We investigate the influence of magnons on the temperature-dependence and the anisotropy of the spin-orbit torque (SOT). For this purpose we use 3rd order perturbation theory in the framework of the Keldysh formalism in order to derive suitable equations to compute the magnonic SOT. We find several contributions to the magnonic SOT, which depend differently on the spin-wave stiffness $\mathcal{A}$ and on the temperature $T$, with the dominating contribution scaling like $T^{2}/\mathcal{A}^{2}$. Based on this formalism we compute the magnonic SOT in the ferromagnetic Rashba model. For large Rashba parameters the magnonic SOT is strongly anisotropic and for small quasiparticle broadening it may become larger than the non-magnonic SOT.
The spin wave transportation through a transverse magnetic domain wall (DW) in a magnetic nanowire is studied. It is found that spin wave passes through a DW without reflection. A magnon, the quantum of the spin wave, carries opposite spins on the two sides of the DW. As a result, there is a spin angular momentum transfer from the propagating magnons to the DW. This magnonic spin-transfer torque can efficiently drive a DW to propagate in the opposite direction to that of the spin wave.
In thin magnetic layers with structural inversion asymmetry and spin-orbit coupling, a Dzyaloshinskii-Moriya interaction arises at the interface. When a spin wave current ${\bf j}_m$ flows in a system with a homogeneous magnetization {\bf m}, this interaction produces an effective field-like torque on the form ${\bf T}_{\rm FL}\propto{\bf m}\times({\bf z}\times{\bf j}_m)$ as well as a damping-like torque, ${\bf T}_{\rm DL}\propto{\bf m}\times[({\bf z}\times{\bf j}_m)\times{\bf m}]$ in the presence of spin-wave relaxation (${\bf z}$ is normal to the interface). These torques mediated by the mag…
Femtosecond laser pulses can induce ultrafast demagnetization as well as generate bursts of hot electron spin currents. In trilayer spin valves consisting of two metallic ferromagnetic layers separated by a nonmagnetic one, hot electron spin currents excited by an ultrashort laser pulse propagate from the first ferromagnetic layer through the spacer reaching the second magnetic layer. When the magnetizations of the two magnetic layers are noncollinear, this spin current exerts a torque on magnetic moments in the second ferromagnet. Since this torque is acting only within the sub-ps timescale, …
Estimation of spin-orbit torques in the presence of current-induced magnon creation and annihilation
Université de Strasbourg, CNRS, Institut de Physique et Chimie des Matériaux de Strasbourg（斯特拉斯堡大学，法国国家科学研究中心，斯特拉斯堡材料与化学物理研究所）；ETH Zurich（苏黎世联邦理工学院）；Politecnico di Milano（米兰理工大学）
We formulate a microscopic linear response theory of nonequilibrium magnonic torques and magnon pumping applicable to multiple-magnonic-band uniform ferromagnets with Dzyaloshinskii-Moriya interactions. From the linear response theory, we identify the extrinsic and intrinsic contributions where the latter is expressed via the Berry curvature of magnonic bands. We observe that in the presence of a time-dependent magnetization Dzyaloshinskii-Moriya interactions can act as fictitious electric fields acting on magnons. We study various current responses to this fictitious field and analyze the rol…
We experimentally demonstrate generation of coherent propagating magnons in ultra-thin magnetic-insulator films by spin-orbit torque induced by dc electric current. We show that this challenging task can be accomplished by utilizing magnetic-insulator films with large perpendicular magnetic anisotropy. We demonstrate simple and flexible spin-orbit torque devices, which can be used as highly efficient nanoscale sources of coherent propagating magnons for insulator-based spintronic applications.
We report a study on spin conductance in ultra-thin films of Yttrium Iron Garnet (YIG), where spin transport is provided by propagating spin waves, that are generated and detected by direct and inverse spin Hall effects in two Pt wires deposited on top. While at low current the spin conductance is dominated by transport of thermal magnons, at high current, the spin conductance is dominated by low-damping non-equilibrium magnons thermalized near the spectral bottom by magnon-magnon interaction, with consequent a sensitivity to the applied magnetic field and a longer decay length. This picture i…
The interplay between spin wave and magnetic texture represents the information exchange between the fast and slow dynamical parts of magnetic systems. Here we formulate a set of magnonic torques acting on background magnetic texture, by extracting time-invariant information from the fast precessing spin waves. Under the frame of magnonic torques, we use theoretical formulations and micromagnetic simulations to investigate the spin wave driven domain wall motion in two typical symmetry-breaking situations: the rotational symmetry broken by the Dzyaloshinkii-Moriya interaction, and the translat…
We investigate a spin-electricity conversion effect in a topological insulator/ferromagnet heterostructure. In the spin-momentum-locked surface state, an electric current generates nonequilibrium spin accumulation, which causes a spin-orbit torque that acts on the ferromagnet. When spins in the ferromagnet are completely parallel to the accumulated spin, this spin-orbit torque is zero. In the presence of spin excitations, however, a coupling between magnons and electrons enables us to obtain a nonvanishing torque. In this paper, we consider a model of the heterostructure in which a three-dimen…
Recent studies have revealed that domain walls in magnetic nanostructures can serve as compact, energy-efficient spin-wave waveguides for building magnonic devices that are considered promising candidates for overcoming the challenges and bottlenecks of today's CMOS technologies. However, imprinting long strip-domain walls into magnetic nanowires remains a challenge, especially in curved geometries. Here, through micromagnetic simulations, we present a method for writing strip-domain walls into curved magnetic nanowires using spin-orbit torque. We employ Y-shaped magnetic nanostructures as wel…
We demonstrate the influence of damping and field-like torques in the magnon-photon coupling process by classically integrating the generalized Landau-Lifshitz-Gilbert equation with RLC equation in which a phase correlation between dynamic magnetization and microwave current through combined Ampère and Faraday effects are considered. We show that the gap between two hybridized modes can be controlled in samples with damping parameter in the order of $10^{-3}$ by changing the direction of the dc current density $J$ if a certain threshold is reached. Our results suggest that an experimental real…
In an antiferromagnet (AF) with uniaxial anisotropy, spin-up and spin-down magnons coexist and form an intrinsic degree of freedom resembling electrons. When polarized by an adjacent ferromagnet (F), a magnonic pure spin current can be thermally generated in an AF. We explore thermal magnon transport in an insulating F/AF/F trilayer where propagating magnons inside the AF spacer can transfer angular momenta between the two Fs. We find that a sufficiently large temperature gradient can switch the downstream F via magnonic spin-transfer torque if it is initially antiparallel with the upstream F.…
We present the temperature dependence of the thermal magnon density in a thin ferromagnetic layer. By employing Brillouin light scattering and varying the temperature, an increase of the magnon density accompanied by a lowering of the spin-wave frequency is observed with increasing temperature. The magnon density follows the temperature according to the Bose-Einstein distribution function which leads to an approximately linear dependency. In addition, the influence of this effect in spin-transfer-torque-driven systems is presented. In particular, the increase in the magnon density with tempera…
Thermally activated domain wall (DW) motion in magnetic insulators has been considered theoretically, with a particular focus on the role of Dzyaloshinskii-Moriya Interaction (DMI) and thermomagnonic torques. The thermally assisted DW motion is a consequence of the magnonic spin current due to the applied thermal bias. In addition to the exchange magnonic spin current and the exchange adiabatic and the entropic spin transfer torques, we also consider the DMI-induced magnonic spin current, thermomagnonic DMI field-like torque and the DMI entropic torque. Analytical estimations are supported by …
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 investigate the domain wall dynamics of a ferromagnetic wire under the combined influence of a spin-polarized current and magnonic spin-transfer torque generated by an external field, taking also into account Rashba spin-orbit coupling interactions. It is demonstrated that current-induced motion of the domain wall may be completely reversed in an oscillatory fashion by applying a magnonic spin-transfer torque as long as the spin-wave velocity is sufficiently high. Moreover, we show that the motion of the domain wall may be fully terminated by means of the generation of spin-waves, suggestin…
We theoretically investigate the role of spin fluctuations in charge transport through a magnetic junction. Motivated by recent experiments that measure a nonlinear dependence of the current on electrical bias, we develop a systematic understanding of the interplay of charge and spin dynamics in nanoscale magnetic junctions. Our model captures two distinct features arising from these fluctuations: magnon-assisted transport and the effect of spin-transfer torque on the magnetoconductance. The latter stems from magnetic misalignment in the junction induced by spin-current fluctuations. As the te…
Impact of current-induced magnons on spin-orbit torque analysis
Budapest University of Technology and Economics（布达佩斯技术与经济大学）；University of Groningen（格罗宁根大学）；HUN-REN Centre for Energy Research, Institute of Technical Physics and Materials Science（匈牙利研究与教育网络能源研究中心技术物理与材料科学研究所）
The emerging field of nano-magnonics utilizes high-frequency waves of magnetization - the spin waves - for the transmission and processing of information on the nanoscale. The advent of spin-transfer torque has spurred significant advances in nano-magnonics, by enabling highly efficient local spin-wave generation in magnonic nanodevices. Furthermore, the recent emergence of spin-orbitronics, which utilizes spin-orbit interaction as the source of spin torque, has provided a unique ability to exert spin torque over spatially extended areas of magnonic structures, enabling enhanced spin-wave tran…
The combination of parametric pumping and spin-transfer torque is a powerful approach that enables high-level control over magnetic excitations in thin-film ferromagnets. The excitation parameters, such as pumping power and external field strength, affect the instabilities of individual magnon modes. We theoretically explore how the simultaneous effects of parametric pumping and spin transfer torque influence these magnetic instabilities in a thin-film ferromagnet. Within the Landau-Lifshitz-Gilbert framework, we perform micromagnetic simulations of magnon excitations in yttrium iron garnet by…
To address thermal stability issues for spintronic devices with a reduced size, we investigate spin-orbit torque in Co/Pt multilayers with strong perpendicular magnetic anisotropy. Note that the spin-orbit torque arises from the global imbalance of the spin currents from the top and bottom interfaces for each Co layer. By inserting Ta or Cu layers to strengthen the top-down asymmetry, the spin-orbit torque efficiency can be greatly modified without compromised perpendicular magnetic anisotropy. Above all, the efficiency builds up as the number of layers increases, realizing robust thermal stab…
The field of magnonics, which utilizes propagating spin waves for nano-scale transmission and processing of information, has been significantly advanced by the advent of the spin-orbit torque. The latter phenomenon can allow one to overcome two main drawbacks of magnonic devices - low energy efficiency of conversion of electrical signals into spin wave signals, and fast spatial decay of spin waves in thin-film waveguiding structures. At first glance, the excitation and amplification of spin waves by spin-orbit torques can seem to be straightforward. Recent research indicates, however, that the…
We report on the excitation and detection of short-waved spin waves with wave vectors up to about $40\,\mathrm{rad}\,μ\mathrm{m}^{-1}$ in spin-wave waveguides made from ultrathin, in-plane magnetized Co$_{8}$Fe$_{72}$B$_{20}$ (CoFeB). The CoFeB is incorporated in a layer stack of Ta/CoFeB/Mgo, a layer system featuring large spin orbit torques and a large perpendicular magnetic anisotropy constant. The short-waved spin waves are excited by nanometric coplanar waveguides and are detected via spin rectification and microfocussed Brillouin light scattering spectroscopy. We show that the large perp…
We study domain wall (DW) motion induced by spin waves (magnons) in the presence of Dzyaloshinskii-Moriya interaction (DMI). The DMI exerts a torque on the DW when spin waves pass through the DW, and this torque represents a linear momentum exchange between the spin wave and the DW. Unlike angular momentum exchange between the DW and spin waves, linear momentum exchange leads to a rotation of the DW plane rather than a linear motion. In the presence of an effective easy plane anisotropy, this DMI induced linear momentum transfer mechanism is significantly more efficient than angular momentum t…
We discover that the way spin-waves exert magnetic torques in multiferroic materials can cause not only domain wall motion, but also magnetization dynamics for homogeneous magnetization textures. Interestingly, the domain wall motion can be controlled via purely electrical means with the spin-waves being generated by an ac electric field $E$ while the direction of the wall motion also is sensitive to an applied dc $E$ field. Moreover, we determine the interaction between spin-transfer torque from an electric current and a magnetic domain wall in multiferroics and show that the Walker breakdown…
We investigate the physical origin of nonlinear damping due to mode coupling between several auto-oscillatory modes driven by spin-orbit torque in constricted Py/Pt heterostructures by examining the dependence of auto-oscillation on temperature and applied field orientation. We observe a transition in the nonlinear damping of the auto-oscillation modes extracted from the total oscillation power as a function of drive current, which coincides with the onset of power redistribution amongst several modes and the crossover from linewidth narrowing to linewidth broadening in all individual modes. T…
Thermally-driven spin-transfer torques have recently been reported in electrically insulating ferromagnet$|$normal-metal heterostructures. In this paper, we propose two physically distinct mechanisms for such torques. The first is a local effect: out-of-equilibrium, thermally-activated magnons in the ferromagnet, driven by a spin Seebeck effect, exert a torque on the magnetization via magnon-magnon scattering with coherent dynamics. The second is a nonlocal effect which requires an additional magnetic layer to provide the symmetry breaking necessary to realize a thermal torque. The simplest st…
Traveling spin waves in magnonic waveguides undergo severe attenuation, which tends to result in a finite propagation length of spin waves, even in magnetic materials with the accessible lowest damping constant, heavily restricting the development of magnonic devices. Compared with the spin waves in traditional waveguides, propagating spin waves along strip domain wall are expected to exhibit enhanced transmission. Here, we demonstrate, theoretically and through micromagnetic simulations, that spin-orbit torque associated with a ferromagnet/heavy metal bilayer can efficiently control the atten…
Magnetic domain wall (DW) motion induced by a localized Gaussian temperature profile is studied in a Permalloy nanostrip within the framework of the stochastic Landau-Lifshitz-Bloch equation. The different contributions to thermally induced DW motion, entropic torque and magnonic spin transfer torque, are isolated and compared. The analysis of magnonic spin transfer torque includes a description of thermally excited magnons in the sample. A third driving force due to a thermally induced dipolar field is found and described. Finally, thermally induced DW motion is studied under realistic condit…
Spin torque nano-oscillator has been extensively studied both theoretically and experimentally in recent decades due to its potential applications in future microwave communication technology and neuromorphic computing. In this work, we present a skyrmion-based spin torque nano-oscillator driven by a spatially uniform direct current, where the skyrmion is confined by two pinning sites. Different from other skyrmion-based oscillators that arise from the circular motion or the breathing mode of a skyrmion, the steady-state oscillatory motions are produced by the periodic deformation of an elonga…
We point out a relation between the dissipative spin-transfer-torque parameter $β$ and the contribution of magnon drag to the thermoelectric power in conducting ferromagnets. Using this result we estimate $β$ in iron at low temperatures, where magnon drag is believed to be the dominant contribution to the thermopower. Our results may be used to determine $β$ from magnon-drag-thermopower experiments, or, conversely, to infer the strength of magnon drag via experiments on spin transfer.
We investigate the magnetization dynamics that arise when a thin-film ferromagnet is deposited on a topological insulator (TI), focusing in particular on domain-wall motion via current and the possibility of a spin-wave torque acting on the magnetization. We show analytically that the coupling between the magnetic domain wall and the TI removes the degeneracy of the wall profile with respect to its chirality and topological charge. Moreover, we find that the threshold for Walker breakdown of domain wall motion is substantially increased and determined by the interaction with the TI, allowing f…
Here we demonstrate numerically that shape anisotropy in MgO-based spin-torque nano-oscillators consisting of an out-of-plane magnetized free layer and an in-plane polarizer is necessary to stabilize out-of-plane magnetization precession without the need of external magnetic fields. As the in-plane anisotropy is increased, a gradual tilting of the magnetization towards the in-plane easy direction is introduced, favouring zero-field dynamics over static in-plane states. Above a critical value, zero-field dynamics are no longer observed. The optimum ratio of in-plane shape to out-of-plane uniaxi…
Role of material-dependent properties in THz field-derivative-torque-induced nonlinear magnetization dynamics
School of Physical Sciences, National Institute of Science Education and Research（国家科学教育研究所物理科学学院）；Department of Physics, Indian Institute of Technology (ISM) Dhanbad（印度理工学院（ISM）达纳巴德物理系）
The influence of an asymmetric in-plane magnetic anisotropy on the thermally activated spin current is studied theoretically for two different systems; (i) the system consisting of a ferromagnetic insulator in a direct contact with a nonmagnetic metal, and the sandwich structure consisting of a ferromagnetic insulating part sandwiched between two nonmagnetic metals. It is shown that when the difference between the temperatures of the two nonmagnetic metals in a structure is not large, the spin pumping currents from the magnetic part to the nonmagnetic ones are equal in amplitude and have oppos…
We studied the effect of inserting 0.5 nm-thick spacer layers (Ti, V, Cr, Mo, W) at the Pt/Co interface on the spin-orbit torques, Hall effect, magnetoresistance, saturation magnetization, and magnetic anisotropy. We find that the damping-like spin-orbit torque decreases substantially for all samples with a spacer layer compared to the reference Pt/Co bilayer, consistently with the opposite sign of the atomic spin-orbit coupling constant of the spacer elements relative to Pt. The reduction of the damping-like torque is monotonic with atomic number for the isoelectronic 3d, 4d, and 5d elements,…
We use three-terminal magnetic tunnel junctions (MTJs) designed for field-free switching by spin-orbit torques (SOTs) to systematically study the impact of dual voltage pulses on the switching performances. We show that the concurrent action of an SOT pulse and an MTJ bias pulse allows for reducing the critical switching energy below the level typical of spin transfer torque while preserving the ability to switch the MTJ on the sub-ns time scale. By performing dc and real-time electrical measurements, we discriminate and quantify three effects arising from the MTJ bias: the voltage-controlled …
Transition metal dichalcogenides (TMDs) are promising materials for efficient generation of current-induced spin-orbit torques on an adjacent ferromagnetic layer. Numerous effects, both interfacial and bulk, have been put forward to explain the different torques previously observed. Thus far, however, there is no clear consensus on the microscopic origin underlying the spin-orbit torques observed in these TMD/ferromagnet bilayers. To shine light on the microscopic mechanisms at play, here we perform thickness dependent spin-orbit torque measurements on the semiconducting WSe$_{2}$/permalloy bi…
We experimentally identify coherent spin pumping in the magnon-magnon hybrid modes of permalloy/yttrium iron garnet (Py/YIG) bilayers. Using broadband ferromagnetic resonance, an "avoided crossing" is observed between the uniform mode of Py and the spin wave mode of YIG due to the fieldlike interfacial exchange coupling. We also identify additional linewidth suppression and enhancement for the in-phase and out-of-phase hybrid modes, respectively, \textcolor{black}{which can be interpreted as concerted dampinglike torque from spin pumping}. Our analysis predicts inverse proportionality of both …
Applications based on spin currents strongly profit from the control and reduction of their effective damping and their transport properties. We here experimentally observe magnon mediated transport of spin (angular) momentum through a 13.4 nm thin yttrium iron garnet film with full control of the magnetic damping via spin-orbit torque. Above a critical spin-orbit torque, the fully compensated damping manifests itself as an increase of magnon conductivity by almost two orders of magnitude. We compare our results to theoretical expectations based on recently predicted current induced magnon con…
The recent experiment [Y. Wang et al., Science 366, 1125 (2019)] on magnon-mediated spin-transfer torque (MSTT) was interpreted in terms of a picture where magnons are excited within an antiferromagnetic insulator (AFI), by applying nonequilibrium electronic spin density at one of its surfaces, so that their propagation across AFI deprived of conduction electrons eventually leads to reversal of magnetization of a ferromagnetic metal (FM) attached to the opposite surface of AFI. We employ a recently developed time-dependent nonequilibrium Green functions combined with the Landau-Lifshitz-Gilber…
It has been shown that the spin Hall effect from heavy transition metals can generate sufficient spin-orbit torque and further produce current-induced magnetization switching in the adjacent ferromagnetic layer. However, if the ferromagnetic layer has in-plane magnetic anisotropy, probing such switching phenomenon typically relies on tunneling magnetoresistance measurement of nano-sized magnetic tunnel junctions, differential planar Hall voltage measurement, or Kerr imaging approaches. We show that in magnetic heterostructures with spin Hall metals, there exist current-induced in-plane spin Ha…
We investigate magnetization dynamics in a spin-Hall oscillator using a direct current measurement as well as conventional microwave spectrum analysis. When the current applies an anti-damping spin-transfer torque, we observe a change in resistance which we ascribe to the excitation of incoherent exchange magnons. A simple model is developed based on the reduction of the effective saturation magnetization, quantitatively explaining the data. The observed phenomena highlight the importance of exchange magnons on the operation of spin-Hall oscillators.
The magnetization dynamics in nanostructures has been extensively studied in the last decades, and nanomagnetism has evolved significantly over that time, discovering new effects, developing numerous applications, and identifying promising new directions. This includes magnonics, an emerging research field oriented on the study of spin-wave dynamics and their applications. In this context, thin ferromagnetic films with perpendicular magnetic anisotropy (PMA) offer interesting opportunities to study spin waves, in particular, due to out-of-plane magnetization in remanence or at relatively weak …
Spin orbit torque (SOT) provides an efficient way of generating spin current that promises to significantly reduce the current required for switching nanomagnets. However, an in-plane current generated SOT cannot deterministically switch a perpendicularly polarized magnet due to symmetry reasons. On the other hand, perpendicularly polarized magnets are preferred over in-plane magnets for high-density data storage applications due to their significantly larger thermal stability in ultra-scaled dimensions. Here we show that it is possible switch a perpendicularly polarized magnet by SOT without …
We analyze dispersion relations of magnons in ferromagnetic nanostructures with uniaxial anisotropy taking into account inertial terms, i.e. magnetic nutation. Inertial effects are parametrized by damping-independent parameter $β$, which allows for an unambiguous discrimination of inertial effects from Gilbert damping parameter $α$. The analysis of magnon dispersion relation shows its two branches are modified by the inertial effect, albeit in different ways. The upper nutation branch starts at $ω=1/ β$, the lower branch coincides with FMR in the long-wavelength limit and deviates from the zer…
We report that by measuring current-induced hysteresis loop shift versus in-plane bias magnetic field, the spin Hall effect (SHE) contribution of the current-induced effective field per current density, $χ_{SHE}$, can be estimated for Pt and Ta-based magnetic heterostructures with perpendicular magnetic anisotropy (PMA). We apply this technique to a Pt-based sample with its ferromagnetic (FM) layer being wedged-deposited and discover an extra effective field contribution, $χ_{Wedged}$, due to the asymmetric nature of the deposited FM layer. We confirm the correlation between $χ_{Wedged}$ and t…
