The precession of the magnetization of a ferromagnet is shown to transfer spins into adjacent normal metal layers. This "pumping" of spins slows down the precession corresponding to an enhanced Gilbert damping constant in the Landau-Lifshitz equation. The damping is expressed in terms of the scattering matrix of the ferromagnetic layer, which is accessible to model and first-principles calculations. Our estimates for permalloy thin films explain the trends observed in recent experiments. DOI: 10.1103/PhysRevLett.88.117601 PACS numbers: 76.50. +g, 72.25.Mk, 73.40. -c, 75.75. +a The magnetization dynamics of a bulk ferromagnet is well described by the phenomenological Landau-Lifshitz-where m is the magnetization direction, g is the gyromagnetic ratio, and H eff is the effective magnetic field including the external, demagnetization, and crystal anisotropy fields. The second term on the right-hand side of Eq. (1) was first introduced by Gilbert [1] and the dimensionless coefficient a is called the Gilbert damping constant. For a constant H eff and a 0, m precesses around the field vector with frequency v gH eff . When damping is switched on a . 0, the precession spirals down to a time independent magnetization along the field direction on a time scale of 1͞av. The study of a in bulk metallic ferromagnets has drawn significant interest over several decades. Notwithstanding the large body of both experimental [2] and theoretical [3] work, the damping mechanism in bulk ferromagnets is not yet fully understood.The magnetization dynamics in thin magnetic films and microstructures is technologically relevant for, e.g., magnetic recording applications at high bit densities. Recent interest by the basic physics community in this topic is motivated by the spin-current induced magnetization switching in layered structures [4 -6]. The Gilbert damping constant was found to be 0.04 , a , 0.22 for Cu-Co and Pt-Co [5,7], which is considerably larger than the bulk value a 0 ഠ 0.005 in Co [6,8]. Previous attempts to explain the additional damping in magnetic multilayer systems involved an enhanced electron-magnon scattering near the interface [9] and other mechanisms [10], both in equilibrium and in the presence of a spin-polarized current.In this Letter we propose a novel mechanism for the Gilbert damping in normal-metal-ferromagnet ͑N-F͒ hybrids. According to Eq. (1), the precession of the magnetization direction m is caused by the torque~m 3 H eff . This is physically equivalent to a volume injection of what we call a "spin current." The damping occurs when the spin current is allowed to leak into a normal metal in contact with the ferromagnet. Our mechanism is thus the inverse of the spin-current induced magnetization switching: A spin current can exert a finite torque on the ferromagnetic order parameter, and, vice versa, a moving magnetization vector loses torque by emitting a spin current. In other words, the magnetization precession acts as a spin pump which transfers angular momentum from the ferromagnet into the norma...

In this paper, we study transport properties of non-equilibrium systems under the application of light in many-terminal measurements, using the Floquet picture. We propose and demonstrate that the quantum transport properties can be controlled in materials such as graphene and topological insulators, via the application of light. Remarkably, under the application of off-resonant light, topological transport properties can be induced; these systems exhibits quantum Hall effects in the absence of a magnetic field with a near quantization of the Hall conductance, realizing so-called quantum Hall systems without Landau levels first proposed by Haldane.

The magnetization of a magnetic material can be reversed by using electric currents that transport spin angular momentum. In the reciprocal process a changing magnetization orientation produces currents that transport spin angular momentum. Understanding how these processes occur reveals the intricate connection between magnetization and spin transport, and can transform technologies that generate, store or process information via the magnetization direction. Here we explain how currents can generate torques that affect the magnetic orientation and the reciprocal effect in a wide variety of magnetic materials and structures. We also discuss recent state-of-the-art demonstrations of current-induced torque devices that show great promise for enhancing the functionality of semiconductor devices.

We formulate a theory of spin dependent transport in an electronic circuit involving ferromagnetic elements with noncollinear magnetization which is based on the conservation of spin and charge current. The theory considerably simplifies the calculation of the transport properties of complicated ferromagnet-normal metal systems. We illustrate the theory by considering a novel three-terminal device.PACS numbers: 72.10. Bg, 75.70.Pa Electron transport in hybrid systems involving ferromagnetic and normal metals has been shown to exhibit new phenomena due to the interplay between spin and charge. The giant magnetoresistance (GMR) effect in metallic magnetic multilayers is a result of spin dependent scattering [1]. The manganese oxides exhibit a colossal magnetoresistance [2] due to a ferromagnetic phase transition. The dependence of the current on the relative angle between the magnetization directions has been reported in transport through tunnel junctions between ferromagnetic reservoirs [3]. Transport involving ferromagnets with noncollinear magnetizations has also been studied theoretically in Ref. [4] Johnson and Silsbee demonstrated that spin dependent effects are also important in systems with more than two terminals [5]. Their ferromagnetic-normal-ferromagnetic (F-N-F ) device manifests a transistor effect that depends on the relative orientation of the magnetization directions. Recently, another three-terminal spin electronics device was realized; a ferromagnetic single-electron transistor [6]. In this case the current depends on the relative orientation of the magnetization of the source, the island and the drain, and of the electrostatic potential of the island tuned by a gate voltage [7].These examples illustrate that devices with ferromagnetic order deserve a thorough theoretical investigation. Inspired by the circuit theory of Andreev reflection [8], we present a finite-element theory for transport in hybrid ferromagnetic-normal metal systems based on the conservation of charge and spin current. We demonstrate that spin transport can be understood in terms of four generalized conductances for each contact between a ferromagnet and a normal metal. The relations between these conductance parameters and the microscopic details of the contacts are derived and calculated for diffuse, tunnel, and ballistic contacts. Finally, we illustrate the theory by computing the current through a novel three-terminal device.Let us first explain the basic idea of the finite-element theory of spin transport. The system can be divided into (normal or ferromagnetic) "nodes," where each node is characterized by the appropriate generalization of the distribution function, viz. a 2 3 2 distribution matrix in spin space. The nodes are connected to each other and to the reservoirs by "contacts" which limit the total conductance but are arbitrary otherwise. The charge and spin current through the contacts is related to the distribution matrices of the adjacent nodes. Provided these relations are known, we can solve for the 2 3 ...

We study the magnetization dynamics in thin ferromagnetic films and small ferromagnetic particles in contact with paramagnetic conductors. A moving magnetization vector causes ''pumping'' of spins into adjacent nonmagnetic layers. This spin transfer affects the magnetization dynamics similar to the Landau-LifshitzGilbert phenomenology. The additional Gilbert damping is significant for small ferromagnets, when the nonmagnetic layers efficiently relax the injected spins, but the effect is reduced when a spin accumulation build-up in the normal metal opposes the spin pumping. The damping enhancement is governed by ͑and, in turn, can be used to measure͒ the mixing conductance or spin-torque parameter of the ferromagnet-normal-metal interface. Our theoretical findings are confirmed by agreement with recent experiments in a variety of multilayer systems.

Spin pumping and spin-transfer torques are two reciprocal phenomena widely studied in ferromagnetic materials. However, pumping from antiferromagnets and its relation to current-induced torques have not been explored. By calculating how electrons scatter off a normal metal-antiferromagnetic interface, we derive pumped spin and staggered spin currents in terms of the staggered field, the magnetization, and their rates of change. For both compensated and uncompensated interfaces, spin pumping is of a similar magnitude as in ferromagnets with a direction controlled by the polarization of the driving microwave. The pumped currents are connected to current-induced torques via Onsager reciprocity relations. PACS numbers: 76.50.+g, 72.25.Mk, 75.50.Ee A major task of spintronics is understanding the mutual control of spin transport and magnetic properties. This inspires intense studies in fundamental physics which opens new avenues in, e.g., magnetic recording technologies. A new direction in this field aims at harnessing spin dynamics in materials with a vanishing magnetization, such as antiferromagnets (AFs) with compensated magnetic moments on an atomic scale. As compared to ferromagnets (Fs), AFs operate at a much higher frequency in the Tera Hertz (THz) ranges [1-3] which makes it possible to perform ultra fast information processing and communication. At the same time, since there are no stray fields in AFs, they are more robust against magnetic perturbations, an attractive feature of AFs for use in next-generation data storage material. However, to build a viable magnetic device using AF, it is vital to find observable effects induced by the rotation of the order parameter. The recent discovery of tunneling anisotropic magnetoresistance in AF may potentially fulfill this demand [4,5]. Nevertheless, in such experiments, the AF is dragged passively by an adjacent F, which is rotated by a magnetic field. Will an AF interact directly with (spin) currents without the inclusion of a F or a magnetic field?Partial answers are available from recent investigations. While the observation of a current-induced change of the exchange bias on a F|AF interface indicates spintransfer torques (STTs) in AFs [6,7], theoretical models of STT have been developed in a variety of contexts [8][9][10][11][12][13][14][15]. To achieve a general understanding of spintronics based on AFs, we recall a crucial insight from well-established ferromagnetic spintronics: STT and spin pumping are two reciprocal processes intrinsically connected [16][17][18]; they are derivable from each other [19]. To the best our knowledge, all existing studies on AF have focused on STT, whereas spin pumping has received no attention because it seems to be naively believed that the vanishing magnetization spoils any spin pumping in an AF.Spin pumping is the generation of spin currents by the precessing magnetization [18,19]. When the magnetization m of a F varies in time, a spin current proportional to m ×ṁ is pumped into an adjacent normal (N) metal. In contrast, m...

Precessing ferromagnets are predicted to inject a spin current into adjacent conductors via Ohmic contacts, irrespective of a conductance mismatch with, for example, doped semiconductors. This opens the way to create a pure spin source spin battery by the ferromagnetic resonance. We estimate the spin current and spin bias for different material combinations.Comment: The estimate for the magnitude of the spin bias is improved. We find that it is feasible to get a measurable signal of the order of the microwave frequency already for moderate rf intensitie

A long-ranged dynamic interaction between ferromagnetic films separated by normal-metal spacers is reported, which is communicated by nonequilibrium spin currents. It is measured by ferromagnetic resonance (FMR) and explained by an adiabatic spin-pump theory. In FMR the spin-pump mechanism of spatially separated magnetic moments leads to an appreciable increase in the FMR line width when the resonance fields are well apart, and results in a dramatic line-width narrowing when the FMR fields approach each other.PACS numbers: 75.40. Gb,75.70.Cn,76.50.+g,75.30.Et The giant magnetoresistance [1] accompanying realignment of magnetic configurations in metallic multilayers by an external magnetic field is routinely employed in magnetic read heads and is essential for high-density nonvolatile magnetic random-access memories. These typically consist of ferromagnetic/normal/ferromagnetic (F/N/F ) metal hybrid structures, i.e., magnetic bilayers which are an essential building block of the so called spin valves. The static Ruderman-Kittel-Kasuya-Yosida (RKKY) interlayer exchange between ferromagnets in magnetic multilayers [2] is suppressed in these devices by a sufficiently thick nonmagnetic spacer N or a tunnel barrier. The interest of the community shifts increasingly from the static to the dynamic properties of the magnetization [3]. This is partly motivated by curiosity, partly by the fact that the magnetization switching characteristics in memory devices is a real technological issue. A good grasp of the fundamental physics of the magnetization dynamics becomes of essential importance to sustain the exponential growth of device performance factors.In this Letter we study the largely unexplored dynamics of magnetic bilayers in a regime when there is no discernible static interaction between the magnetization vectors. Surprisingly, the magnetizations still turn out to be coupled, which we explain by emission and absorption of nonequilibrium spin currents. Under special conditions the two magnetizations are resonantly coupled by spin currents and carry out a synchronous motion, quite analogous to two connected pendulums. This dynamic interaction is an entirely new concept and physically very different from the static RKKY coupling. E.g., the former does not oscillate as a function of thickness and its range is exponentially limited by the spin-flip relaxation length of spacer layers and algebraically by the elastic mean free path. This coupling can have profound effects on magnetic relaxation and switching behavior in hybrid structures and devices.The unit vector m = M/M of the magnetization M(t) of a ferromagnet changes its direction in the presence of a noncollinear magnetic field. The motion of m in a single domain is described by the Landau-Lifshitz-Gilbert (LLG) equationwith γ being the absolute value of the gyromagnetic ratio. The first term on the right-hand side represents the torque induced by the effective magnetic field H eff = −∂F/∂M, where the free-energy functional F [M] consists of the Zeeman energy, ma...