Spin-vorticity Coupling Research Articles

Surface acoustic wave-spin wave coupling and magneto-acoustic nonreciprocal devices

Surface acoustic wave (SAW) is a new means of exciting and controlling spin wave (SW), which has not only high excitation efficiency, but also long transmission length up to millimeter order. Based on the SAW-SW coupling (phonon-magnon coupling), a wide variety of new devices and applications such as high-sensitivity weak magnetic field sensors, energy-efficient spintronic devices, solid-state acoustic isolators, and nonreciprocal phase shifters, have been realized. Therefore, it is of great value to study the physical mechanism of magneto-acoustic coupling, develop new magneto-acoustic coupling effects, and improve the efficiency of magneto-acoustic coupling. In this work, different types of physical mechanisms of magneto-acoustic coupling are reviewed. The effective driven magnetic fields of magnetoelastic coupling, spin-vorticity coupling (including injection of alternating spin current from a non-magnetic layer and Barnett effect inside magnetic material itself), and magneto-rotation coupling under different modes of SAW excitation are compared. The angular dependence of these driven fields and the frequency dependence of the corresponding power absorption are discussed, which provides theoretical support for distinguishing and utilizing various magneto-acoustic coupling in practical applications. In addition, we also introduce two methods to realize nonreciprocal SAW transmission by magneto-acoustic coupling, including the helicity mismatch effect and nonreciprocal spin-wave dispersion magnetic structures, and discuss their physical mechanisms as well as advantages and disadvantages. For such magneto-acoustic nonreciprocal devices, the properties of higher isolation, lower insertion loss and wider bandwidth are always desired. In order to improve the properties of the devices, it is important to find magnetic structures with stronger SW nonreciprocity, reduce the insertion loss introduced by magnetic structure, and fully consider the effective driven field characteristics of different modes of SAW. We hope that this review can serve as a guide for future design and development of solid acoustic isolators and circulators in the RF and microwave frequency bands.

Anomalous Hall effect in naturally oxidized normal-metal Al/Cu double films

An unexpectedly larger current-induced spin–orbit torque in oxidized Cu (CuO x )/ferromagnet (FM) than heavy-metal/FM has recently attracted intense attention in spintronic studies. Although the two mechanisms, interfacial Rashba Edelstein effect and spin-vorticity coupling, have been put forward based on the two different conductive features of CuO x , i.e. electrical insulator and gradient of electrical mobility, the detailed investigation of transport of CuO x is still lacking. Here we experimentally report the positive and negative anomalous Hall effect (AHE) in naturally oxidized normal-metal Al/Cu double films. We found that the onset temperature of AHE corresponds to magnetic transition temperature of CuO x . Furthermore, by comparing Hall resistance of the crystalline and amorphous Cu/Al double films, we identify that the positive anomalous Hall resistance attributes to magnetic moment of CuO x itself, while the negative anomalous Hall resistance can originate from the spin or orbital currents generated at the CuO x /AlO x interface interact with magnetization of CuO x and its inverse process.

Giant spin-vorticity coupling excited by shear-horizontal surface acoustic waves

A non-magnetic layer can inject spin-polarized currents into an adjacent ferromagnetic layer via spin vorticity coupling (SVC), inducing spin wave resonance (SWR). In this work, we present the theoretical model of SWR generated by shear-horizontal surface acoustic wave (SH-SAW) via SVC, which contains distinct vorticities from well-studied Rayleigh SAW. Both Rayleigh- and SH-SAW delay lines have been designed and fabricated with a Ni81Fe19/Cu bilayer integrated on ST-cut quartz. Given the same wavelength, the measured power absorption of SH-SAW is four orders of magnitudes higher than that of the Rayleigh SAW. In addition, a high-order frequency dependence of the SWR is observed in the SH-SAW, indicating SVC can be strong enough to compare with magnetoelastic coupling.

Spin hydrodynamic generation in unsteady flows

We theoretically investigate a spin-mediated conversion from fluid dynamics to voltage, known as spin hydrodynamic generation (SHDG), in oscillatory and transient unsteady flows. We consider unsteady flows of liquid metal between two parallel infinite planes and then calculate its vorticity fields based on the Navier–Stokes equation for an incompressible viscous fluid. The spin accumulation and spin current generated by unsteady flows are derived using a spin-diffusion equation, including spin-vorticity coupling, which is a couple of angular momentum between electron spin and vorticity field in unsteady flows. The estimation of SHDG in liquid mercury flow suggests that an observable magnitude of voltage can be induced in unsteady flows. Our results are expected to enable the realization of high-speed spin devices with unsteady flows and broaden the range of fluid spintronics applicability.

Enhanced Spin Current in Ni81 Fe19 /Cu-CuOx Bilayer with Top and Sideways Oxidization.

Generation and manipulation of spin current are the cores of spintronic devices, which are intensely pursued. Heavy metals with strong spin-orbit coupling are commonly used for the generation of spin current, but areincompatible with the mass production of devices, and the polarization of spin current is limited to be in-plane. Here, it is shown that the spin current with strong out-of-plane polarization component can be generated and transmitted in Ni81 Fe19 /Cu-CuOx bilayer with sideways and top oxidizations. The charge-to-spin current conversion efficiency can be enhanced through the spin currents consisting of both out-of-plane polarization (σz ) and in-plane polarization (σy ) induced by spin-vorticity coupling. Such a spin current is demonstrated to be closely related to the lateral oxidization gradient and can be controlled by changing the temperatures and times of annealing. The finding here provides a novel degree of freedom to produce and control the spin current in spintronic devices.

Medium Correction to Gravitational Form Factors

We generalize the gravitational form factor for chiral fermion in vacuum, which reproduces the well-known spinvorticity coupling. We also calculate radiative correction to the gravitational form factors in quantum electrodynamics plasma. We find two structures in the form factors contributing to the scattering amplitude of fermion in vorticity field, one is from the fermon self-energy correction, pointing to suppression of spin-vorticity coupling in medium; the other strucutre comes from graviton-fermion vertex correction, which does not adopt potential interpretation, but corresponds to transition matrix element between initial and final states. Both structures contribute to chiral vortical effect. The net effect is that radiative correction enhances the chiral vortical effect. Our results claify the relation and difference between spin-vorticity coupling and chiral vortical effect from the perspective of form factors. We also discuss the application of the results in QCD plasma, indicating radiative correction might have an appreciable effect in spin polarization effect in heavy ion collisions.

Medium correction to gravitational form factors

We generalize the gravitational form factor for chiral fermion in vacuum, which reproduces the well-known spin-vorticity coupling. We also calculate radiative correction to the gravitational form factors in quantum electrodynamics plasma. We find two structures in the form factors contributing to the scattering amplitude of fermion in vorticity field, one is from the fermon self-energy correction, pointing to suppression of spin-vorticity coupling in medium; the other strucutre comes from graviton-fermion vertex correction, which does not adopt potential interpretation, but corresponds to transition matrix element between initial and final states. Both structures contribute to chiral vortical effect. The net effect is that radiative correction enhances the chiral vortical effect. Our results claify the relation and difference between spin-vorticity coupling and chiral vortical effect from the perspective of form factors. We also discuss the application of the results in QCD plasma, indicating radiative correction might have an appreciable effect in spin polarization effect in heavy ion collisions.

Acoustic spin transport by superconducting quasiparticles

We theoretically study the generation of spin current due to a surface acoustic wave (SAW) in a superconductor. We model an $s$-wave superconductor as the mean-field Hamiltonian and calculate spin current generated via spin-vorticity coupling based on quantum kinetic theory. The results suggest that the spin current can be driven in a single-superconductor layer, and our estimation suggests that the detectable magnitude of the spin current can be generated in aluminum. Our proposal may contribute to the advancement of spin transport in superconductors from application and fundamental physics aspects.

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.

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.

Electrical voltage by electron spin-vorticity coupling in laminar ducts

A tiny electrical voltage can be generated by the collective coupling of the electron spins to the flow vorticity in laminar and turbulent liquid metal flows. Here, we demonstrate a linear scaling law between electrical voltage and pressure drop for laminar flows through capillaries with different cross sections, both, analytically and experimentally.

Spin-vorticity coupling for massive vector mesons

Recent experiments at Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) have indicated that hadrons containing strange quarks produced in non-central heavy ion collisions can be polarized. We investigate in detail the coupling of spin and vorticity for electrically neutral, massive vector bosons using the Proca equation, and provide the nonrelativistic reduction of the field equations via a single Foldy--Wouthuysen transformation. We find that the resulting Hamiltonian is not-Hermitian, but ${\cal PT}$ invariant, and involves a spin dependent term $\textstyle{\frac{1}{2}} s_z \hbar \omega$ to leading order in vorticity. We also calculate further relativistic and quantum corrections to the Hamiltonian.

Highly nonlinear frequency-dependent spin-wave resonance excited via spin-vorticity coupling

A nonuniform vorticity of lattice deformation in a surface acoustic wave (SAW) can generate a spin current (SC) in nonmagnetic metals via spin-vorticity coupling (SVC). We demonstrated a strong enhancement of SVC-derived SC generated in Cu and Pt films with increasing the frequency of the SAW by observing the spin-wave resonance (SWR) in an adjacent NiFe film. The comparative amplitudes and high-order frequency variations of SWR in NiFe/Cu and NiFe/Pt bilayers imply that the amplitude of the SC generated via SVC in a SAW is robust against the strength of spin-orbit interaction in nonmagnetic metals.

Chiral vortical effect in relativistic and nonrelativistic systems

We formulate the chiral vortical effect (CVE) and its generalization called generalized vortical effect using the semiclassical theory of wave packet dynamics. We take the spin-vorticity coupling into account and calculate the transport charge current by subtracting the magnetization one from the Noether local one. We find that the transport charge current in the CVE always vanishes in relativistic chiral fermions. This result implies that it cannot be observed in transport experiments in condensed matter systems such as Dirac/Weyl semimetals with the pseudo-Lorentz symmetry. We also demonstrate that the anisotropic CVE can be observed in nonrelativistic systems that belong to the point groups $D_n, C_n (n = 2, 3, 4, 6)$, and $C_1$, such as $n$-type tellurium.

Extrinsic spin Hall effect in inhomogeneous systems

Charge-to-spin conversion in inhomogeneous systems is studied theoretically. We consider free electrons subject to impurities with spin-orbit interaction and with spatially modulated distribution, and calculate spin accumulation and spin current induced by an external electric field. It is found that the spin accumulation is induced by the vorticity of electron flow through the side-jump and skew-scattering processes, and the differences of the two processes are discussed. The results can be put in a form of generalized spin diffusion equation with a spin source term given by the divergence of the spin Hall current. This spin source term reduces to the form of spin-vorticity coupling when the spin Hall angle is independent of impurity concentration. We also study the effects of long-range Coulomb interaction, which is indispensable when the process involves charge inhomogeneity and accumulation as in the present problem.

Electrical evaluation of the alternating spin current generated via spin-vorticity coupling

In many interacting-electron systems, the microscopic spin angular momentum of electrons is conserved along with the macroscopic angular momentum in electrical current flows, i.e., vorticity. Such spin-vorticity coupling expands the choice of materials for spintronics devices. In this paper, we evaluate the magnitude of an alternating spin current generated by the spin-vorticity coupling with a gigahertz-order surface acoustic wave in a Cu thin film. We measure the gigahertz alternating spin current by an electrical method based on the inverse spin-Hall effect. From the amplitude of the spin current, we can determine the conversion efficiency of the angular momentum between local lattice rotation and electron spin in the Cu film. The conversion efficiency is four orders of magnitude larger than the case of spin current generation via kilohertz-order vorticity in turbulent flow of liquid mercury [M. Matsuo et al., Phys. Rev. B 96, 020401(R) (2017)]. Such a huge conversion efficiency is attributable to a smaller inconsistency of energy scale between lattice rotation and electron spin than the case of liquid vorticity.

Electron Spin-Vorticity Coupling in Pipe Flows at Low and High Reynolds Number

Spin-hydrodynamic coupling is a recently discovered method to directly generate electricity from an electrically conducting fluid flow in the absence of Lorentz forces. This method relies on a collective coupling of electron spins---the internal quantum-mechanical angular momentum of the electrons---with the local vorticity of a fluid flow. In this work, we experimentally investigate the spin-hydrodynamic coupling in circular- and noncircular-capillary pipe flows and extend a previously obtained range of Reynolds numbers to smaller and larger values, $20<\mathrm{Re}<21\phantom{\rule{0.1em}{0ex}}500$, using the conducting liquid-metal alloy ($\mathrm{Ga}$,$\mathrm{In}$)$\mathrm{Sn}$ as the working liquid. In particular, we provide experimental evidence for the linear dependence of the generated electric voltage with respect to the bulk-flow velocity in the laminar regime of the circular pipe flow as predicted by Matsuo et al. [Phys. Rev. B. 96, 020401 (2017)]. Moreover, we show analytically that this behavior is universal in the laminar regime regardless of the cross-sectional shape of the pipe. Finally, the proposed scaling law by Takahashi et al. [Nat. Phys. 12, 52 (2016)] for the generated voltage in turbulent circular pipe flows is experimentally evaluated at Reynolds numbers higher than in previous studies. Our results verify the reliability of the proposed scaling law for Reynolds numbers up to $\mathrm{Re}=21\phantom{\rule{0.1em}{0ex}}500$ for which the flow is in a fully developed turbulent state.

Microscopic description for polarization in particle scattering

We propose a microscopic description for the polarization from the first principle through the spin-orbit coupling in particle collisions. The model is different from previous ones based on local equilibrium assumptions for the spin degree of freedom. It is based on scatterings of particles as wave packets, an effective method to deal with particle scatterings at specified impact parameters. The polarization is then the consequence of particle collisions in a non-equilibrium state of spins. The spin-vorticity coupling naturally emerges from the spin-orbit one encoded in polarized scattering amplitudes of collisional integrals when one assumes local equilibrium in momentum but not in spin.

Probing vorticity in heavy ion collision with dilepton production

We study the effect of vorticity present in heavy ion collisions (HICs) on the temperature evolution of hot quark-gluon plasma in the presence of spin-vorticity coupling. The initial global rotation entails a nontrivial dependence of the longitudinal flow velocity on the transverse coordinates and also develops a transverse velocity component that depends upon the longitudinal coordinate. Both of these velocities lead to a 2+1 dimensional expansion of the fireball. It is observed that with finite vorticity and spin-polarization the fireball cools faster as compared to the case without vorticity. Furthermore, we discuss the consequence of this on the production of thermal dileptons.

Chiral kinetic theory in curved spacetime

Many-body systems with chiral fermions exhibit anomalous transport phenomena originated from quantum anomalies. Based on quantum field theory, we derive the kinetic theory for chiral fermions interacting with an external electromagnetic field and a background curved geometry. The resultant framework respects the covariance under the U(1) gauge, local Lorentz, and diffeomorphic transformations. It is particularly useful to study the gravitational or non-inertial effects for chiral systems. As the first application, we study the chiral dynamics in a rotating coordinate and clarify the roles of the Coriolis force and spin-vorticity coupling in generating the chiral vortical effect (CVE). We also show that the CVE is an intrinsic phenomenon of a rotating chiral fluid, and thus independent of observer's frame.