Generalization of Faraday's Law to include nonconservative spin forces

Enhanced emergent electromagnetic inductance in Tb5Sb3 due to highly disordered helimagnetism

In helimagnetic metals, ac current-driven spin motions can generate emergent electric fields acting on conduction electrons, leading to emergent electromagnetic induction (EEMI). Recent experiments reveal the EEMI signal generally shows a strongly current-nonlinear response. In this study, we investigate the EEMI of Tb5Sb3, a short-period helimagnet. Using small angle neutron scattering we show that Tb5Sb3 hosts highly disordered helimagnetism with a distribution of spin-helix periodicity. The current-nonlinear dynamics of the disordered spin helix in Tb5Sb3 indeed shows up as the nonlinear electrical resistivity (real part of ac resistivity), and even more clearly as a nonlinear and huge EEMI (imaginary part of ac resistivity) response. The magnitude of the EEMI reaches as large as several tens of μH for Tb5Sb3 devices on the scale of several tens of μm, originating to noncollinear spin textures possibly even without long-range helimagnetic order.

Emergent Inductance from Spin Fluctuations in Strongly Correlated Magnets

Recently, the intriguing phenomenon of emergent inductance has been theoretically proposed and experimentally observed in nanoscale spiral spin systems subjected to oscillating currents. Building upon these recent developments, we put forward the concept of emergent inductance in strongly correlated magnets in the normal state with spin fluctuations. It is argued that the inductance shows a positive peak at temperatures above the ordering temperature. As for the frequency dependence, in systems featuring a single-band structure or a gapped multiband, we observe a Drude-type inductance, while in gapless multiband systems, a non-Drude inductance with a sharp dip near zero frequency. These results offer valuable insights into the behavior of strongly correlated magnets and open up new possibilities for harnessing emergent inductance in practical applications.

Unified theory of spin and charge in a ferromagnet

We derive a unified theory of spin and charge degrees of freedom in a ferromagnet. The spin-transfer torque and spin electromotive force are examined from the coarse-grained perspective of collective coordinates. The resulting equations of motion reflect a balance of conservative, gyroscopic (Berry-phase), and dissipative forces. We then expand the space of collective coordinates by adding the electric charge. The adiabatic spin-transfer torque and spin electromotive force (emf) turn out to be a gyroscopic force; their nonadiabatic counterparts are a dissipative force.

Magnetoelectric effects in Josephson junctions

The review is devoted to the fundamental aspects and characteristic features of the magnetoelectric effects, reported in the literature on Josephson junctions (JJs). The main focus of the review is on the manifestations of the direct and inverse magnetoelectric effects in various types of Josephson systems. They provide a coupling of the magnetization in superconductor/ferromagnet/superconductor JJs to the Josephson current. The direct magnetoelectric effect is a driving force of spin torques acting on the ferromagnet inside the JJ. Therefore it is of key importance for the electrical control of the magnetization. The inverse magnetoelectric effect accounts for the back action of the magnetization dynamics on the Josephson subsystem, in particular, making the JJ to be in the resistive state in the presence of the magnetization dynamics of any origin. The perspectives of the coupling of the magnetization in JJs with ferromagnetic interlayers to the Josephson current via the magnetoelectric effects are discussed.

Theory of Emergent Inductance with Spin-Orbit Coupling Effects

We extend the theory of emergent inductance, which has recently been discovered in spiral magnets, to arbitrary magnetic textures by taking into account spin-orbit couplings arising in the absence of spatial inversion symmetry. We propose a new concept of spin-orbit emergent inductance, which can be formulated as originating from a dynamical Aharonov-Casher phase of an electron in ferromagnets. The spin-orbit emergent inductance universally arises in the coexistence of magnetism and the spin-orbit couplings, even with spatially uniform magnetization, allowing its stable operation in wide ranges of temperature and frequency. Revisiting the widely studied systems involving ferromagnets with spatial inversion asymmetry, with the new perspective offered by our work, will lead to opening a new paradigm in the study of spin-orbit physics and the spintronics-based power management in ultrawideband frequency range.

Spin Elastodynamic Motive Force

The spin-motive force (SMF) in a simple ferromagnetic monolayer caused by a surface acoustic wave is studied theoretically via spin-vorticity coupling (SVC). The SMF has two mechanisms. The first is the SVC-driven SMF, which produces the first harmonic electromotive force, and the second is the interplay between the SVC and the magnetoelastic coupling, which produces the dc and second harmonic electromotive forces. We show that these electric voltages induced by a Rayleigh-type surface acoustic wave can be detected in polycrystalline nickel. No sophisticated device structures, noncollinear magnetic structures, or strong spin-orbit materials are used in our approach. Consequently, it is intended to broaden the spectrum of SMF applications considerably.

Emergent electromagnetic induction beyond room temperature

Emergent electromagnetic induction based on electrodynamics of noncollinear spin states may enable dramatic miniaturization of inductor elements widely used in electric circuits, yet the research is still in its infancy and many issues must be resolved toward its application. One such problem is how to increase working temperature to room temperature, and possible thermal agitation effects on the quantum process of the emergent induction are unknown. We report here large emergent electromagnetic induction achieved around and above room temperature, making use of a few tens of micrometer-sized devices based on the high-temperature (up to 330 K) and short-period (≤ 3 nm) spin-spiral states of a metallic helimagnet. The observed inductance value L and its sign are observed to vary to a large extent, depending not only on the spin-helix structure controlled by temperature and applied magnetic field but also on the applied current density. The present finding on room-temperature operation and possible sign control of L may provide a step toward realizing microscale quantum inductors on the basis of emergent electromagnetism in spin-helix states.

Magnetic Skyrmion Materials

Skyrmion, a concept originally proposed in particle physics half a century ago, can now find the most fertile field for its applicability, that is, the magnetic skyrmion realized in helimagnetic materials. The spin swirling vortex-like texture of the magnetic skyrmion can define the particle nature by topology; that is, all the constituent spin moments within the two-dimensional sheet wrap the sphere just one time. Such a topological nature of the magnetic skyrmion can lead to extraordinary metastability via topological protection and the driven motion with low electric-current excitation, which may promise future application to spintronics. The skyrmions in the magnetic materials frequently show up as the crystal lattice form, e.g., hexagonal lattice, but sometimes as isolated or independent particles. These skyrmions in magnets were initially found in acentric magnets, such as chiral, polar, and bilayered magnets endowed with antisymmetric spin exchange interaction, while the skyrmion host materials have been explored in a broader family of compounds including centrosymmetric magnets. This review describes the materials science and materials chemistry of magnetic skyrmions using the classification scheme of the skyrmion forming microscopic mechanisms. The emergent phenomena and functions mediated by skyrmions are described, including the generation of emergent magnetic and electric field by statics and dynamics of skrymions and the inherent magnetoelectric effect. The other important magnetic topological defects in two or three dimensions, such as biskyrmions, antiskyrmions, merons, and hedgehogs, are also reviewed in light of their interplay with the skyrmions.

Emergent electromagnetic induction in a helical-spin magnet

An inductor, one of the most fundamental circuit elements in modern electronic devices, generates a voltage proportional to the time derivative of the input current¹. Conventional inductors typically consist of a helical coil and induce a voltage as a counteraction to time-varying magnetic flux penetrating the coil, following Faraday's law of electromagnetic induction. The magnitude of this conventional inductance is proportional to the volume of the inductor's coil, which hinders the miniaturization of inductors². Here, we demonstrate an inductance of quantum-mechanical origin³, generated by the emergent electric field induced by current-driven dynamics of spin helices in a magnet. In microscale rectangular magnetic devices with nanoscale spin helices, we observe a typical inductance as large as -400 nanohenry, comparable in magnitude to that of a commercial inductor, but in a volume about a million times smaller. The observed inductance is enhanced by nonlinearity in current and shows non-monotonous frequency dependence, both of which result from the current-driven dynamics of the spin-helix structures. The magnitude of the inductance rapidly increases with decreasing device cross-section, in contrast to conventional inductors. Our findings may pave the way to microscale, simple-shaped inductors based on emergent electromagnetism related to the quantum-mechanical Berry phase.

Generation of charge current from magnetization oscillation via the inverse of voltage-controlled magnetic anisotropy effect

It is well known that oscillating magnetization induces charge current in a circuit via Faraday's law of electromagnetic induction. New physical phenomena by which magnetization dynamics can produce charge current have gained considerable interest recently. For example, moving magnetization textures, such as domain walls, generates charge current through the spin-motive force. Here, we examine an entirely different effect, which couples magnetization and electric field at the interface between an ultrathin metallic ferromagnet and dielectric. We show that this coupling can convert magnetic energy into electrical energy. This phenomenon is the Onsager reciprocal of the voltage-controlled magnetic anisotropy effect. The effect provides a previously unexplored probe to measure the magnetization dynamics of nanomagnets.

Resistive State of Superconductor-Ferromagnet-Superconductor Josephson Junctions in the Presence of Moving Domain Walls

We describe resistive states of the system combining two types of orderings-a superconducting and a ferromagnetic one. It is shown that in the presence of magnetization dynamics such systems become inherently dissipative and in principle cannot sustain any amount of the superconducting current because of the voltage generated by the magnetization dynamics. We calculate generic current-voltage characteristics of a superconductor-ferromagnet-superconductor Josephson junction with an unpinned domain wall and find the low-current resistance associated with the domain wall motion. We suggest the finite slope of Shapiro steps as the characteristic feature of the regime with domain wall oscillations driven by the ac external current flowing through the junction.

Cooperative Charge Pumping and Enhanced Skyrmion Mobility

It is well known that moving magnetic textures may pump spin and charge currents along the direction of motion, a phenomenon called electronic pumping. Here, the electronic pumping arising from the steady motion of ferromagnetic skyrmions is investigated by solving the time evolution of the Schrödinger equation implemented on a tight-binding model with the statistical physics of the many-body problem. In contrast with rigid one-dimensional magnetic textures, we show that steadily moving magnetic skyrmions are able to pump large dc currents. This ability arises from their nontrivial magnetic topology, i.e., the coexistence of the spin-motive force and the topological Hall effect. Based on an adiabatic scattering theory, we compute the pumped current and demonstrate that it scales with the reflection coefficient of the conduction electrons against the skyrmion. In other words, in the semiclassical limit, reducing the size of the skyrmion and the width of the nanowire enhances this effect, making it scalable. We propose that such a phenomenon can be exploited in the context of racetrack devices, where the electronic pumping enhances the collective motion of the train of skyrmions.

Newton's second law in spin-orbit torque

Spin-orbit torque (SOT) refers to the excitation of magnetization dynamics via spin-orbit coupling (SOC) under the application of a charged current. In this work, we introduce a simple and intuitive description of the SOT in terms of spin force. In Rashba SOC system, the damping-like SOT can be expressed as [Formula: see text], in analogy to the classical torque-force relation, where R _c is the effective radius characterizing the Rashba splitting in the momentum space. As a consequence, the magnetic energy is transferred to the conduction electrons, which dissipates through Joule heating at a rate of [Formula: see text], with j _e being the applied current. Finally, we propose an experimental verification of our findings via measurement of the anisotropic magnetoresistance effect.

Energy Storage via Topological Spin Textures

We formulate an energy-storage concept based on the free energy associated with metastable magnetic configurations. Despite the active magnetic region of the battery being electrically insulating, it can sustain effective hydrodynamics of spin textures, whose conservation law is governed by topology. To illustrate the key physics and potential functionality, we focus here on the simplest quasi-one-dimensional case of planar winding of the magnetic order parameter. The energy is stored in the metastable winding number, which can be injected electrically by an appropriately tailored spin torque. Because of the nonvolatility and the endurance of magnetic systems, the injected energy can be stored essentially indefinitely, with the topological charge cycles that do not degrade over time.

Theory of the Topological Spin Hall Effect in Antiferromagnetic Skyrmions: Impact on Current-Induced Motion

We demonstrate that the nontrivial magnetic texture of antiferromagnetic Skyrmions (AFM Sks) promotes a nonvanishing topological spin Hall effect (TSHE) on the flowing electrons. This effect results in a substantial enhancement of the nonadiabatic torque and, hence, improves the Skyrmion mobility. This nonadiabatic torque increases when decreasing the Skyrmion size, and, therefore, scaling down results in a much higher torque efficiency. In clean AFM Sks, we find a significant boost of the TSHE close to the van Hove singularity. Interestingly, this effect is enhanced away from the band gap in the presence of nonmagnetic interstitial defects. Furthermore, unlike their ferromagnetic counterpart, the TSHE in AFM Sks increases with an increase in the disorder strength, thus opening promising avenues for materials engineering of this effect.

Magnetic Domain Walls as Hosts of Spin Superfluids and Generators of Skyrmions

A domain wall in a magnet with easy-axis anisotropy is shown to harbor spin superfluid associated with its spontaneous breaking of the U(1) spin-rotational symmetry. The spin superfluid is shown to have several topological properties, which are absent in conventional superfluids. First, the associated phase slips create and destroy Skyrmions to obey the conservation of the total Skyrmion charge, which allows us to use a domain wall as a generator and detector of Skyrmions. Second, the domain wall engenders the emergent magnetic flux for magnons along its length, which are proportional to the spin supercurrent flowing through it, and thereby provides a way to manipulate magnons. Third, the spin supercurrent can be driven by the magnon current traveling across it owing to the spin transfer between the domain wall and magnons, leading to the magnonic manipulation of the spin superfluid. The theory for superfluid spin transport within the domain wall is confirmed by numerical simulations.

Noncentrosymmetric Magnets Hosting Magnetic Skyrmions

The concept of a skyrmion, which was first introduced by Tony Skyrme in the field of particle physics, has become widespread in condensed matter physics to describe various topological orders. Skyrmions in magnetic materials have recently received particular attention; they represent vortex-like spin structures with the character of nanometric particles and produce fascinating physical properties rooted in their topological nature. Here, a series of noncentrosymmetric ferromagnets hosting skyrmions is reviewed: B20 metals, Cu₂ OSeO₃ , Co-Zn-Mn alloys, and GaV₄ S₈ , where Dzyaloshinskii-Moriya interaction plays a key role in the stabilization of skyrmion spin texture. Their topological spin arrangements and consequent emergent electromagnetic fields give rise to striking features in transport and magnetoelectric properties in metals and insulators, such as the topological Hall effect, efficient electric-drive of skyrmions, and multiferroic behavior. Such electric controllability and nanometric particle natures highlight magnetic skyrmions as a potential information carrier for high-density magnetic storage devices with excellent energy efficiency.

Enhanced Nonadiabaticity in Vortex Cores due to the Emergent Hall Effect

We present a combined theoretical and experimental study, investigating the origin of the enhanced nonadiabaticity of magnetic vortex cores. Scanning transmission x-ray microscopy is used to image the vortex core gyration dynamically to measure the nonadiabaticity with high precision, including a high confidence upper bound. We show theoretically, that the large nonadiabaticity parameter observed experimentally can be explained by the presence of local spin currents arising from a texture induced emergent Hall effect. This study demonstrates that the magnetic damping α and nonadiabaticity parameter β are very sensitive to the topology of the magnetic textures, resulting in an enhanced ratio (β/α>1) in magnetic vortex cores or Skyrmions.

Dynamic Feedback in Ferromagnet-Spin Hall Metal Heterostructures

In ferromagnet-normal-metal heterostructures, spin pumping and spin-transfer torques are two reciprocal processes that occur concomitantly. Their interplay introduces a dynamic feedback effect interconnecting energy dissipation channels of both magnetization and current. By solving the spin diffusion process in the presence of the spin Hall effect in the normal metal, we show that the dynamic feedback gives rise to (i) a nonlinear magnetic damping that is crucial to sustain uniform steady-state oscillations of a spin Hall oscillator at large angles and (ii) a frequency-dependent spin Hall magnetoimpedance that reduces to the spin Hall magnetoresistance in the dc limit.

A spin dynamics approach to solitonics

In magnetic materials a variety of non-collinear ground state configurations may emerge as a result of competition among exchange, anisotropy, and dipole-dipole interaction, yielding magnetic states far more complex than those of homogenous ferromagnets. Of particular interest in this study are particle-like configurations. These particle-like states, e.g., magnetic solitons, skyrmions, or domain walls, form a spatially localised clot of magnetic energy. In this paper we address topologically protected magnetic solitons and explore concepts that potentially might be relevant for logical operations and/or information storage in the rapidly advancing filed of solitonics (and skyrmionics). An ability to easily create, address, and manipulate such structures is among the prerequisite forming a basis of "-onics technology", and is investigated in detail here using numerical and analytical tools.

Intrinsic spin torque without spin-orbit coupling

We derive an intrinsic contribution to the non-adiabatic spin torque for non-uniform magnetic textures. It differs from previously considered contributions in several ways and can be the dominant contribution in some models. It does not depend on the change in occupation of the electron states due to the current flow but rather is due to the perturbation of the electronic states when an electric field is applied. Therefore it should be viewed as electric-field-induced rather than current-induced. Unlike previously reported non-adiabatic spin torques, it does not originate from extrinsic relaxation mechanisms nor spin-orbit coupling. This intrinsic non-adiabatic spin torque is related by a chiral connection to the intrinsic spin-orbit torque that has been calculated from the Berry phase for Rashba systems.

Magnetic nanoparticle thermometer: an investigation of minimum error transmission path and AC bias error

The signal transmission module of a magnetic nanoparticle thermometer (MNPT) was established in this study to analyze the error sources introduced during the signal flow in the hardware system. The underlying error sources that significantly affected the precision of the MNPT were determined through mathematical modeling and simulation. A transfer module path with the minimum error in the hardware system was then proposed through the analysis of the variations of the system error caused by the significant error sources when the signal flew through the signal transmission module. In addition, a system parameter, named the signal-to-AC bias ratio (i.e., the ratio between the signal and AC bias), was identified as a direct determinant of the precision of the measured temperature. The temperature error was below 0.1 K when the signal-to-AC bias ratio was higher than 80 dB, and other system errors were not considered. The temperature error was below 0.1 K in the experiments with a commercial magnetic fluid (Sample SOR-10, Ocean Nanotechnology, Springdale, AR, USA) when the hardware system of the MNPT was designed with the aforementioned method.

Spinmotive force due to motion of magnetic bubble arrays driven by magnetic field gradient

Interaction between local magnetization and conduction electrons is responsible for a variety of phenomena in magnetic materials. It has been recently shown that spin current and associated electric voltage can be induced by magnetization that depends on both time and space. This effect, called spinmotive force, provides for a powerful tool for exploring the dynamics and the nature of magnetic textures, as well as a new source for electromotive force. Here we theoretically demonstrate the generation of electric voltages in magnetic bubble array systems subjected to a magnetic field gradient. It is shown by deriving expressions for the electric voltages that the present system offers a direct measure of phenomenological parameter β that describes non-adiabaticity in the current induced magnetization dynamics. This spinmotive force opens a door for new types of spintronic devices that exploit the field-gradient.

Observation of a geometric Hall effect in a spinor Bose-Einstein condensate with a Skyrmion spin texture

For a spin-carrying particle moving in a spatially varying magnetic field, effective electromagnetic forces can arise due to the geometric phase associated with adiabatic spin rotation of the particle. We report the observation of a geometric Hall effect in a spinor Bose-Einstein condensate with a Skyrmion spin texture. Under translational oscillations of the spin texture, the condensate resonantly develops a circular motion in a harmonic trap, demonstrating the existence of an effective Lorentz force. When the condensate circulates, quantized vortices are nucleated in the boundary region of the condensate and the vortex number increases over 100 without significant heating. We attribute the vortex nucleation to the shearing effect of the effective Lorentz force from the inhomogeneous effective magnetic field.

Chirality from interfacial spin-orbit coupling effects in magnetic bilayers

As nanomagnetic devices scale to smaller sizes, spin-orbit coupling due to the broken structural inversion symmetry at interfaces becomes increasingly important. Here, we study interfacial spin-orbit coupling effects in magnetic bilayers using a simple Rashba model. The spin-orbit coupling introduces chirality into the behavior of the electrons and through them into the energetics of the magnetization. In the derived form of the magnetization dynamics, all of the contributions that are linear in the spin-orbit coupling follow from this chirality, considerably simplifying the analysis. For these systems, an important consequence is a correlation between the Dzyaloshinskii-Moriya interaction and the spin-orbit torque. We use this correlation to analyze recent experiments.

Magnetization relaxation and geometric forces in a Bose ferromagnet

We construct the hydrodynamic theory for spin-1/2 Bose gases at arbitrary temperatures. This theory describes the coupling between the magnetization and the normal and superfluid components of the gas. In particular, our theory contains the geometric forces on the particles that arise from their spin's adiabatic following of the magnetization texture. The phenomenological parameters of the hydrodynamic theory are calculated in the Bogoliubov approximation and using the Boltzmann equation in the relaxation-time approximation. We consider the topological Hall effect due to the presence of a Skyrmion, and show that this effect manifests itself in the collective modes of the system. The dissipative coupling between the magnetization and the normal component is shown to give rise to magnetization relaxation that is fourth order in spatial gradients of the magnetization direction.

Prediction of giant spin motive force due to Rashba spin-orbit coupling

Magnetization dynamics in a ferromagnet can induce a spin-dependent electric field through a spin motive force. Spin current generated by the spin-dependent electric field can in turn modify the magnetization dynamics through spin-transfer torque. While this feedback effect is usually weak and thus ignored, we predict that in Rashba spin-orbit coupling systems with a large Rashba parameter α(R), the coupling generates the spin-dependent electric field [±(α(R)m(e)/eħ)(z[over ^]×∂m/∂t)], which can be large enough to modify the magnetization dynamics significantly. This effect should be relevant for device applications based on ultrathin magnetic layers with strong Rashba spin-orbit coupling.

Current-induced torques in magnetic materials

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.

Time-domain observation of the spinmotive force in permalloy nanowires

The spinmotive force associated with a moving domain wall is observed directly in Permalloy nanowires using real time voltage measurements with proper subtraction of the electromotive force. Whereas the wall velocity exhibits nonlinear dependence on magnetic field, the generated voltage increases linearly with the field. We show that the sign of the voltage reverses when the wall propagation direction is altered. Numerical simulations explain quantitatively these features of spinmotive force and indicate that it scales with the field even in a field range where the wall motion is no longer associated with periodic angular rotation of the wall magnetization.

Continuous generation of spinmotive force in a patterned ferromagnetic film

We study, both experimentally and theoretically, the generation of a dc spinmotive force. By exciting a ferromagnetic resonance of a comb-shaped ferromagnetic thin film, a continuous spinmotive force is generated. Experimental results are well reproduced by theoretical calculations, offering a quantitative and microscopic understanding of this spinmotive force.

Single electron spintronics

Single electron electronics is now well developed, and allows the manipulation of electrons one-by-one as they tunnel on and off a nanoscale conducting island. In the past decade or so, there have been concerted efforts in several laboratories to construct single electron devices incorporating ferromagnetic components in order to introduce spin functionality. The use of ferromagnetic electrodes with a non-magnetic island can lead to spin accumulation on the island. On the other hand, making the dot also ferromagnetic introduces new physics such as tunnelling magnetoresistance enhancement in the cotunnelling regime and manifestations of the Kondo effect. Such nanoscale islands are also found to have long spin lifetimes. Conventional spintronics makes use of the average spin-polarization of a large ensemble of electrons: this new approach offers the prospect of accessing the quantum properties of the electron, and is a candidate approach to the construction of solid-state spin-based qubits.

Effects of mechanical rotation on spin currents

We study the Pauli-Schrödinger equation in a uniformly rotating frame of reference to describe a coupling of spins and mechanical rotations. The explicit form of the spin-orbit interaction (SOI) with the inertial effects due to the mechanical rotation is presented. We derive equations of motion for a wave packet of electrons in two-dimensional planes subject to the SOI. The solution is a superposition of two cyclotron motions with different frequencies and a circular spin current is created by the mechanical rotation. The magnitude of the spin current is linearly proportional to the lower cyclotron frequency.

Theory of electric polarization in multiorbital Mott insulators

The interaction between the electric field E and spins in multiorbital Mott insulators is studied theoretically. We find a generic coupling mechanism, which works for all crystal lattices and which does not involve relativistic effects. It couples E to the "internal" electric field e originating from the dynamical Berry phase. We discuss several effects of this interaction: (i) an unusual electron spin resonance, (ii) the displacement of spin textures in an applied electric field, and (iii) the resonant absorption of circularly polarized light by Skyrmions, magnetic bubbles, and magnetic vortices.

Intrinsic coupling between current and domain wall motion in (Ga,Mn)As

We consider current-induced domain wall motion and, the reciprocal process, moving domain wall-induced current. The associated Onsager coefficients are expressed in terms of scattering matrices. Uncommonly, in (Ga,Mn)As, the effective Gilbert damping coefficient alphaw and the effective out-of-plane spin-transfer torque parameter betaw are dominated by spin-orbit interaction in combination with scattering off the domain wall, and not scattering off extrinsic impurities. Numerical calculations give alphaw approximately 0.01 and betaw approximately 1 in dirty (Ga,Mn)As. The extraordinarily large betaw parameter allows experimental detection of current or voltage induced by domain wall motion in (Ga,Mn)As.

Generalization of the Landau-Lifshitz-Gilbert equation for conducting ferromagnets

We propose an extension of the Landau-Lifshitz-Gilbert (LLG) equation by explicitly including the role of conduction electrons in magnetization dynamics of conducting ferromagnets. The temporal and spatial dependent magnetization order parameter m(r,t) generates both electrical and spin currents that provide dissipation of the energy and angular momentum of the processing magnet. The resulting LLG equation contains highly spatial dependence of damping term and thus micromagnetic simulations based on the standard LLG equation should be reexamined for magnetization dynamics involving narrow domain walls and spin waves with short wavelengths.

Inverse spin Hall effect driven by spin motive force

The spin Hall effect is a phenomenon in which an electric field induces a spin Hall current. In this Letter, we examine the inverse effect that, in a ferromagnetic conductor, a charge Hall current is induced by a spin motive force, or a spin-dependent effective "electric" field E_{s}, arising from the time variation of magnetization texture. By considering skew-scattering and side-jump processes due to spin-orbit interaction at impurities, we obtain the Hall current density as sigma_{SH}n x E_{s}, where n is the local spin direction and sigma_{SH} is the spin Hall conductivity. The Hall angle due to the spin motive force is enhanced by a factor of P-2 compared to the conventional anomalous Hall effect due to the ordinary electric field, where P is the spin polarization of the current. The Hall voltage is estimated for a field-driven domain-wall oscillation in a ferromagnetic nanowire.

Universal electromotive force induced by domain wall motion

The electromotive force induced by a moving magnetic domain wall in a nanostrip has been calculated theoretically and detected experimentally. It is found that the emf depends only on the domain wall transformation frequency through a universal Josephson type relation, which is closely related to the topological nature of the domain wall. Our experimental measurements confirm the theoretical prediction.

Charge current driven by spin dynamics in disordered Rashba spin-orbit system

Pumping of charge current by spin dynamics in the presence of the Rashba spin-orbit interaction is theoretically studied. Considering a disordered electron, the exchange coupling and spin-orbit interactions are treated perturbatively. It is found that the dominant current induced by spin dynamics is interpreted as a consequence of the conversion from spin current via the inverse spin Hall effect. We also find that the current has an additional component from a fictitious conservative field. The results are applied to the case of a moving domain wall.