In ferromagnets, charge currents can excite magnons via the spin-orbit coupling. We develop a novel and general scattering theory of charge current induced macrospin magnetization torques in normal metal$|$ferromagnet$|$normal metal layers. We apply the formalism to a dirty GaAs$|$(Ga,Mn)As$|$GaAs system. By computing the charge current induced magnetization torques and solving the Landau-Lifshitz-Gilbert equation, we find magnetization switching for current densities as low as $ 5\times 10^{6}$~A/cm$^2$. Our results are in agreement with a recent experimental observation of charge-current induced magnetization switching in (Ga,Mn)As.
The magnetization dynamics of ferromagnets are often formulated in terms of the Landau-Lifshitz-Gilbert (LLG) equation. The reactive part of this equation describes the response of the magnetization in terms of effective fields, whereas the dissipative part is parameterized by the Gilbert damping tensor. We formulate a scattering theory for the magnetization dynamics and map this description on the linearized LLG equation by attaching electric contacts to the ferromagnet. The reactive part can then be expressed in terms of the static scattering matrix. The dissipative contribution to the low-f…
We investigate the reflection coefficient of spin waves propagating in an ultra-thin ferromagnetic film with regions where saturation magnetization is modulated. We find analytically and using micromagnetic simulations that there are transmission resonances that depend on the width of the regions and on the energy of excitation. Our results resemble the quantum mechanical Ramsauer-Townsend effect in which an electron with certain energies can propagate above a potential field without scattering. Our findings are useful for reconfigurable magnonic devices where the saturation magnetization can …
The dependence on temperature of the spin magnetization of a two-dimensional electron gas at filling factor unity is studied. Using classical Monte Carlo simulations we analyze the effect that the equivalence between topological and electrical charge has on the the behavior of the magnetization. We find that at intermediate temperatures the spin polarization increases in a thirty per cent due to the Hartree interaction between charge fluctuations.
We theoretically study the spin and charge generation along with the electron transport on a disordered surface of a doped three-dimensional topological insulator/magnetic insulator junction by using Green's function techniques. We find that the spin and charge current are induced by not only local but also nonlocal magnetization dynamics through nonmagnetic impurity scattering on the disordered surface of the doped topological insulator. We also clarify that the spin current as well as charge density are induced by spatially inhomogeneous magnetization dynamics, and the spin current diffusive…
In inhomogeneous bulk ferromagnets, the dominating sources of spin disorder are related to spatial variations of (i) the magnitude of the local saturation magnetization and of (ii) the magnitude and/or direction of the magnetic anisotropy field. For the particular example of a porous ferromagnet, where the magnetization inhomogeneity is at maximum, we demonstrate, by means of experimental neutron scattering data and micromagnetic simulations, the anisotropic character of magnetization fluctuations induced by the dipolar interaction.
Inelastic neutron scattering in variable magnetic field and high-field magnetization measurements, at the milikelvin temperature range, were performed to gain insight into the low-energy magnetic excitation spectrum and the field-induced level crossings in the molecular spin cluster \{Cr$_8$\}-cubane. These complementary techniques provide consistent estimates of the lowest level-crossing field. The overall features of the experimental data are explained using an isotropic Heisenberg model, based on three distinct exchange interactions linking the eight Cr$^{\text{III}}$ paramagnetic centers (…
We observe a strong correlation between magnetization relaxation and electrical resistivity in thin Permalloy (Ni$_{81}$Fe$_{19}$, ``Py'') films. Electron scattering rates in the films were affected by varying film thickness and deposition conditions. This shows that the magnetization relaxation mechanism is analogous to ``bulk'' relaxation, where phonon scattering in bulk is replaced by surface and defect scattering in thin films. Another interesting finding is the increased magnetization damping with Pt layers adjacent to the Py films. This is attributed to the strong spin-orbit coupling in …
We study the non-equilibrium dynamics in a mesoscopic graphene ring excited by picoseconds shaped electromagnetic pulses. We predict an ultrafast buildup of charge polarization, currents and orbital magnetization. Applying the light pulses identified here, non-equilibrium valley currents are generated in a graphene ring threaded by a stationary magnetic flux. We predict a finite graphene ring magnetization even for a vanishing charge current; the magnetization emerges due to the light-induced difference of the valley populations.
We study spin and charge currents pumped by precessing magnetization of a single ferromagnetic layer within F|I|N or F|I|F (F-ferromagnet; I-insulator; N-normal-metal) multilayers of nanoscale thickness attached to two normal metal electrodes with no applied bias voltage between them. Both simple one-dimensional model, consisting of a single precessing spin and a potential barrier as the "sample," and realistic three-dimensional devices are investigated. In the rotating reference frame, where the magnetization appears to be static, these junctions are mapped onto a four-terminal dc circuit who…
The spin-charge coupled dynamics in a thin, magnetized metallic system are investigated. The effective driving force acting on the charge carriers is generated by a dynamical magnetic texture, which can be induced, e.g., by a magnetic material in contact with a normal-metal system. We consider a general inversion-asymmetric substrate/normal-metal/magnet structure, which, by specifying the precise nature of each layer, can mimick various experimentally employed setups. Inversion symmetry breaking gives rise to an effective Rashba spin-orbit interaction. We derive general spin-charge kinetic equ…
The origins of the spin-orbit torque (SOT) at ferromagnet/topological insulator (FM/TI) interfaces are incompletely understood. Theory has overwhelmingly focussed on the Edelstein effect due to the surface states in the presence of a scalar scattering potential. We investigate here the contribution to the SOT due to extrinsic spin-orbit scattering of the surface states, focusing on the case of an out-of-plane magnetization. We show that spin-orbit scattering brings about a sizable renormalization of the field-like SOT, which exceeds 20$\%$ at larger strengths of the extrinsic spin-orbit parame…
To study the effect of spin-orbit coupling (SOC) on spin-transfer torque in magnetic materials, we have implemented two theoretical formalisms that can accommodate SOC. Using the "charge-pumping" formalism, we find two contributions to the out-of-plane spin-transfer torque parameter $β$ in ballistic Ni domain walls (DWs). For short DWs, the nonadiabatic reflection of conduction electrons caused by the rapid spatial variation of the exchange potential results in an out-of-plane torque that increases rapidly with decreasing DW length. For long DWs, the Fermi level conduction channel anisotropy t…
Using the charge-conserving Floquet-Green function approach to open quantum systems driven by external time periodic potential, we analyze how spin current pumped (in the absence of any dc bias voltage) by the precessing magnetization of a ferromagnetic (F) layer is injected {\em laterally} into the interface with strong spin-orbit coupling (SOC) and converted into charge current flowing in the same direction. In the case of metallic interface with the Rashba SOC used in experiments [Nature Comm. {\bf 4}, 2944 (2013)], both spin $I^{S_α}$ and charge $I$ current flow within it where $I/I^{S_α} …
Recently, signatures of quantum anomalous Hall states with spontaneous ferromagnetism were observed in twisted bilayer graphenes (TBGs) near 3/4 filling [1, 2]. Importantly, it was demon-strated that an extremely small current can switch the direction of the magnetization. This offers the prospect of realizing low energy dissipation magnetic memories. However, the mechanism of the current-driven magnetization switching is poorly understood as the charge currents in graphene layers are generally believed to be non-magnetic. In this work, we demonstrate that, in TBGs, the twist-induced reduction…
We have considered the effect of different spin-orbit interaction mechanisms on the process of demagnetization under the influence of short-pulse lasers. All-optical magnetization reversal of perpendicularly magnetized thin films can occur if there are sufficient strong spin-Hall, skew scattering, and Rashba interactions. In the presence of spin-orbit interactions, the transient charge currents provide the generation of transverse-spin currents and accumulations, which eventually exert spin-transfer torque on the magnetization. By combining the optically excited spin-dependent diffusive transp…
We present a new setup to measure element-selective magnetization dynamics using the ALICE chamber (RSI \textbf{74}, 4048 (2003)) at the BESSY II synchrotron at the Helmholtz-Zentrum Berlin. A magnetic field pulse serves as excitation, and the magnetization precession is probed by element selective X-ray Resonant Magnetic Scattering (XRMS). With the use of single bunch generated x-rays a temporal resolution well below 100 ps is reached. The setup is realized in reflection geometry and enables investigations of thin films described here, multilayers, and laterally structured samples. The combin…
We present a microscopic calculation of magnetization damping for a magnetic "toy model." The magnetic system consists of itinerant carriers coupled antiferromagnetically to a dispersionless band of localized spins, and the magnetization damping is due to coupling of the itinerant carriers to a phonon bath in the presence of spin-orbit coupling. Using a mean-field approximation for the kinetic exchange model and assuming the spin-orbit coupling to be of the Rashba form, we derive Boltzmann scattering integrals for the distributions and spin coherences in the case of an antiferromagnetic exchan…
In this paper, we present the observation of the electric field control on the charge-ordering and metamagnetic transitions during the magnetization measurements in a single crystal of Pr0.6Ca0.4MnO3 (PCMO). We have demonstrated that the complete melting of charge ordering can be realized in a single crystal of PCMO by applying a voltage as small as 2.5 V, which otherwise needs magnetic fields in excess of 11 T. The maximum change in magnetization with applied voltage occurs across the charge-ordering transition temperature (TCO = 235 K). Even though the electric field does not seem to affect …
We theoretically study the axial current $\bm{j}_5$ (defined as the difference between the charge current with opposite chirality) in doped Weyl semimetal using a Green's function technique. We show that the axial current is controlled by the magnetization dynamics in a magnetic insulator attached to a Weyl semimetal. We find that the induced axial current can be detected by using ferromagnetic resonance or the inverse spin Hall effect and can be converted into charge current with no accompanying energy loss. These properties make Weyl semimetal advantageous for application to low-consumption …
The classical Bloch equations of spin magnetization transport is extended to fully time-dependent and highly-nonlinear nonequilibrium spin magnetization quantum distribution function transport (SMQDFT) equations. The relevant variables are the spinor correlation functions which separate into charge and spin magnetization distributions that becomes highly coupled in SMQDFT equa- tions. The leading terms consist of the Boltzmann kinetic equation with spin-orbit coupling in a magnetic eld together with spin-dependent scattering terms which contribute to the torque. These do not have analogue with…
We compute the Gilbert damping in (Ga,Mn)As based on the scattering theory of magnetization relaxation. The disorder scattering is included non-perturbatively. In the clean limit, the spin-pumping from the localized d-electrons to the itinerant holes dominates the relaxation processes. In the diffusive regime, the breathing Fermi-surface effect is balanced by the effects of interband scattering, which cause the Gilbert damping constant to saturate at around 0.005. In small samples, the system shape induces a large anisotropy in the Gilbert damping.
We have used numerical micromagnetics for the calculation of the magnetic (small-angle) neutron scattering cross section of nanocomposites. The novel aspect of our approach consists in the possibility to study the applied-field dependence of the individual contributions to the total magnetic scattering. Such a micromagnetic tool ideally complements neutron experiments in which one generally measures only a weighted sum of the Fourier components of the magnetization. The procedure furnishes unique and fundamental information regarding the magnetic microstructure and corresponding magnetic scatt…
By scattering theory we show that spin current noise in normal electric conductors in contact with nanoscale ferromagnets increases the magnetization noise by means of a fluctuating spin-transfer torque. Johnson-Nyquist noise in the spin current is related to the increased Gilbert damping due to spin pumping, in accordance with the fluctuation-dissipation theorem. Spin current shot noise in the presence of an applied bias is the dominant contribution to the magnetization noise at low temperatures.
The shot noise in a quantum ring, connected to leads, is studied in the presence of electron interactions in the sequential tunneling regime. Two qualitatively different noise correlations with distinctly different behaviors are identified and studied in a large range of parameters. Noise in the total current is due to the discreteness of the electron charge and can become super-Poissonian as result of electron interaction. The noise in the magnetization current is comparatively insensitive to the interaction but can be greatly enhanced if population inversion of the angular states is assumed.…
We propose a multiterminal nanostructure for electrical probing of the quantum spin Hall effect (QSHE) in two-dimensional (2D) topological insulators. The device consists of a ferromagnetic (FM) island with precessing magnetization that pumps (in the absence of any bias voltage) pure spin current symmetrically into the left and right adjacent 2D TIs modeled as graphene nanoribbons with the intrinsic spin-orbit (SO) coupling. The QSH regime of the six-terminal TI|FM|TI nanodevice, attached to two longitudinal and four transverse normal metal electrodes, is characterized by the SO-coupling-induc…
We investigate two schemes for pumping spin adiabatically from a ferromagnet through an interacting quantum dot into a normal lead, which exploit the possibility to vary in time the ferromagnet's magnetization, either its amplitude or its direction. For this purpose, we extend a diagrammatic real-time technique for pumping to situations in which the leads' properties are time dependent. In the first scheme, the time-dependent magnetization amplitude is combined with a time-dependent level position of the quantum dot to establish both a charge and a spin current. The second scheme uses a unifor…
We study electron tunneling through two small ferromagnetic dots. Quantum charge fluctuations and interdot coupling make each Coulomb peak of the conductance at zero interdot coupling split across. The interdot tunnel coupling is determined by the relative orientation of magnetizations of the two dots, leading to different splitting energies of the Coulomb peaks in parallel and antiparallel magnetization alignments. As a result, a very large tunneling magnetoresistance occurs near the Coulomb peaks, and its sign may be either positive or negative.
We describe spin transfer in a ferromagnet/normal metal/ferromagnet spin-valve point contact. Spin is transferred from the spin-polarized device current to the magnetization of the free layer by the mechanism of incoherent magnon emission by electrons. Our approach is based on the rate equation for the magnon occupation, using Fermi's golden rule for magnon emission and absorption and the non-equilibrium electron distribution for a biased spin valve. The magnon emission reduces the magnetization of the free layer. For anti-parallel alignment of the magnetizations of the layers and at a critica…
We develop a time-dependent nonequilibrium Green function (NEGF) approach to the problem of spin pumping by precessing magnetization in one of the ferromagnetic layers within F/I/F magnetic tunnel junctions (MTJs) or F/I/N semi-MTJs in the presence of intrinsic Rashba spin-orbit coupling (SOC) at the F/I interface or the extrinsic SOC in the bulk of F layers of finite thickness (F-ferromagnet; N-normal metal; I-insulating barrier). To express the time-averaged pumped charge current, or the corresponding dc voltage signal in open circuits that was measured in recent experiments on semi-MTJs [T.…
A Datta-Das spin field effect transistor is built of a one-dimensional weak link, with Rashba spin orbit interactions (SOI), which connects two magnetized reservoirs. The particle and spin currents between the two reservoirs are calculated to lowest order in the tunneling through the weak link and in the wide-band approximation, with emphasis on their dependence on the origins of the `bare' magnetizations in the reservoirs. The SOI is found to generate magnetization components in each reservoir, which rotate in the plane of the electric field (generating the SOI) and the weak link, only if the…
X ray resonant magnetic scattering (XRMS) was used to characterize the magnetization of 2D arrays of trilayer submicron magnets. The interpretation of the data required the understanding of the morphology of the magnets which was also deduced from the scattered intensity. The magnets consisted of two magnetostatically coupled ferromagnetic layers separated by a non-magnetic spacer. The scattered intensity from the disks resulted to be dependent on the disks surface curvature. This made the collected intensity at each Bragg reflection (BR) to be correlated to the reflected light from locations …
We present a phenomenological theory for coupled spin-charge dynamics in magnetic van der Waals heterostructures. The system studied consists of a layered antiferromagnet inserted into a capacitive vdW heterostructure. It has been recently demonstrated that charge doping in such layered antiferromagnets can modulate the strength, and even the sign, of exchange coupling between the layer magnetizations. This provides a mechanism for electrically generating magnetization dynamics. The central result we predict here is that the magnetization dynamics reciprocally results in inducing charge dynami…
We explore spin and charge transport phenomena in two dimensional electron gas in presence of Rashba spin-orbit coupling connected to two ideal Ferromagnetic leads. In particular we show through a combination of analytical and numerical calculation that the spin polarization which is transported depends on the Magnetization direction of ferromagnet even if the magnetization of both FM's are parallel.Conductance is also shown to be anisotropic. These anisotrpies present in spin and charge transport are a consequence of breaking of rotational invariance due to Rashba spin-orbit interaction and a…
In this paper, we investigate the two competing effects of strains and magnetic fields in single-layer graphene to explore its impact on various phenomena of quantum field theory, such as induced charge density, magnetic catalysis, symmetry breaking, dynamical mass generation and magnetization. We show that the interplay between strains and magnetic fields produces not only a breaking of chiral symmetry, as it happens in QED$_{2+1}$, but also parity and time-reversal symmetry breaking. The last two symmetry breakings are related to the dynamical generation of a Haldane mass term. We find that …
We introduce a highly sensitive and relatively simple technique to observe magnetization motion in single Ni nanoparticles, based on charge sensing by electron tunneling at millikelvin temperature. Sequential electron tunneling via the nanoparticle drives nonequilibrium magnetization dynamics, which induces an effective charge noise that we measure in real time. In the free spin diffusion regime, where the electrons and magnetization are in detailed balance, we observe that magnetic damping time exhibits a peak with the magnetic field, with a record long damping time of $\simeq 10$~ms.
Brillouin light scattering is an established technique to study magnons, the elementary excitations of a magnet. Its efficiency can be enhanced by cavities that concentrate the light intensity. Here, we theoretically study inelastic scattering of photons by a magnetic sphere that supports optical whispering gallery modes in a plane normal to the magnetization. Magnons with low angular momenta scatter the light in the forward direction with a pronounced asymmetry in the Stokes and the anti-Stokes scattering strength, consistent with earlier studies. Magnons with large angular momenta constitute…
We investigate transverse charge and spin dc supercurrents in a ferromagnet coupled to a superconductor where the ferromagnet has inhomogeneous magnetic structure. These transverse supercurrents arise from non-trivial structure of the magnetization. The magnetic structure manifested in the transverse charge supercurrent is essentially different from that discussed in the context of anomalous Hall effect, reflecting the disspationless nature of supercurrent. Possible candidates of magnetic structure to verify our prediction are also discussed.
A theory of spin-transport in hybrid normal metal - ferromagnetic electronic circuits is developed, taking into account non-collinear spin-accumulation. Spin-transport through resistive elements is described by 4 conductance parameters. Microscopic expression for these conductances are derived in terms of scattering matrices and explicitly calculated for simple models. The circuit theory is applied to 2-terminal and 3-terminal devices attached to ferromagnetic reservoirs.
We analyze the micromagnetics of short longitudinal modulations of a high-magnetization material in cylindrical nanowires made of a soft-magnetic material of lower magnetization such as permalloy, combining magnetic microscopy, analytical modeling, and micromagnetic simulations. The mismatch of magnetization induces curling of magnetization around the axis in the modulations, in an attempt to screen the interfacial magnetic charges. The curling angle increases with modulation length, until a plateau is reached with nearly full charge screening for a specific length scale~$Δ_\mathrm{mod}$, larg…
In metallic ferromagnets, the spin-transfer torque and spin-motive force are known to exhibit a reciprocal relationship. Recent experiments on ferromagnets with strong spin-orbit coupling have revealed a rich complexity in the interaction between itinerant charge carriers and magnetization, but a full understanding of this coupled dynamics is lacking. Here, we develop a general phenomenology of the two reciprocal processes of charge pumping by spin-motive forces and current-driven magnetization dynamics. The formalism is valid for spin-orbit coupling of any strength and presents a systematic s…
Materials with spin-momentum locked surface or interface states provide an interesting playground for studying physics and application of charge-spin current conversion. To characterize their non-equilibrium magnetic and transport properties in the presence of a time-dependent external magnetic field and a spin injection from a contact, we introduce three macroscopic variables: a vectorial helical magnetization, a scaler helical magnetization, and the conventional magnetization. We derive a set of closed dynamic equations for these variables by using the spinor Boltzmann approach with the coll…
We investigate cooling of a vibrational mode of a magnetic quantum dot by a spin-polarized tunneling charge current, exploiting the interaction between the magnetization and the vibration. The spin-polarized charge current polarizes the magnetic nanoisland, lowering its energy. Inevitable Ohmic energy losses due to the charge current flow will heat up the vibration. A small but finite coupling between the vibration and the local magnetic moment then permits an energy exchange, resulting in a lower energy, i.e., cooling, of the vibrational mode. We determine parameter regimes for the cooling of…
We study the effects of the coupling between magnetization dynamics and the electronic degrees of freedom in a heterostructure of a metallic nanomagnet with dynamic magnetization coupled with a superconductor containing a steady spin-splitting field. We predict how this system exhibits a non-linear spin torque, which can be driven either with a temperature difference or a voltage across the interface. We generalize this notion to arbitrary magnetization precession by deriving a Keldysh action for the interface, describing the coupled charge, heat and spin transport in the presence of a precess…
We extend a field theoretic approach for the investigation of the electronic charge-current density response of crystalline systems to arbitrary applied electromagnetic fields. The approach leads to the introduction of microscopic polarization and magnetization fields, as well as free charge and current densities, the dynamics of which are described by a lattice gauge theory. The spatial averages of such quantities constitute the fields of macroscopic electrodynamics. We implement this formalism to study the orbital electronic response of a class of insulators to applied uniform dc electric an…
The magnetization dynamics of a single domain ferromagnet in contact with a thermal bath is studied by scattering theory. We recover the Landau-Liftshitz-Gilbert equation and express the effective fields and Gilbert damping tensor in terms of the scattering matrix. Dissipation of magnetic energy equals energy current pumped out of the system by the time-dependent magnetization, with separable spin-relaxation induced bulk and spin-pumping generated interface contributions. In linear response, our scattering theory for the Gilbert damping tensor is equivalent with the Kubo formalism.
One of the key challenges in magnetism remains the determination of the nanoscopic magnetization profile within the volume of thick samples, such as permanent ferromagnets. Thanks to the large penetration depth of neutrons, magnetic small-angle neutron scattering (SANS) is a powerful technique to characterize bulk samples. The major challenge regarding magnetic SANS is accessing the real-space magnetization vector field from the reciprocal scattering data. In this letter, a fast iterative algorithm is introduced that allows one to extract the underlying two-dimensional magnetic correlation fun…
The prospect of combining the dissipationless nature of superconducting currents with the spin-polarization of magnetic materials is interesting with respect to exploring superconducting analogues of topics in spintronics. In order to accomplish this aim, it is pivotal to understand how spin-supercurrents interact dynamically with magnetization textures. We investigate the appearance of a spin-supercurrent and the resulting magnetization dynamics in a textured magnetic Josephson current by using three experimentally relevant models: i) a S/F/S junction with spin-active interfaces, ii) a S/F1/F…
The precessing magnetization of a magnetic islands coupled to a quantum spin Hall edge pumps charge along the edge. Conversely, a bias voltage applied to the edge makes the magnetization precess. We point out that this device realizes an adiabatic quantum motor and discuss the efficiency of its operation based on a scattering matrix approach akin to Landauer-B"uttiker theory. Scattering theory provides a microscopic derivation of the Landau-Lifshitz-Gilbert equation for the magnetization dynamics of the device, including spin-transfer torque, Gilbert damping, and Langevin torque. We find that …
We study dynamics of the magnetization coupled to the surface Dirac fermions of a three di- mensional topological insulator. By solving the Landau-Lifshitz-Gilbert equation in the presence of charge current, we find current induced magnetization dynamics and discuss the possibility of mag- netization reversal. The torque from the current injection depends on the transmission probability through the ferromagnet and shows nontrivial dependence on the exchange coupling. The mag- netization dynamics is a direct manifestation of the inverse spin-galvanic effect and hence another ferromagnet is unne…
Spin pumping by a moving magnetization gives rise to an electric voltage over a spin valve. Thermal fluctuations of the magnetization manifest themselves as increased thermal voltage noise with absorption lines at the ferromagnetic resonance frequency and/or zero frequency. The effect depends on the magnetization configuration and can be of the same order of magnitude as the Johnson-Nyquist thermal noise. Measuring colored voltage noise is an alternative to ferromagnetic resonance experiments for nano-scale ferromagnetic circuits.
We report the observation of efficient charge-to-spin conversion in the three-dimensional topological insulator (TI) Bi2Se3 and Ag bilayer by the spin-torque ferromagnetic resonance technique. The spin orbit torque ratio in the Bi2Se3/Ag/CoFeB heterostructure shows a significant enhancement as the Ag thickness increases to ~2 nm and reaches a value of 0.5 for 5 nm Ag, which is ~3 times higher than that of Bi2Se3/CoFeB at room temperature. The observation reveals the interfacial effect of Bi2Se3/Ag exceeds that of the topological surface states (TSS) in the Bi2Se3 layer and plays a dominant rol…
The interface-induced magnetization damping of thin ferromagnetic films in contact with normal-metal layers is calculated from first principles for clean and disordered Fe/Au and Co/Cu interfaces. Interference effects arising from coherent scattering turn out to be very small, consistent with a very small magnetic coherence length. Because the mixing conductances which govern the spin transfer are to a good approximation real valued, the spin pumping can be described by an increased Gilbert damping factor but an unmodified gyromagnetic ratio. The results also confirm that the spin-current indu…
We report nonlocal spin injection and detection experiments on mesoscopic Co-Al2O3-Cu spin valves. We have observed a temperature dependent asymmetry in the nonlocal resistance between parallel and antiparallel configurations of the magnetic injector and detector. This strongly supports the existence of a nonequilibrium resistance that depends on the relative orientation of the detector magnetization and the nonequilibrium magnetization in the normal metal providing evidence for increasing interface spin scattering with temperature.
