We investigate the spin-pumping-induced electric current on the surface of a three-dimensional topological insulator hybridized with a ferromagnet, namely, ferromagnetic topological insulator. In order to do this, we establish the microscopic formalism and construct the perturbation theory using a Keldysh Green's function approach. We analyze how this electric current is generated by an exchange interaction and an external ac magnetic field, which is the driving force of ferromagnetic resonance as well as the spin pumping. The mechanism is as follows. First, the ferromagnetic resonance is driven and a zero-momentum magnon emerges. It is the fluctuation from the saturation magnetization pointing parallel to the precession axis of the ferromagnetic resonance. After then, the spin pumping is generated with the zero-momentum magnon being the carrier of spin. The zero-momentum magnon and the topological insulator surface state couples through the exchange interaction and the spin carried by the magnon is transferred to it. Owing to the spin-momentum locking, the transferred spin is converted into the momentum of topological insulator surface state leading to the generation of electric current flowing perpendicular to the precession axis of the ferromagnetic resonance. It is quadratic in the amplitude of external ac magnetic field whereas it is linear to the strength of the exchange interaction. The associated electric voltage is described by the spectrum of zero-momentum magnon. The non-linearity of spin-pumping-induced electric current in the ac magnetic field as well as the linearity in the exchange-interaction strength reflects that the surface of ferromagnetic topological insulator has a high-performing functionality of generating the electric charge current by magnetic controlling.
We study transport in ferromagnetic-superconductor/normal-metal systems. It is shown that charge and spin currents are pumped from ferromagnetic superconductors into adjacent normal metals by adiabatic changes in the order parameters induced by external electromagnetic fields. Spin and charge pumping identify the symmetry of the superconducting order parameter, e.g., singlet pairing or triplet pairing with opposite or equal spin pairing. Consequences for ferromagnetic-resonance experiments are discussed.
We study the quantized charge pumping of higher-order topological insulators (HOTIs) with edge-corner correspondences based on the combination of the rotation of in-plane magnetic field and the quantum spin Hall effect. A picture of a specific charge pumping process is uncovered with the help of the non-equilibrium Green's function method. Significantly, we demonstrate that the quantized charge pumping current is achieved without the participation of bulk states, and the charges move along the boundary of the sample. Furthermore, the effects of external parameters on the pumping current is als…
Precessing magnetization in a thin film magnetic insulator pumps spins into adjacent metals; however, this phenomenon is not quantitatively understood. We present a theory for the dependence of spin-pumping on the transverse mode number and in-plane wave vector. For long-wavelength spin waves, the enhanced Gilbert damping for the transverse mode volume waves is twice that of the macrospin mode, and for surface modes, the enhancement can be ten or more times stronger. Spin-pumping is negligible for short-wavelength exchange spin waves. We corroborate our analytical theory with numerical calcula…
The spin waves and ferromagnetic resonance (FMR) contribution to the spin pumping signal is studied in the Ta/CoFeB interface under different excitation bias fields. Ferromagnetic resonance is excited utilizing a coplanar waveguide and a microwave generator. Using a narrow waveguide of about 3 μm, magnetostatic surface spin waves with large wavevector (k) of about 0.81 μm^-1 are excited. A large k value results in dissociation of spin waves and FMR frequencies according to the surface spin wave dispersion relation. Spin waves and FMR contribution to the spin pumping are calculated based on the…
We extend the theory of dipole moments in crystalline insulators to higher multipole moments. In this paper, we expand in great detail the theory presented in Ref. 1, and extend it to cover associated topological pumping phenomena, and a novel class of 3D insulator with chiral hinge states. In quantum-mechanical crystalline insulators, higher multipole bulk moments manifest themselves by the presence of boundary-localized moments of lower dimension, in exact correspondence with the electromagnetic theory of classical continuous dielectrics. In the presence of certain symmetries, these moments …
Using a multilayer structure containing (cobalt detector layer)/(copper spacer)/(Permalloy source layer), we show experimentally how the non-reorientable spin-orbit torque generated by the Permalloy source layer (the component of spin-orbit torque that does not change when the Permalloy magnetization is rotated) can be measured using spin-torque ferromagnetic resonance (ST-FMR) with lineshape analysis. We find that dynamic spin pumping between the magnetic layers exerts torques on the magnetic layers as large or larger than the spin-orbit torques, so that if dynamic spin pumping is neglected t…
Voltage induced magnetization dynamics of magnetic thin films is a valuable tool to study anisotropic fields, exchange couplings, magnetization damping and spin pumping mechanism. A particularly well established technique is the ferromagnetic resonance (FMR) generated by the coupling of microwave photons and magnetization eigenmodes in the GHz range. Here we review the basic concepts of the so-called acoustic ferromagnetic resonance technique (a-FMR) induced by the coupling of surface acoustic waves (SAW) and magnetization of thin films. Interestingly, additional to the benefits of the microwa…
We investigate adiabatic quantum pumping of Dirac fermions on the surface of a strong 3D topological insulator. Two different geometries are studied in detail, a normal metal -- ferromagnetic -- normal metal (NFN) junction and a ferromagnetic -- normal metal -- ferromagnetic (FNF) junction. Using a scattering matrix approach, we first calculate the tunneling conductance and then the adiabatically pumped current using different pumping mechanisms for both types of junctions. We explain the oscillatory behavior of the conductance by studying the condition for resonant transmission in the junctio…
A general definition of the Spintronics concept of spin-pumping is proposed as generalized forces conjugated to the spin degrees of freedom in the framework of the theory of mesoscopic non-equilibrium thermodynamics. It is shown that at least three different kinds of spin-pumping forces and associated spin-currents can be defined in the most simple spintronics system (the Ferromagnetic/Non-Ferromagnetic metal interface). Furthermore, the generalized force associated to the ferromagnetic collective variable is also introduced in an equal footing, in order to describe the coexistence of the spin…
Topological insulators (TIs) are a new quantum state of matter discovered recently, which are characterized by unconventional bulk topological invariants. Proposals for practical applications of the TIs are mostly based upon their metallic surface or edge states. Here, we report the theoretical discovery of a bulk quantum pumping effect in a two-dimensional TI electrically modulated in adiabatic cycles. In each cycle, an amount of spin proportional to the sample width can be pumped into a nonmagnetic electrode, which is attributed to nonzero spin Chern numbers $C_{\pm}$. Moreover, by using a h…
We study adiabatic pumping of electrons through quantum dots attached to ferromagnetic leads. Hereby we make use of a real-time diagrammatic technique in the adiabatic limit that takes into account strong Coulomb interaction in the dot. We analyze the degree of spin polarization of electrons pumped from a ferromagnet through the dot to a nonmagnetic lead (N-dot-F) as well as the dependence of the pumped charge on the relative leads' magnetization orientations for a spin-valve (F-dot-F) structure. For the former case, we find that, depending on the relative coupling strength to the leads, spin …
We demonstrate that a quantum spin Hall current, spontaneously generated at the edge of a two-dimensional topological insulator, acts as a source of spin-pumping for a magnetic impurity with uniaxial anisotropy. One can then manipulate the impurity spin direction by means of an electrical current without using either magnetic electrodes or an external magnetic field. Furthermore we show that the unique properties of the quantum spin Hall topological state have profound effects on the inelastic electron tunneling spectrum of the impurity. For low current densities inelastic spin-flip events do …
We determined the spin-transport properties of Pd and Pt thin films by measuring the increase in ferromagnetic resonance damping due to spin-pumping in ferromagnetic (FM)-nonferromagnetic metal (NM) multilayers with varying NM thicknesses. The increase in damping with NM thickness depends strongly on both the spin- and charge-transport properties of the NM, as modeled by diffusion equations that include both momentum- and spin-scattering parameters. We use the analytical solution to the spin-diffusion equations to obtain spin-diffusion lengths for Pt and Pd. By measuring the dependence of cond…
We demonstrate that a sizable chiral charge pumping can be achieved at room temperature in graphene/Yttrium Iron Garnet (YIG) bilayer systems. The effect, which cannot be attributed to the ordinary spin pumping, reveals itself in the creation of a dc electric field/voltage in graphene as a response to the dynamic magnetic excitations (spin waves) in an adjacent out-of-plane magnetized YIG film. We show that the induced voltage changes its sign when the orientation of the static magnetization is reversed, clearly indicating the broken spatial inversion symmetry in the studied system. The streng…
We describe electrical detection of spin pumping in metallic nanostructures. In the spin pumping effect, a precessing ferromagnet attached to a normal-metal acts as a pump of spin-polarized current, giving rise to a spin accumulation. The resulting spin accumulation induces a backflow of spin current into the ferromagnet and generates a dc voltage due to the spin dependent conductivities of the ferromagnet. The magnitude of such voltage is proportional to the spin-relaxation properties of the normal-metal. By using platinum as a contact material we observe, in agreement with theory, that the v…
Based on spin-dependent transport theory and thermodynamics, we develop a generalized theory of the Joule heating in the presence of a spin current. Along with the conventional Joule heating consisting of an electric current and electrochemical potential, it is found that the spin current and spin accumulation give an additional dissipation because the spin-dependent scatterings inside bulk and ferromagnetic/nonmagnetic interface lead to a change of entropy. The theory is applied to investigate the dissipation due to pure spin-current generated by spin pumping across a ferromagnetic/nonmagneti…
We investigated the dependence of the seed [Ta/Pt, Ta/Au] and capping [Pt/Ta, Au/Ta] layers on spin pumping effect in the ferromagnetic 3 nm thick Co thin film using ferromagnetic resonance spectroscopy. The data is fitted with Kittel equation to evaluate damping constant and g-factor. A strong dependence of seed and capping layers on spin pumping has been discussed. The value of damping constant {alpha} is found to be relatively large i.e. 0.0326 for the Ta{3}/Pt{3}/Co{3}/Pt{3}/Ta{3} {nm} multi-layer structure, while it is 0.0104 for Ta{3}/Co{3}/Ta{3} {nm}. Increase in {alpha} is observed due…
Spin pumping in nonmagnetic/ferromagnetic metal multilayers is studied both theoretically and experimentally. We show that the line widths of the ferromagnetic resonance (FMR) spectrum depend on the thickness of the ferromagnetic metal layers, which must not be in resonance with the oscillating magnetic field. We also show that the penetration depths of the transverse spin current in ferromagnetic metals can be determined by analyzing the line widths of their FMR spectra. The obtained penetration depths in NiFe, CoFe and CoFeB were 3.7 [nm], 2.5 [nm] and 12.0 [nm], respectively.
The transport of energy through 1-dimensional (1D) waveguiding channels can be affected by sub-wavelength disorder, resulting in undesirable localization and backscattering phenomena. However, quantized disorder-resilient transport is observable in the edge currents of 2-dimensional (2D) topological band insulators with broken time-reversal symmetry. Topological pumps are able to reduce this higher-dimensional topological insulator phenomena to lower dimensionality by utilizing a pumping parameter (either space or time) as an artificial dimension. Here we demonstrate the first temporal topolog…
Spin pumping by ferromagnetic resonance is one of the most common technique to determine spin hall angles, Edelstein lengths or spin diffusion lengths of a large variety of materials. In recent years, rising concerns have appeared regarding the interpretation of these experiments, underlining that the signal could arise purely from thermoelectric effects, rather than from coherent spin pumping. Here, we propose a method to evaluate the presence or absence of thermal effects in spin pumping signals, by combining bolometry and spin pumping by ferromagnetic resonance measurements, and comparing t…
The magnetic behaviour of ultrathin ferromagnetic films deposited on substrates is strongly affected by the properties of the substrate. We investigate the spin pumping rate, interlayer exchange coupling and dynamic exchange coupling between ultrathin ferromagnetic films through palladium, a non-magnetic substrate that displays strong Stoner enhancement. We find that the interlayer exchange coupling, both in the static and dynamic versions, is qualitatively affected by the substrate's Stoner enhancement. For instance, the oscillatory behavior that is a hallmark property of the RKKY exchange co…
The magnon pumping effect in ferromagnetic insulators under an external time-dependent transverse magnetic field is theoretically studied. Generation of a magnon current is discussed by calculating the magnon source term in the spin continuity equation. This term represents the non-conservation of magnons arising from an applied transverse magnetic field. The magnon source term has a resonance structure as a function of the angular frequency of the transverse field, and this fact is useful to enhance the pumping effect.
Magnetic insulators are promising materials for the development of energy-efficient spintronics. Unlike metallic counterparts, the magnetic insulators are characterized by imaginary part of the interfacial spin mixing conductance as well in a bilayer with heavy metals and it is responsible for the field-like toque in spin-orbit torque devices. Here, we study the underlying theoretical constructs and develop a general strategy to determine the complex spin mixing conductance from the experimental results of ferromagnetic resonance and spin pumping. The results show that the imaginary part of th…
We have demonstrated spin pumping from a paramagnetic state of an insulator La2NiMnO6 into a Pt film. Single-crystalline films of La2NiMnO6 which exhibit a ferromagnetic order at TC ~ 270 K were grown by pulsed laser deposition. The inverse spin Hall voltage induced by spin-current injection has been observed in the Pt layer not only in the ferromagnetic phase of La2NiMnO6 but also in a wide temperature range above TC. The efficient spin pumping in the paramagnetic phase is ascribable to ferromagnetic correlation, not to ferromagnetic order.
The relative contribution of spin pumping and spin rectification from the ferromagnetic resonance of CoFeB/non-magnetic bilayers was investigated as a function of non-magnetic electrode resistance. Samples with highly resistive electrodes of Ta or Ti exhibit a stronger spin rectification signal, which may result in over-(or under-)estimation of the spin Hall angle of the materials, while those with low resistive electrodes of Pt or Pd show the domination of the inverse spin Hall effect from spin pumping. By comparison with samples of single FM layer and an inverted structure, we provide a prop…
The Edelstein effect caused by the pristine surface states of three-dimensional topological insulators is investigated by means of a semiclassical approach. The combined effect of random impurity scattering and the spin-momentum locking of the gapless Dirac cone yields a current-induced surface spin accumulation independent from chemical potential and temperature. In a nearby ferromagnet that does not make direct contact with the topological insulator, the bound state nature of the pristine surface state causes a spin-transfer torque that is entirely field-like, whose magnitude is highly influ…
We consider an antiferromagnetic insulator that is in contact with a metal. Spin accumulation in the metal can induce spin-transfer torques on the staggered field and on the magnetization in the antiferromagnet. These torques relate to spin pumping: the emission of spin currents into the metal by a precessing antiferromagnet. We investigate how the various components of the spin-transfer torque are affected by spin-independent disorder and spin-flip scattering in the metal. Spin-conserving disorder reduces the coupling between the spins in the antiferromagnet and the itinerant spins in the met…
Lowering of the thickness of a thin-film three-dimensional topological insulator down to a few nanometers results in the gap opening in the spectrum of topologically protected two-dimensional surface states. This phenomenon, which is referred to as the anomalous finite-size effect, originates from hybridization between the states propagating along the opposite boundaries. In this work, we consider a bismuth-based topological insulator and show how the coupling to an intense high-frequency linearly polarized pumping can further be used to manipulate the value of a gap. We address this effect wi…
Pure spin currents are shown to be generated by an electrically controlled quantum pump applied at the edges of a topological insulator. The electric rather than the more conventional magnetic control offers several advantages and avoids, in particular, the necessity of delicate control of magnetization dynamics over tiny regions. The pump is implemented by pinching the sample at two quantum point contacts and phase modulating two external gate voltages between them. The spin current is generated for the full range of parameters. On the other hand, pumping via amplitude modulation of the inter…
We report a theoretical study of the quantized spin pump in a traditional two-parameter quantum pump device that is based on the helical edge states of a quantum spin Hall insulator. By introducing two time-dependent magnetizations out of phase as the pumping parameters, we found that when the Fermi energy resides in the energy gap opened by magnetization, an integer number of charges or spins can be pumped out in a pumping cycle and ascribed to the possible topological interface state born in between the two pumping potentials. The quantized pump current can be fully spin-polarized, spin-unpo…
We present experimental results on the conversion of a spin current into a charge current by spin pumping into the Dirac cone with helical spin polarization of the elemental topological insulator (TI) α-Sn[1-3]. By angle-resolved photoelectron spectroscopy (ARPES) we first confirm that the Dirac cone at the surface of α-Sn (0 0 1) layers subsists after covering with Ag. Then we show that resonant spin pumping at room temperature from Fe through Ag into α-Sn layers induces a lateral charge current that can be ascribed to the Inverse Edelstein Effect[4-5]. Our observation of an Inverse Edelstein…
We study spin pumping into an anisotropic Dirac electron system induced by microwave irradiation to an adjacent ferromagnetic insulator theoretically. We formulate the Gilbert damping enhancement due to the spin current flowing into the Dirac electron system using second-order perturbation with respect to the interfacial exchange coupling. As an illustration, we consider the anisotropic Dirac system realized in bismuth to show that the Gilbert damping varies according to the magnetization direction in the ferromagnetic insulator. Our results indicate that this setup can provide helpful informa…
It is often taken for granted that in pump-probe experiments on the topological insulator (TI) Bi2Se3 using IR pumping with a commercial Ti:Sapphire laser [~800 nm (1.55 eV photon energy)], the electrons are excited in the one-photon absorption regime, even when pumped with absorbed fluences in the mJ cm-2 range. Here, using UV-Vis transient absorption (TA) spectroscopy, we show that even at low-power IR pumping with absorbed fluences in the mkJ cm-2 range, the TA spectra of the TI Bi2Se3 extend across a part of the UV and the entire visible region. This observation suggests unambiguously that…
We investigate adiabatic charge pumping in disordered system in one dimension with open and closed boundary conditions. In contrast to the Thouless charge pumping, the system has no gap even though all the states are localized, i.e., strong localization. Charge pumping can be achieved by making a loop adiabatically in the two-dimensional parameter space of the Hamiltonian. It is because there are many $δ$-function-like fluxes distributed over the parameter space with random strength, in sharp contrast to the single $δ$-function in the pure case. This provides a new and more efficient way of ch…
Three-dimensional (3D) topological insulators are known for their strong spin-orbit coupling and the existence of spin-textured topological surface states which could be potentially exploited for spintronics. Here, we investigate spin pumping from a metallic ferromagnet (CoFeB) into a 3D topological insulator (Bi2Se3) and demonstrate successful spin injection from CoFeB into Bi2Se3 and the direct detection of the electromotive force generated by the inverse spin Hal effect (ISHE) at room temperature. The spin pumping, driven by the magnetization dynamics of the metallic ferromagnet, introduces…
We theoretically consider spin pumping in a junction between a ferromagnetic insulator (FI) and a two-dimensional electron gas (2DEG) in which the Rashba and Dresselhaus spin-orbit interactions coexist. Using second-order perturbation theory, we derive an increase in linewidth in the case of an interfacial exchange coupling in a ferromagnetic resonance (FMR) experiment. We clarify how the enhancement of Gilbert damping depends on the resonant frequency and spin orientation of the FI. We show that this setup of an FMR experiment can provide information on the spin texture of 2DEG at the Fermi s…
We measure electrically detected ferromagnetic resonance in microdevices patterned from ultra-thin Co/Pt bilayers. Spin pumping and rectification voltages are observed and distinguished via their angular dependence. The spin-pumping voltage shows an unexpected increase as the cobalt thickness is reduced below 2 nm. This enhancement allows more efficient conversion of spin to charge current and motivates a theory modelling the dependence of impurity scattering on surface roughness.
Topological spintronics aims to exploit the spin-momentum locking in the helical surface states of topological insulators for spin-orbit torque devices. We address a fundamental question that still remains unresolved in this context: does the topological surface state alone produce the largest values of spin-charge conversion efficiency or can the strongly spin-orbit coupled bulk states also contribute significantly? By studying the Fermi level dependence of spin pumping in topological insulator/ferrimagnetic insulator bilayers, we show that the spin Hall conductivity is constant when the Ferm…
We show that in excitonic insulators with $s$-wave electron-hole pairing, an applied electric field (either pulsed or static) can induce a $p$-wave component to the order parameter, and further drive it to rotate in the $s+ip$ plane, realizing a Thouless charge pump. In one dimension, each cycle of rotation pumps exactly two electrons across the sample. Higher dimensional systems can be viewed as a stack of one dimensional chains in momentum space in which each chain crossing the fermi surface contributes a channel of charge pumping. Physics beyond the adiabatic limit, including in particular …
We propose a four-terminal device designed to manipulate by all electrical means the spin of a magnetic adatom positioned at the edge of a quantum spin Hall insulator. We show that an electrical gate, able to tune the interface resistance between a quantum spin Hall insulator and the source and drain electrodes, can switch the device between two regimes: one where the system exhibits spin pumping and the other where the adatom remains in its ground state. This demonstrates an all-electrical route to control single spins by exploiting helical edge states of topological materials.
We study the magnetization dynamics in thin ferromagnetic films and small ferromagnetic particles in contact with paramagnetic conductors. A moving magnetization vector causes \textquotedblleft pumping\textquotedblright of spins into adjacent nonmagnetic layers. This spin transfer affects the magnetization dynamics similar to the Landau-Lifshitz-Gilbert 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 s…
We study electronic structures at an interface between a topological insulator and a ferromagnetic insulator by using three-dimensional two-band model. In usual ferromagnetic insulators, the exchange potential is much larger than the bulk gap size in the topological insulators and electronic structures are asymmetric with respect to the fermi level. In such situation, we show that unusual metallic states appear under the magnetic moment pointing the perpendicular direction to the junction plane, which cannot be described by the two-dimensional effective model around the Dirac point. When the m…
Motivated by recent experiments on spin pumping from a ferromagnet into organic materials in which the charge transport is due to hopping, we study theoretically the generation and propagation of spin current in a hopping insulator. Unlike metals, the spin polarization at the boundary with ferromagnet is created as a result of magnon absorption within pairs of localized states and it spreads following the current-currying resistor network (although the charge current is absent). We consider a classic resonant mechanism of the ac absorption in insulators and adapt it to the absorption of magnon…
We investigate pure spin pumping in graphene by imposing a ferromagnet (F) with rotating magnetization on top of it. Using the generalized scattering approach for adiabatic spin pumping, we obtain the spin current pumped through magnetic graphene to a neighboring normal (N) region. The spin current can be easily controlled by gate voltages and under certain conditions, becomes sufficiently large to be measurable in current experimental setups. In fact it reaches a maximum value when one of the spins are completely filtered due to the vanishing density of states of the corresponding spin specie…
We study the spin current injected by spin pumping into single layer graphene and the two-dimensional electron gas (2DEG) with ferromagnetic contacts using scattering theory. The spin currents pumped into graphene are very distinct from that into the 2DEG since importantly affected by Klein tunneling.
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 develop a method for universally resolving the important issue of separating spin pumping (SP) from spin rectification (SR) signals in bilayer spintronics devices. This method is based on the characteristic distinction of SP and SR, as revealed in their different angular and field symmetries. It applies generally for analyzing charge voltages in bilayers induced by the ferromagnetic resonance (FMR), independent of FMR line shape. Hence, it solves the outstanding problem that device specific microwave properties restrict the universal quantification of the spin Hall angle in bilayer devices …
