nanoscale ferromagnets and spin torque devices.
We present a unified theory of magnetic damping in itinerant electron ferromagnets at order $q^2$ including electron-electron interactions and disorder scattering. We show that the Gilbert damping coefficient can be expressed in terms of the spin conductivity, leading to a Matthiessen-type formula in which disorder and interaction contributions are additive. In a weak ferromagnet regime, electron-electron interactions lead to a strong enhancement of the Gilbert damping.
The damping of magnetization, represented by the rate at which it relaxes to equilibrium, is successfully modeled as a phenomenological extension in the Landau-Lifschitz-Gilbert equation. This is the damping torque term known as Gilbert damping and its direction is given by the vector product of the magnetization and its time derivative. Here we derive the Gilbert term from first principles by a non-relativistic expansion of the Dirac equation. We find that the Gilbert term arises when one calculates the time evolution of the spin observable in the presence of the full spin-orbital coupling terms, while recognizing the relationship between the curl of the electric field and the time varying magnetic induction.
A fully quantum mechanical description of the precessional damping of Pt/Co bilayer is presented in the framework of the Keldysh Green function approach using {it ab initio} electronic structure calculations. In contrast to previous calculations of classical Gilbert damping ($alpha_{GD}$), we demonstrate that $alpha_{GD}$ in the quantum case does not diverge in the ballistic regime due to the finite size of the total spin, $S$. In the limit of $Srightarrowinfty$ we show that the formalism recovers the torque correlation expression for $alpha_{GD}$ which we decompose into spin-pumping and spin-orbital torque correlation contributions. The formalism is generalized to take into account a self consistently determined dephasing mechanism which preserves the conservation laws and allows the investigation of the effect of disorder. The dependence of $alpha_{GD}$ on Pt thickness and disorder strength is calculated and the spin diffusion length of Pt and spin mixing conductance of the bilayer are determined and compared with experiments.
We have studied damping in polycrystalline Al nanomechanical resonators by measuring the temperature dependence of their resonance frequency and quality factor over a temperature range of 0.1 - 4 K. Two regimes are clearly distinguished with a crossover temperature of 1 K. Below 1 K we observe a logarithmic temperature dependence of the frequency and linear dependence of damping that cannot be explained by the existing standard models. We attribute these phenomena to the effect of the two-level systems characterized by the unexpectedly long (at least two orders of magnitude longer) relaxation times and discuss possible microscopic models for such systems. We conclude that the dynamics of the two-level systems is dominated by their interaction with one-dimensional phonon modes of the resonators.
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