Spin Motive Force Research Articles

Emergent magneto-inductance effect in permalloy thin films on flexible polycarbonate substrates at room temperature

Emergent inductance has attracted significant interest for its relevance in both interesting fundamental physics and practical applications in magnetic devices that demand miniaturization without compromising inductance. In this Letter, we report the discovery of a stepwise magnetic field-induced emergent magneto-inductance (EML) effect in Permalloy (Py) thin films deposited on polycarbonate (PC) substrates. Remarkably, Py/PC devices exhibit an exceptionally large inductance variation exceeding 1 μH at room temperature, and intriguingly, a sign reversal of inductance occurs around the zero magnetic field. The dependencies of the EML effect on frequency, step magnetic field changes, and film width can be explained from the theory based on the spin motive force driven by transient domain wall motion. This study opens up exciting avenues for advancing our understanding of emergent inductance in fundamental physics and paves the way for practical applications in flexible magnetic devices.

Symmetry of the emergent inductance tensor exhibited by magnetic textures

Metals hosting gradually varying spatial magnetic textures are attracting attention as a new class of inductors. Under the application of an alternating current, the spin-transfer-torque effect induces oscillating dynamics of the magnetic texture, which subsequently yields the spin-motive force as a back action, resulting in an inductive voltage response. In general, a second-order tensor representing a material’s response can have an off-diagonal component. However, it is unclear what symmetries the emergent inductance tensor has and also which magnetic textures can exhibit a transverse inductance response. Here, we reveal both analytically and numerically that the emergent inductance tensor should be a symmetric tensor in the so-called adiabatic limit. By considering this symmetric tensor in terms of symmetry operations that a magnetic texture has, we further characterize the magnetic textures in which the transverse inductance response can appear. This finding provides a basis for exploring the transverse response of emergent inductors, which has yet to be discovered.

Spin motive force by the momentum-space Berry phase in magnetic Weyl semimetals

We show that the magnetic precession of ferromagnetic moments in a noncentrosymmetric magnetic Weyl semimetal induces an electric current through a mechanism analogous to the adiabatic charge pumping. The current is a consequence of a Berry phase in the momentum space resulting from the circular motion of Weyl nodes induced by the precession. This mechanism resembles the Faraday effect, namely, induced magnetic field by circular electric current. The circular motion of Weyl nodes induces magnetic charge current in the momentum space, which results in a Berry phase that describes the adiabatic pump. Experimentally, this phenomenon is similar to spin motive force, which is an electric current induced by magnetic precision in the presence of the spatial gradient of magnetization. However, unlike the conventional spin motive force, this current occurs without a magnetization gradient. The result demonstrates a nontrivial interplay between the topological electronic state and magnetic dynamics.

Thermoelectric effect of a skyrmion crystal confined in a magnetic disk

We theoretically propose that an electric voltage can be generated by a thermal gradient with a rotating skyrmion crystal confined in a magnetic disk. We find that the rotation of a skyrmion crystal induced by diffusive thermal magnon currents in the presence of the temperature gradient gives rise to spinmotive forces in the radial direction through coupling to conduction-electron spins. The amplitude of the generated spinmotive force is larger for a larger temperature gradient at a lower temperature. The proposed phenomenon can be exploited as spintronics-based thermoelectric devices to realize the conversion of heat to electricity.

Spin motive force induced by parametric excitation

Spin motive force generated by parametrically excited magnetization dynamics is numerically investigated. We calculate spin motive force in a permalloy disk under an ac magnetic field with twice the ferromagnetic resonance frequency parallel to the static magnetic field based on the Landau–Lifshitz–Gilbert equation. We found that large spin motive force originating from standing spin waves driven by parametric excitation appears in the system. The observed time dependence of the voltage shows a dc voltage with an ac component oscillating with twice of the resonance frequency. The estimated amplitude of the voltage due to the spin motive force is ∼μV. We also investigate spin motive force driven by different modes of standing spin waves. Our numerical results extend the way to generate spin motive force by making use of the magnetization dynamics with the steep spatial modulation created by nonlinear spin waves excitation, without a non-uniform magnetization structure such as a conventional magnetic domain wall and a vortex.

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.

(Un)balanced Holographic Superconductors with Electric and Spin Motive Force Coupling

We study holographic phase transitions in (2+1) dimensions that possess interacting phases which result from a direct coupling between the two U(1) gauge fields. This can be interpreted as a non-minimal interaction between the electric and spin motive forces of the dual model. We first present a new analytical solution of the Einstein-Maxwell equations that describes a black hole with charge non-equivalent to the sum of the asymptotic charges of the two U(1) gauge fields and briefly discuss formation of uncharged scalar hair on this solution. We then study the formation of charged scalar hair on an uncharged black hole background and discuss the dual description of balanced as well as unbalanced superconductors.

Hydrodynamic theory of vorticity-induced spin transport

Electron spin transport in a disordered metal is theoretically studied from the hydrodynamic viewpoint focusing on the role of electron vorticity. The spin-resolved momentum flux density of electrons is calculated taking account of the spin-orbit interaction and uniform magnetization, and the expression for the spin motive force is obtained as the linear response to a driving electric field. It is shown that the spin-resolved momentum flux density and motive force are characterized by troidal moments expressed as vector products of the applied external electric field and the spin polarization and/or magnetization. The spin-vorticity and magnetization-vorticity couplings studied recently are shown to arise from the toridal moments contribution to the momentum flux density. Spin motive force turns out to have a nonconservative contribution besides the conventional conservative one due to the spin-vorticity coupling. Spin accumulation induced by an electric field is calculated to demonstrate the direct relation between vorticity and induced spin, and the spin Hall effect is interpreted as due to the spin-vorticity coupling. The spin-vorticity coupling is shown to give rise to a vorticity-induced torque and a spin relaxation. The vorticity-induced torque is a linear effect of the spin-orbit interaction and is expected to be larger than the second-order torques such as nonadiabatic ($\beta$) current-induced torque due to magnetization structure. The intrinsic inverse spin Hall effect is argued to correspond to the antisymmetric components of the momentum flux density in the hydrodynamic context.

Spin-Motive Force in Ferromagnetic and Ferrimagnetic Materials

The magnetization dynamics of nonuniform magnetic structures induce the spin-dependent force acting on the conduction electrons via the s–d coupling. This emergent electric field, the so-called spi...

Intrinsic and extrinsic tunability of Rashba spin-orbit coupled emergent inductors

The emergent induction of spiral magnets that was proposed [Jpn. J. Appl. Phys. 58, 120909 (2019)] and recently demonstrated [Nature 586, 232 (2020)] is shown to be further extended by a comprehensive treatment of the Rashba spin-orbit coupling and the electron spin relaxation that affect the underlying processes of spin-transfer torque and spinmotive force. Within adiabatic approximation, we show that the output voltages are widely altered intrinsically via the Rashba effect whereas extrinsically via the nonadiabatic correction due to the spin relaxation and sample disorder. The findings respectively clarify the origins for the amplitude modulation and sign change of the emergent inductance with tunability by electrical gating and careful sample preparation.

Effect of heating on spin-motive force induced by magnetic resonance

The spin-motive force (SMF), which is induced by the dynamics of non-uniform magnetic states having spin chirality, corresponds to the spin version of the electromotive force in Faraday's law of induction. Because magnetic dynamics produce heat through the damping effect, the detected SMF may include the thermoelectromotive force (TEMF) induced by heat, which is disadvantageous. In this study, we investigate the electrode-material dependence of the SMF induced by magnetic resonance and reveal that the heating is lower than 1 K at the most and that the SMF barely includes the TEMF. Moreover, we extract the SMF to remove the slight contribution of the TEMF.

Observation of spin-motive force in ferrimagnetic GdFeCo alloy films

Non-uniform magnetic structures produce emergent electromagnetic phenomena such as the topological Hall effect and the spin-motive force (SMF). The experimental reports on the SMF, however, are very few, and the relationship between the SMF and material parameters is still unclear. In this study, we investigated the SMF in ferrimagnetic GdFeCo alloy films using the spin-torque-induced ferromagnetic resonance method and clarified the relationship. The amplitude of the detected SMF becomes larger than that of the transition metal alloy FeCo by Gd doping and reaches the maximum near a Gd composition of the boundary between in-plane and perpendicularly magnetized films. According to the analytical calculation, the enhancement is related to the trajectory of the magnetization precession. Moreover, we find that the SMF induced by the magnetic resonance is inversely proportional to the square of the damping constant.

Spinmotive force in the out-of-plane direction generated by spin wave excitations in an exchange-coupled bilayer element

Spinmotive force in the out-of-plane direction generated by spin wave excitations in an exchange-coupled bilayer element

Skyrmion-generated spinmotive forces in inversion broken ferromagnets

We present an analytical study on the spinmotive force (SMF) generated by translational motion of magnetic skyrmion. A SMF refers to an electrical voltage induced by dynamical magnetic textures, which reflects the spatiotemporal variation of the magnetization. The dynamics of a skyrmion thus can be detected by a SMF measurement, which may play an important role in future skyrmion-based technologies. We find the dependence of the SMF on skyrmion structure (e.g., skyrmion or anti-skyrmion, N\'{e}el or Bloch type, and the polarity of the skyrmion core) and Rashba and Dresselhaus spin-orbit couplings (SOCs). To this end, we derive explicit formulae for the spin-dependent electric fields originating from the two SOCs. Our findings offer a comprehensive understanding of the phenomenon and an estimation of the electrical voltage signal associated with a moving skyrmion for a given experiment.

DC spinmotive force from microwave-active resonant dynamics of a skyrmion crystal under a tilted magnetic field

We theoretically show that a temporally oscillating spin-driven electromotive force or voltage with a large DC component can be generated by exciting microwave-active spin-wave modes of a skyrmion crystal confined in a quasi two-dimensional magnet under a tilted magnetic field. The DC component and the AC amplitude of the oscillating electric voltage is significantly enhanced when the microwave frequency is tuned to an eigenfrequency of the peculiar spin-wave modes of the skyrmion crystal called ``rotation modes" and ``breathing mode", whereas the sign of the DC component depends on the microwave polarization and on the spin-wave mode. These results provide an efficient means to convert microwaves to a DC electric voltage by using skyrmion-hosting magnets and to switch the sign of the voltage via tuning the microwave frequency, which are important capabilities for spintronic devices.

Time-retarded damping and magnetic inertia in the Landau-Lifshitz-Gilbert equation self-consistently coupled to electronic time-dependent nonequilibrium Green functions

The conventional Landau-Lifshitz-Gilbert (LLG) equation is a widely used tool to describe dynamics of local magnetic moments, viewed as classical vectors of fixed length, with their change assumed to take place simultaneously with the cause. Here we demonstrate that recently developed [M. D. Petrovi\'{c} {\em et al.}, {\tt arXiv:1802.05682}] self-consistent coupling of the LLG equation to time-dependent quantum-mechanical description of electrons microscopically generates time-retarded damping in the LLG equation described by a memory kernel which is also spatially dependent. For sufficiently slow dynamics of local magnetic moments, the memory kernel can be expanded to extract the Gilbert damping (proportional to first time derivative of magnetization) and magnetic inertia (proportional to second time derivative of magnetization) terms whose parameters, however, are time-dependent in contrast to time-independent parameters used in the conventional LLG equation. We use examples of single or multiple magnetic moments precessing in an external magnetic field, as well as field-driven motion of a magnetic domain wall (DW), to quantify the difference in their time evolution computed from conventional LLG equation vs. TDNEGF+LLG quantum-classical hybrid approach. The faster DW motion predicted by TDNEGF+LLG approach reveals that important quantum effects, stemming from finite amount of time which it takes for conduction electron spin to react to the motion of classical local magnetic moments, are missing from conventional classical micromagnetics simulations. We also demonstrate large discrepancy between TDNEGF+LLG-computed numerically exact and, therefore, nonperturbative result for charge current pumped by a moving DW and the same quantity computed by perturbative spin motive force formula combined with the conventional LLG equation.

Microscopic theory of magnon-drag electron flow in ferromagnetic metals

A temperature gradient applied to a ferromagnetic metal induces not only independent flows of electrons and magnons but also drag currents because of their mutual interaction. In this paper, we present a microscopic study of the electron flow induced by the drag due to magnons. The analysis is based on the $s$-$d$ model, which describes conduction electrons and magnons coupled via the $s$-$d$ exchange interaction. Magnetic impurities are introduced in the electron subsystem as a source of spin relaxation. The obtained magnon-drag electron current is proportional to the entropy of magnons and to $\alpha - \beta$ (more precisely, to $1 - \beta/\alpha$), where $\alpha$ is the Gilbert damping constant and $\beta$ is the dissipative spin-transfer torque parameter. This result almost coincides with the previous phenomenological result based on the magnonic spin-motive forces, and consists of spin-transfer and momentum-transfer contributions, but with a slight disagreement in the former. The result is interpreted in terms of the nonequilibrium spin chemical potential generated by nonequilibrium magnons.

Nonlocal spin-charge conversion via Rashba spin-orbit interaction

We show theoretically that conversion between spin and charge by spin-orbit interaction in metals occurs even in a non-local setup where magnetization and spin-orbit interaction are spatially separated if electron diffusion is taken into account. Calculation is carried out for the Rashba spin-orbit interaction treating the coupling with a ferromagnet perturbatively. The results indicate the validity of the concept of effective spin gauge field (spin motive force) in the non-local configuration. The inverse Rashba-Edelstein effect observed for a trilayer of a ferromagnet, a normal metal and a heavy metal can be explained in terms of the non-local effective spin gauge field.

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.

Spin-motive force due to domain-wall motion in the presence of Dzyaloshinskii-Moriya interaction

We theoretically demonstrate that the presence of Dzyaloshinskii-Moriya Interaction (DMI) can lead to enhancement of the spin-motive force (SMF) arising due to field-induced ferromagnetic domain wall motion. A SMF refers to an electric voltage induced by dynamical magnetic textures, which reflects the temporal and spatial variations of the magnetization. A DMI can introduce extra spatial rotation of the magnetization in the domain wall region, which turns out to cause the enhancement of the SMF. We derive an expression for the SMF, and examine the field- and DMI-dependences of the SMF. We find that the SMF can be amplified by up to an order of magnitude in the low field regime, where the external field is lower than the so-called Walker breakdown field.