Enhancement of the Gilbert damping constant due to spin pumping in noncollinear ferromagnet/nonmagnet/ferromagnet trilayer systems

We analyzed the enhancement of the Gilbert damping constant due to spin pumping in non-collinear ferromagnet / non-magnet / ferromagnet trilayer systems. We show that the Gilbert damping constant depends both on the precession angle of the magnetization of the free layer and on the direction of the magntization of the fixed layer. We find the condition to be satisfied to realize strong enhancement of the Gilbert damping constant.Comment: 4 pages, 3 figures, to be published in Phys. Rev.

Low relaxation rate in a low-Z alloy of iron

The longest relaxation time and sharpest frequency content in ferromagnetic precession is determined by the intrinsic (Gilbert) relaxation rate \emph{$G$}. For many years, pure iron (Fe) has had the lowest known value of $G=\textrm{57 Mhz}$ for all pure ferromagnetic metals or binary alloys. We show that an epitaxial iron alloy with vanadium (V) possesses values of $G$ which are significantly reduced, to 35$\pm$5 Mhz at 27% V. The result can be understood as the role of spin-orbit coupling in generating relaxation, reduced through the atomic number $Z$.Comment: 14 pages, 4 figure

The magneto-optical gradient effect in an exchange-biased thin film: Experimental evidence for classical diffraction theory

The magneto-optical gradient effect decorates the boundaries of in-plane domains even at perpendicular incidence of light in an optical polarization microscope. For its explanation, the classical magneto-optical diffraction theory was previously used to derive the effect from the same gyrotropic interaction as the Kerr effect. In order to explain the symmetry of the experimentally observed contrast on bulk ferromagnetic crystals, planar as well as perpendicular subsurface gradients in the magnetization had to be assumed. This was particularly needed when the surface magnetizations in neighboring domains pointed head-on and a gradient contrast appeared also in conditions of vanishing gyrotropic interaction at the surface. The gradient contrast in such conditions should not appear in very thin films where perpendicular magnetization gradients are not enforced by reduction of magnetostatic energy. Here we present the first experimental confirmation of this expectation, thus closing an experimental gap in verifying the predictions of the diffraction theory

Thermal fluctuation field for current-induced domain wall motion

Current-induced domain wall motion in magnetic nanowires is affected by thermal fluctuation. In order to account for this effect, the Landau-Lifshitz-Gilbert equation includes a thermal fluctuation field and literature often utilizes the fluctuation-dissipation theorem to characterize statistical properties of the thermal fluctuation field. However, the theorem is not applicable to the system under finite current since it is not in equilibrium. To examine the effect of finite current on the thermal fluctuation, we adopt the influence functional formalism developed by Feynman and Vernon, which is known to be a useful tool to analyze effects of dissipation and thermal fluctuation. For this purpose, we construct a quantum mechanical effective Hamiltonian describing current-induced domain wall motion by generalizing the Caldeira-Leggett description of quantum dissipation. We find that even for the current-induced domain wall motion, the statistical properties of the thermal noise is still described by the fluctuation-dissipation theorem if the current density is sufficiently lower than the intrinsic critical current density and thus the domain wall tilting angle is sufficiently lower than pi/4. The relation between our result and a recent result, which also addresses the thermal fluctuation, is discussed. We also find interesting physical meanings of the Gilbert damping alpha and the nonadiabaticy parameter beta; while alpha characterizes the coupling strength between the magnetization dynamics (the domain wall motion in this paper) and the thermal reservoir (or environment), beta characterizes the coupling strength between the spin current and the thermal reservoir.Comment: 16 page, no figur

Identification of the dominant precession damping mechanism in Fe, Co, and Ni by first-principles calculations

The Landau-Lifshitz equation reliably describes magnetization dynamics using a phenomenological treatment of damping. This paper presents first-principles calculations of the damping parameters for Fe, Co, and Ni that quantitatively agree with existing ferromagnetic resonance measurements. This agreement establishes the dominant damping mechanism for these systems and takes a significant step toward predicting and tailoring the damping constants of new materials.Comment: 4 pages, 1 figur

Dynamics of magnetization coupled to a thermal bath of elastic modes

We study the dynamics of magnetization coupled to a thermal bath of elastic modes using a system plus reservoir approach with realistic magnetoelastic coupling. After integrating out the elastic modes we obtain a self-contained equation for the dynamics of the magnetization. We find explicit expressions for the memory friction kernel and hence, {\em via} the Fluctuation-Dissipation Theorem, for the spectral density of the magnetization thermal fluctuations. For magnetic samples in which the single domain approximation is valid, we derive an equation for the dynamics of the uniform mode. Finally we apply this equation to study the dynamics of the uniform magnetization mode in insulating ferromagnetic thin films. As experimental consequences we find that the fluctuation correlation time is of the order of the ratio between the film thickness, $h$, and the speed of sound in the magnet and that the line-width of the ferromagnetic resonance peak should scale as $B_1^2h$ where $B_1$ is the magnetoelastic coupling constant.Comment: Revised version as appeared in print. 12 pages 9 figure

Magnetization damping in a local-density approximation

The linear response of itinerant transition metal ferromagnets to transverse magnetic fields is studied in a self-consistent adiabatic local-density approximation. The susceptibility is calculated from a microscopic Hamiltonian, including spin-conserving impurities, impurity induced spin-orbit interaction and magnetic impurities using the Keldysh formalism. The Gilbert damping constant in the Landau-Lifshitz-Gilbert equation is identified, parametrized by an effective transverse spin dephasing rate, and is found to be inversely proportional to the exchange splitting. Our result justify the phenomenological treatment of transverse spin dephasing in the study of current-induced magnetization dynamics in weak, itinerant ferromagnets by Tserkovnyak \textit{et al.}. We show that neglect of gradient corrections in the quasiclassical transport equations leads to incorrect results when the exchange potential becomes of the order of the Fermi energy.Comment: 11 pages, 41 references, no figure

A method for atomistic spin dynamics simulations: implementation and examples

We present a method for performing atomistic spin dynamic simulations. A comprehensive summary of all pertinent details for performing the simulations such as equations of motions, models for including temperature, methods of extracting data and numerical schemes for performing the simulations is given. The method can be applied in a first principles mode, where all interatomic exchange is calculated self-consistently, or it can be applied with frozen parameters estimated from experiments or calculated for a fixed spin-configuration. Areas of potential applications to different magnetic questions are also discussed. The method is finally applied to one situation where the macrospin model breaks down; magnetic switching in ultra strong fields.Comment: 14 pages, 19 figure

Gilbert Damping in Magnetic Multilayers

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. \textbf{88},117601 (2002)].Comment: 1 figure, 5page

Emergence of anisotropic Gilbert damping in ultrathin Fe layers on GaAs (001)

As a fundamental parameter in magnetism, the phenomenological Gilbert damping constant a determines the performance of many spintronic devices. For most magnetic materials, a is treated as an isotropic parameter entering the Landau-Lifshitz-Gilbert equation. However, could the Gilbert damping be anisotropic? Although several theoretical approaches have suggested that anisotropic a could appear in single-crystalline bulk systems, experimental evidence of its existence is scarce. Here, we report the emergence of anisotropic magnetic damping by exploring a quasi-two-dimensional single-crystalline ferromagnetic metal/semiconductor interface-that is, a Fe/GaAs(001) heterojunction. The observed anisotropic damping shows twofold C-2v symmetry, which is expected from the interplay of interfacial Rashba and Dresselhaus spin-orbit interaction, and is manifested by the anisotropic density of states at the Fe/GaAs (001) interface. This discovery of anisotropic damping will enrich the understanding of magnetization relaxation mechanisms and can provide a route towards the search for anisotropic damping at other ferromagnetic metal/semiconductor interfaces