In metallic ferromagnets, the spin-transfer torque and spin-motive force are known to exhibit a reciprocal relationship. Recent experiments on ferromagnets with strong spin-orbit coupling have revealed a rich complexity in the interaction between itinerant charge carriers and magnetization, but a full understanding of this coupled dynamics is lacking. Here, we develop a general phenomenology of the two reciprocal processes of charge pumping by spin-motive forces and current-driven magnetization dynamics. The formalism is valid for spin-orbit coupling of any strength and presents a systematic scheme for deriving all possible torque and charge-pumping terms that obey the symmetry requirements imposed by the point group of the system. We demonstrate how the different charge pumping and torque contributions are connected via the Onsager reciprocal relations. The formalism is applied to two important classes of systems: isotropic ferromagnets with non-uniform magnetization and homogeneous ferromagnets described by the point group $C_{2v}$.
The introduction of a strong Rashba spin orbit coupling (SOC) had been predicted to enhance the spin motive force (SMF) [see Phys. Rev. Lett. {\bf 108}, 217202 (2012)]. In this work, we predict further enhancement of the SMF by time modulation of the Rashba coupling $α_R$, which induces an additional electric field $E^R_d={\dot α_R} m_e/e\hbar({\hat z}\times {\mathbf m})$. When the modulation frequency is higher than the magnetization precessing frequency, the amplitude of this field is significantly larger than previously predicted results. Correspondingly, the spin torque on the magnetizatio…
We predict that magnon motive force can lead to temperature dependent, nonlinear chiral damping in both conducting and insulating ferromagnets. We estimate that this damping can significantly influence the motion of skyrmions and domain walls at finite temperatures. We also find that in systems with low Gilbert damping moving chiral magnetic textures and resulting magnon motive forces can induce large spin and energy currents in the transverse direction.
We demonstrate numerically the existence of a spin-motive force acting on spin-carriers when moving in a time and space dependent internal field. This is the case of electrons in a one-dimensional wires with a precessing domain wall. The effect can be explained solely by considering adiabatic dynamics and it is shown to exist for both classical and quantum systems.
It is shown that the current-induced torques between a ferromagnetic layer and an antiferromagnetic layer with a compensated interface vanish when the ferromagnet is aligned with an axis of spin-rotation symmetry of the antiferromagnet. For properly chosen geometries this implies that the current induced torque can stabilize the out-of-plane (or hard axis) orientation of the ferromagnetic layer. This current-induced torque relies on phase coherent transport, and we calculate the robustness of this torque to phase breaking scattering. From this it is shown that the torque is not linearly depend…
We have investigated the current-induced spin transfer torque of a ferromagnet-insulator-ferromagnet tunnel junction by taking the spin-flip scatterings into account. It is found that the spin-flip scattering can induce an additional spin torque, enhancing the maximum of the spin torque and giving rise to an angular shift compared to the case when the spin-flip scatterings are neglected. The effects of the molecular fields of the left and right ferromagnets on the spin torque are also studied. It is found that $τ^{Rx}/I_{e}$ ($τ^{Rx}$ is the spin-transfer torque acting on the right ferromagnet…
We theoretically study the spin current and spin-transfer torque generation in a conventional spin- valve hybrid structure of type ferromagnetic/normal metal/ferromagnetic (FM/NM/FM) made of the topological insulator (TI), in which a gate voltage is attached to the normal layer. We demonstrate the penetration of the spin-transfer torque into the right ferromagnetic layer and show that, unlike graphene spin-valve junction, the spin-transfer torque in TI is very sensitive to the chemical potential of the NM region. As an important result, by changing the chemical potential of the NM spacer and m…
We present a microscopic theory of spin-dependent motive force ("spin motive force") induced by magnetization dynamics in a conducting ferromagnet, by taking account of spin relaxation of conduction electrons. The theory is developed by calculating spin and charge transport driven by two kinds of gauge fields; one is the ordinary electromagnetic field $A^{\rm em}_μ$, and the other is the effective gauge field $A^{z}_μ$ induced by dynamical magnetic texture. The latter acts in the spin channel and gives rise to a spin motive force. It is found that the current induced as a linear response to $A…
We predict that a temperature gradient can induce a magnon-mediated intrinsic torque and a transverse spin current in systems with non-trivial magnon Berry curvature. With the help of a microscopic linear response theory of nonequilibrium magnon-mediated torques and spin currents we identify the interband and intraband components that manifest in ferromagnets with Dzyaloshinskii-Moriya interactions and magnetic textures. To illustrate and assess the importance of such effects, we apply our theory to the magnon-mediated spin Nernst and torque responses in a kagome lattice ferromagnet.
We present a phenomenological theory of spin-orbit torques in a metallic ferromagnet with spin-relaxing boundaries. The model is rooted in the coupled diffusion of charge and spin in the bulk of the ferromagnet, where we account for the anomalous Hall effects as well as the anisotropic magnetoresistance in the corresponding constitutive relations for both charge and spin sectors. The diffusion equations are supplemented with suitable boundary conditions reflecting the spin-sink capacity of the environment. In inversion-asymmetric heterostructures, the uncompensated spin accumulation exerts a d…
We calculate the current and the spin-torque in small symmetric double tunnel barrier ferromagnet - superconductor - ferromagnet (F-S-F) systems. Spin-accumulation on the superconductor governs the transport properties when the spin-flip relaxation time is longer than the transport dwell time. In the elastic transport regime, it is demonstrated that the relative change in the current (spin-torque) for F-S-F systems equals the relative change in the current (spin-torque) for F-N-F systems upon changing the relative magnetization direction of the two ferromagnets. This differs from the results i…
Spin relaxation torque ${\cal T}$ in uniform metallic ferromagnets with the spin-orbit interaction arising from random impurities is calculated microscopically. ${\cal T}$ is shown to be written by spatial derivatives of the electric field, but is not always given as a divergence of a torque dipole density. The result is due to the fast dissipation of the orbital angular momentum, and thus a conserving spin current cannot be defined. It is discussed that the $β$ term in the spin transfer torque can also be asymmetric.
Based on Keldysh's nonequilibrium Green function method, the spin-dependent transport properties in a ferromagnet-quantum dot (QD)-ferromagnet coupled system are investigated. It is shown the spin current shows quite different characteristics from its electrical counterpart, and by changing the relative orientation of both magnetizations, it can change its magnitude even sign. The current-induced spin transfer torque (CISTT) is uncovered to be greatly enhanced when the bias voltage meets with the discrete levels of the QD at resonant positions. The relationship between the CISTT, the electrica…
In systems with small spin-orbit coupling, current-induced torques on the magnetization require inhomogeneous magnetization textures. For large spin-orbit coupling, such torques exist even without gradients in the magnetization direction. Here, we consider current-induced torques in ferromagnetic metals with both Rashba spin-orbit coupling and inhomogeneous magnetization. We first phenomenologically construct all torques that are allowed by the symmetries of the system, to first order in magnetization-direction gradients and electric field. Second, we use a Boltzmann approach to calculate the …
We theoretically examine the spin-transfer torque in the presence of spin-orbit interaction (SOI) at impurities in a ferromagnetic metal on the basis of linear response theory. We obtained, in addition to the usual spin-transfer torque, a new contributioin $\sim {\bm j}_{\rm SH}^{\phantom{\dagger}} \cdot \nabla {\bm n}$ in the first order in SOI, where ${\bm j}_{\rm SH}^{\phantom{\dagger}}$ is the spin Hall current driven by an external electric field. This is a reaction to inverse spin Hall effect driven by spin motive force in a ferromagnet.
We compute the power spectrum of the noise in the current due to spin motive forces by a fluctuating domain wall. We find that the power spectrum of the noise in the current is colored, and depends on the Gilbert damping, the spin transfer torque parameter $β$, and the domain-wall pinning potential and magnetic anisotropy. We also determine the average current induced by the thermally-assisted motion of a domain wall that is driven by an external magnetic field. Our results suggest that measuring the power spectrum of the noise in the current in the presence of a domain wall may provide a new …
We present a microscopic theory of spin torque due to diffusive spin currents induced by spin accumulation. The obtained expression is a natural extension of the existing one due to 'local' spin currents associated with ordinary electric currents, and is the reciprocal of the spin motive force which induces charge accumulation as studied recently [J. Shibata and H. Kohno, Phys. Rev. B84, 184408 (2011)]. The result is applied to a domain wall motion in a nonlocal spin injection system, and the torque and force due to diffusive spin current are evaluated.
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 …
We analyse the influence of current induced torques on the magnetization configuration of a ferromagnet in a circuit containing a compensated antiferromagnet. We argue that these torques are generically non-zero and support this conclusion with a microscopic NEGF calculation for a circuit containing antiferromagnetic NiMn and ferromagnetic Co layers. Because of symmetry dictated differences in the form of the current-induced torque, the phase diagram which expresses the dependence of ferromagnet configuration on current and external magnetic field differs qualitatively from its ferromagnet-onl…
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…
We study the magnetization dynamics of spin valve structures with a free composite synthetic ferromagnet (SyF) that consists of two ferromagnetic layers coupled through a normal metal spacer. A ferromagnetically coupled SyF can be excited into dynamical precessional states by an applied current without external magnetic fields. We analytically determine the stability of these states in the space spanned by the current density and SyF interlayer exchange coupling. Numerical simulations confirm our analytical results.
Motivated by recent experimental studies of thin-film devices containing a single ferromagnetic layer, we develop a quantum kinetic theory of current-induced magnetic torques in Rashba-model ferromagnets. We find that current-induced spin-densities that are responsible for the switching behavior are due most essentially to spin-dependent quasiparticle lifetimes and derive analytic expressions for relevant limits of a simple model. Quantitative model parameter estimates suggest that spin-orbit coupling in the adjacent metal normal magnetic layer plays an essential role in the strength of the sw…
We study the optically induced torques in thin film ferromagnetic layers under excitation by circularly polarized light. We study cases both with and without Rashba spin-orbit coupling using a 4-band model. In the absence of Rashba spin-orbit coupling, we derive an analytic expression for the optical torques, revealing the conditions under which the torque is mostly derived from optical spin transfer torque (i.e. when the torque is along the direction of optical angular momentum), versus when the torque is derived from the inverse Faraday effect (i.e. when the torque is perpendicular to the op…
Magnetization dynamics in a ferromagnet can induce a spin-dependent electric field through 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 large Rashba parameter $α_{\rm R}$, the coupling generates the spin-dependent electric field [$\pm(α_{\rm R}m_e/e\hbar) (\vhat{z}\times \partial \vec{m}/\partial t)]$, which can be large enough to modify the magnetization dynamics sig…
We study the spatial distribution of spin torque induced by a strong Rashba spin-orbit coupling (RSOC) in a ferromagnetic (FM) metal layer, using the Keldysh non-equilibrium Green's function method. In the presence of the s-d interaction between the non-equilibrium conduction electrons and the local magnetic moments, the RSOC effect induces a torque on the moments, which we term as the Rashba spin torque. A correlation between the Rashba spin torque and the spatial spin current is presented in this work, clearly mapping the spatial distribution of Rashba Spin torque in a nano-sized ferromagnet…
We present a theoretical analysis of current driven ferromagnetic resonance in a ferromagnet/normal-metal/ferromagnet tri-layer. This method of driving ferromagnetic resonance was recently realized experimentally by Tulapurkar et al. [Nature 438, 339 (2005)] and Sankey et al. [Phys. Rev. Lett. 96, 227601 (2006)]. The precessing magnetization rectifies the alternating current applied to drive the ferromagnetic resonance and leads to the generation of a dc voltage. Our analysis shows that a second mechanism to generate a dc voltage, rectification of spin currents emitted by the precessing magnet…
Spin transfer torque in magnetic structures occurs when the transverse component of the spin current that flows from the nonmagnetic medium to ferromagnetic medium are absorbed by the interface. In this paper, considering the Rashba effect on semiconductor region, we have discussed the spin transfer torque in semiconductor/ferromagnetic structure and obtained the components of spin-current density for two models: (I)-single electron and (II)- the distribution of electrons. We have shown that whatever the difference between Fermi surfaces in semiconductor and Fermi spheres for the up and down s…
Using a semiclassical approach that simultaneously incorporates the spin Hall effect (SHE), spin diffusion, quantum well states, and interface spin-orbit coupling (SOC), we address the interplay of these mechanisms as the origin of the in-plane current induced spin torque observed in the normal metal/ferromagnetic metal bilayer thin films. Focusing on the bilayers with a ferromagnet much thinner than its spin diffusion length, such as Pt/Co with $\sim 10$nm thickness, our approach addresses simultaneously the two contributions to the spin torque, namely the spin-transfer torque (SHE-STT) due t…
A complete set of the generalized drift-diffusion equations for a coupled charge and spin dynamics in ferromagnets in the presence of extrinsic spin-orbit coupling is derived from the quantum kinetic approach, covering major transport phenomena, such as the spin and anomalous Hall effects, spin swapping, spin precession and relaxation processes. We argue that the spin swapping effect in ferromagnets is enhanced due to spin polarization, while the overall spin texture induced by the interplay of spin-orbital and spin precessional effects displays a complex spatial dependence that can be exploit…
We investigate the anisotropic spin motive force in $α$-(BEDT-TTF)$_2$I$_3$, which is a multi-layered massless Dirac fermion system under pressure. Assuming the interlayer antiferromagnetic interaction and the interlayer anisotropic ferromagnetic interaction, we numerically examine the spin ordered state of the ground state using the steepest descent method. The anisotropic interaction leads to the anisotropic spin ordered state. We calculate the spin motive force produced by the anisotropic spin texture. The result quantitatively agrees with the experiment.
Spin orbit torques are of great interest for switching the magnetization direction in nanostructures, moving skyrmions and exciting spin waves. The standard method of determining their efficiency is by spin torque ferromagnetic resonance (ST-FMR), a technique that involves analyzing the resonance linewidth or lineshape. On microstuctures these two analysis methods are quite consistent. Here we present ST-FMR results on permalloy (Ni$_{80}$Fe$_{20}$) nanowires -- with widths varying from $150$ to 800 nm -- that show that the standard model used to analyze the resonance linewidth and lineshape g…
We present the theory of the spin motive force in antiferromagnets. We consider a one-dimensional antiferromagnetic domain wall strongly coupled with conduction electrons via an exchange interaction. We carry out a unitary transformation that rotates the spin coordinate system of the conduction electron locally, so that the quantization axis is in the direction of the localized spin. By numerically solving the time-dependent Schr$ö$dinger equation, we clearly demonstrate that the spin motive force acts on the conduction electron. The result suggests that there is no distinction between antifer…
Spin torque from spin current applied to a nanoscale region of a ferromagnet can act as negative magnetic damping and thereby excite self-oscillations of its magnetization. In contrast, spin torque uniformly applied to the magnetization of an extended ferromagnetic film does not generate self-oscillatory magnetic dynamics but leads to reduction of the saturation magnetization. Here we report studies of the effect of spin torque on a system of intermediate dimensionality - a ferromagnetic nanowire. We observe coherent self-oscillations of magnetization in a ferromagnetic nanowire serving as the…
In this work we report observation of in-plane current induced out-of-plane magnetic field driven torque in spin valve structure. Since ferromagnet has high spin orbit coupling it is expected to be the source of spin-orbit-torque as it possesses anomalous-Hall-effect (AHE: equivalent to spin Hall effect in heavy metal). So we have carried out spin-torque ferromagnetic resonance (ST-FMR) experiment in a spin valve (consists of a fixed magnet and a free magnet which are separated by Cu spacer), passing in-plane radio frequency current and measuring DC voltage. Our experimental results eventually…
Current-driven spin-orbit torques are investigated in a heterostructure composed of a ferromagnet deposited on top of a three dimensional topological insulator using the linear response formalism. We develop a tight-binding model of the heterostructure adopting a minimal interfacial hybridization scheme that promotes induced magnetic exchange on the topological surface states, as well as induced Rashba-like spin-orbit coupling in the ferromagnet. Therefore, our model accounts for spin Hall effect from bulk states together with inverse spin galvanic and magnetoelectric effects at the interface …
Within the s-d model description, we derive the current-driven spin torque in a ferromagnet, taking explicitly into account a spin-relaxing Caldeira-Leggett bath coupling to the s-electrons. We derive Bloch-Redfield equations of motion for the s-electron spin dynamics, and formulate a systematic gradient expansion to obtain non-adiabatic (higher-order) corrections to the well-known adiabatic (first-order) spin torque. We provide simple analytical expressions for the second-order spin torque. The theory is applied to current-driven domain wall motion. Second-order contributions imply a deformat…
We demonstrate that spin-orbit coupled electrons in a magnetically doped system exert a spin torque on the local magnetization, without a flowing current, when the chemical potential is modulated in a magnetic field. The spin torque is proportional to the anomalous Hall conductivity, and its effective field strength may overcome the Zeeman field. Using this effect, the direction of the local magnetization is switched by gate control in a thin film. This charge-induced spin torque is essentially an equilibrium effect, in contrast to the conventional current-induced spin-orbit torque, and, thus,…
In a ferromagnetic heterostructure, the interplay between a Rashba spin-orbit coupling and an exchange field gives rise to a current-driven spin torque. In a realistic device setup, we investigate the Rashba spin torque in the diffusive regime and report two major findings: (i) a nonvanishing torque exists at the edges of the device even when the magnetization and effective Rashba field are aligned; (ii) anisotropic spin relaxation rates driven by the Rashba spin-orbit coupling assign the spin torque a general expression ${\bm T}=T^y_{\para}(θ){\bm m}\times(\hat{\bm y}\times{\bm m})+T^y_{\bot}…
We demonstrate that the spin Hall effect in a thin film with strong spin-orbit scattering can excite magnetic precession in an adjacent ferromagnetic film. The flow of alternating current through a Pt/NiFe bilayer generates an oscillating transverse spin current in the Pt, and the resultant transfer of spin angular momentum to the NiFe induces ferromagnetic resonance (FMR) dynamics. The Oersted field from the current also generates an FMR signal but with a different symmetry. The ratio of these two signals allows a quantitative determination of the spin current and the spin Hall angle.
A skyrmion can be stabilized in a nanodisc geometry in a ferromagnetic material with Dzyaloshinskii-Moriya (DM) interaction. We apply spin torque uniform in space and time and observe numerically that the skyrmion is set in steady rotational motion around a point off the nanodisc center. We give a theoretical description of the emerging auto-oscillation dynamics based on the coupling of the rotational motion to the breathing mode of the skyrmion and to the associated oscillations of the in-plane magnetization. The analysis shows that the achievement of auto-oscillations in this simple set-up i…
Spin-torque ferromagnetic resonance (ST-FMR) is a common method used to measure spin-orbit torques (SOTs) in heavy metal/ferromagnet bilayer structures. In the course of a measurement, other resonant processes such as spin pumping (SP) and heating can cause spin current or heat flows between the layers, inducing additional resonant voltage signals via the inverse spin Hall effect (ISHE) and Nernst effects (NE). In the standard ST-FMR geometry, these extra artifacts exhibit a dependence on the angle of an in-plane magnetic field that is identical to the rectification signal from the SOTs. We sh…
We study theoretically the spin transfer effect on a domain wall in disordered weak ferromagnets. We have identified the adiabatic condition for the disordered case as $λ\gg λ_{\rm D}\equiv \sqrt{{\hbar D}/{\spol}}$, where $D$ and $\spol$ are the diffusion constant and the spin splitting energy due to the $s$-$d$ type exchange interaction, respectively, and found out that perfect spin-transfer effect occurs even in weak ferromagnets as long as this condition is satisfied. The effective $β$ term arising from the force turns out to govern the wall dynamics, and therefore, the wall motion can be …
Spin-orbit torques in bilayers of ferromagnetic and nonmagnetic materials hold promise for energy efficient switching of magnetization in nonvolatile magnetic memories. Previously studied spin Hall and Rashba torques originate from spin-orbit interactions within the nonmagnetic material and at the bilayer interface, respectively. Here we report a spin-orbit torque that arises from planar Hall current in the ferromagnetic material of the bilayer and acts as either positive or negative magnetic damping. This planar Hall torque exhibits unusual biaxial symmetry in the plane defined by the applied…
Spin-torque oscillators are strong candidates as nano-scale microwave generators and detectors. However, because of large amplitude-phase coupling (non-linearity), phase noise is enhanced over other linear auto-oscillators. One way to reduce nonlinearity is to use ferromagnetic layers as a resonator and excite them at localized spots, making a resonator-excitor pair. We investigated the excitation of oscillations in dipole-coupled ferromagnetic layers, driven by localized current at ferromagnetic nano-contacts. Oscillations possessed properties of optical-mode spin-waves and at low field ($\ap…
We study theoretically the detection and possible utilization of electric current-induced mechanical torques in ferromagnetic-normal metal heterostructures that are generated by spin-flip scattering or the absorption of transverse spin currents by a ferromagnet. To this end, we analyze the DC voltage signals over a spin valve that is driven by an AC current. In agreement with recent studies, this "rectification", measured as a function of AC frequency and applied magnetic field, contains important information on the magnetostatics and --dynamics. Subsequently, we show that the vibrations excit…
We investigate a possible correlation between spin orbit torque (SOT) and exchange-bias (EB) in IrMn-layer/ferromagnetic-ribbon heterostructure by performing magnetoimpedance (MI) measurements. To uncover this correlation, we benefit from EB training effect probed by MI effect at room temperature. A damping-like SOT driven by ac current through the antiferromagnetic IrMn applies to the ferromagnetic ribbon layer, determined by MI magnetic field and frequency sweeps. Importantly, magnitude of the SOT is observed to remain intact against EB training and decrease of EB through alternative magneti…
Spin motive force induced by the Rashba interaction in the presence of strong sd interaction between conduction electron and localized spin is theoretically studied. The motive force is calculated by evaluating the time-derivative of the current density on the basis of microscopic formalism. It is shown that there are two motive forces, one proportional to $\EvR\times\dot{\nv}$, the other, perpendicular component, proportional to $\EvR\times(\nv\times\dot{\nv})$, where $\EvR$ and $\nv$ are the Rashba electric field and localized spin direction, respectively. The second type arises in the stron…
We consider a quasi one-dimensional configuration consisting of two small pieces of ferromagnetic material separated by a metallic one and contacted by two metallic leads. A spin-polarized current is injected from one lead. Our goal is to investigate the correlation induced between the magnetizations of the two ferromagnets by spin-transfer torque. This torque results from the interaction between the magnetizations and the spin polarization of the current. We discuss the dynamics of a single ferromagnet, the extension to the case of two ferromagnets, and give some estimates for the parameters …
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 magentoelastic coupling, which produces the d.c. 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, non-collinear …
We consider theoretically the impact of Rashba spin-orbit coupling on spin torque oscillators (STOs) in synthetic ferromagnets and antiferromagnets that have either a bulk multilayer or a thin film structure. The synthetic magnets consist of a fixed polarizing layer and two free magnetic layers that interact through the Ruderman-Kittel-Kasuya-Yosida interaction. We determine analytically which collinear states along the easy axis that are stable, and establish numerically the phase diagram for when the system is in the STO mode and when collinear configurations are stable, respectively. It is …
We investigate the injection of quasiparticle spin currents into a superconductor via spin pumping from an adjacent FM layer.$\;$To this end, we use NbN/\ch{Ni80Fe20}(Py)-heterostructures with a Pt spin sink layer and excite ferromagnetic resonance in the Py-layer by placing the samples onto a coplanar waveguide (CPW). A phase sensitive detection of the microwave transmission signal is used to quantitatively extract the inductive coupling strength between sample and CPW, interpreted in terms of inverse current-induced torques, in our heterostructures as a function of temperature. Below the sup…
Spin-transfer torque (STT) effects on the stationary forced response of nanoscale ferromagnets subject to thermal fluctuations and driven by an ac magnetic field of arbitrary strength and direction are investigated via a generic nanopillar model of a spin-torque device comprising two ferromagnetic strata representing the free and fixed layers and a nonmagnetic conducting spacer all sandwiched between two ohmic contacts. The STT effects are treated via the Brown magnetic Langevin equation generalized to include the Slonczewski STT term thereby extending the statistical moment method [Y. P. Kalm…
When spin-orbit torques are measured using spin-torque ferromagnetic resonance (ST-FMR), two alternative ways of analyzing the results to extract the torque efficiencies -- lineshape analysis and analysis of the change in linewidth versus DC current -- often give inconsistent results. We identify a source for these inconsistencies. We show that fits of ST-FMR data to the standard analysis framework leave significant residuals that we identify as due to (i) current-induced excitations of a small volume of magnetic material with magnetic damping much larger than the bulk of the magnetic layer, t…
Magnetic damping is a key metric for emerging technologies based on magnetic nanoparticles, such as spin torque memory and high-resolution biomagnetic imaging. Despite its importance, understanding of magnetic dissipation in nanoscale ferromagnets remains elusive, and the damping is often treated as a phenomenological constant. Here we report the discovery of a giant frequency-dependent nonlinear damping that strongly alters the response of a nanoscale ferromagnet to spin torque and microwave magnetic field. This novel damping mechanism originates from three-magnon scattering that is strongly …
The spin torque exerted on a magnetic moment is a reaction to spin filtering when spin-polarized electrons interact with a thin ferromagnetic film. We show that, for certain conditions, a spin transmission resonance (STR) gives rise to a failure of spin filtering. As a consequence, no spin is transfered to the ferromagnet. The condition for STR depends on the incoming energy of electrons and the thickness of the film. For a simple model we find that when the STR condition is satisfied, the ferromagnetic film is transparent to the incoming electrons.
The Rashba-Edelstein effect stems from the interaction between the electron's spin and its momentum induced by spin-orbit interaction at an interface or a surface. It was shown that the inverse Rashba-Edelstein effect can be used to convert a spin- into a charge current. Here, we demonstrate that a Bi/Ag Rashba interface can even drive an adjacent ferromagnet to resonance. We employ a spin-torque ferromagnetic resonance excitation/detection scheme which was developed originally for a bulk spin-orbital effect, the spin Hall effect. In our experiment, the direct Rashba-Edelstein effect generates…
We study the motion of several types of domain wall profiles in spin-orbit coupled magnetic nanowires and also the influence of spin-orbit interaction on the ferromagnetic resonance of uniform magnetic films. We extend previous studies by fully considering not only the field-like contribution from the spin-orbit torque, but also the recently derived Slonczewski-like spin-orbit torque. We show that the latter interaction affects both the domain wall velocity and the Walker breakdown threshold non-trivially, which suggests that it should be accounted in experimental data analysis. We find that t…
We predict an unconventional spin-transfer torque (STT) acting on the magnetization of a free ferromagnetic (F) layer within N/TI/F vertical heterostructures which originates from strong spin-orbit coupling (SOC) on the surface of a three-dimensional topological insulator (TI), as well as from charge current becoming spin-polarized in the direction of transport as it flows from the normal metal (N) across the bulk of the TI slab. Unlike conventional STT in symmetric F'/I/F magnetic tunnel junctions, where only the in-plane STT component is non-zero in the linear response, both the in-plane and…
