Exchange Torque Research Articles

Real-space nonlocal Gilbert damping from exchange torque correlation applied to bulk ferromagnets and their surfaces

Real-space nonlocal Gilbert damping from exchange torque correlation applied to bulk ferromagnets and their surfaces

Spin transfer exchange torque in ferromagnet/ferromagnet structures made of half-metals with large exchange gaps

Spin transfer exchange torque in ferromagnet/ferromagnet structures made of half-metals with large exchange gaps

Highly efficient spin-orbit torque in a perpendicular synthetic ferrimagnet

Perpendicular synthetic ferrimagnet (pSFi) due to the low stray field and net magnetization is expected to replace single ferromagnet as a free layer to optimize the memory devices for high storage density and low-energy consumption. Here, we investigate the dependence of exchange-coupling strength on the thickness of the spacer Ru and current-induced magnetization reversal due to spin-orbit torque in $\mathrm{Ta}/\mathrm{Pt}/{[\mathrm{Pt}/\mathrm{Co}]}_{2}/\mathrm{Ru}/{[\mathrm{Co}/\mathrm{Pt}]}_{4}/\mathrm{Pt}$ structure with a perpendicular magnetic anisotropy. An oscillating interlayer exchange coupling as a function of Ru spacer layer thickness with a period of 1.16 nm is determined by combining the anomalous Hall effect and the polar magnetic-optical Kerr effect. Furthermore, current-controllable magnetization reversal experiments reveal that the magnetizations of top and bottom layers with antiferromagnetic coupling switch simultaneously due to the combination of spin-orbit torque generated from the two adjacent heavy-metal layers and the interlayer exchange torque. The SOT efficiency $\ensuremath{\chi}\ensuremath{\sim}57.52\phantom{\rule{0.16em}{0ex}}\mathrm{Oe}/({10}^{6}\phantom{\rule{0.16em}{0ex}}\mathrm{A}/\mathrm{c}{\mathrm{m}}^{2})$, corresponding to an effective spin Hall angle $\phantom{\rule{4pt}{0ex}}{\ensuremath{\xi}}_{DL}\ensuremath{\sim}0.68$, is estimated by analyzing current-dependent anomalous Hall resistance with our proposed quasistatic balance equation of magnetic moments. In addition to the advantage of minimizing stray field acting on the storage layer, the observed low switching current density and high spin-orbit torque efficiency suggest that the pSFi structure with a high thermal stability factor has great potential to realize the high-density and low-power consumption of nonvolatile magnetic memory devices.

Exchange-Torque-Triggered Fast Switching of Antiferromagnetic Domains.

The antiferromagnet is considered to be a promising hosting material for the next generation of magnetic storage due to its high stability and stray-field-free property. Understanding the switching properties of the antiferromagnetic (AFM) domain state is critical for developing AFM spintronics. By utilizing the magneto-optical birefringence effect, we experimentally demonstrate the switching rate of the AFM domain can be enhanced by more than 2 orders of magnitude through applying an alternating square-wave field on a single crystalline Fe/CoO bilayer. The observed extraordinary speed can be much faster than that triggered by a constant field with the same amplitude. The effect can be understood as the efficient suppression of the pinning of AFM domain walls by the strong exchange torque triggered by the reversal of the Fe magnetization, as revealed by spin dynamics simulations. Our finding opens up new opportunities to design the antiferromagnet-based spintronic devices utilizing the ferromagnet-antiferromagnet heterostructure.

Ionitronic manipulation of current-induced domain wall motion in synthetic antiferromagnets

The current induced motion of domain walls forms the basis of several advanced spintronic technologies. The most efficient domain wall motion is found in synthetic antiferromagnetic (SAF) structures that are composed of an upper and a lower ferromagnetic layer coupled antiferromagnetically via a thin ruthenium layer. The antiferromagnetic coupling gives rise to a giant exchange torque with which current moves domain walls at maximum velocities when the magnetic moments of the two layers are matched. Here we show that the velocity of domain walls in SAF nanowires can be reversibly tuned by several hundred m/s in a non-volatile manner by ionic liquid gating. Ionic liquid gating results in reversible changes in oxidation of the upper magnetic layer in the SAF over a wide gate-voltage window. This changes the delicate balance in the magnetic properties of the SAF and, thereby, results in large changes in the exchange coupling torque and the current-induced domain wall velocity. Furthermore, we demonstrate an example of an ionitronic-based spintronic switch as a component of a potential logic technology towards energy-efficient, all electrical, memory-in-logic.

Controlled Localized Domain Wall Writing in Antiferromagnetic Nano Stripes With In-Plane Transverse Currents

In order for textures in intrinsic antiferromagnets to be applied in proposed spintronics devices, localized and controllable writing is required. Here, the feasibility of a simple scheme for spin-Hall torque driven localized writing of chiral antiferromagnetic (AFM) domain wall (DW) pairs at a chosen location in AFM nano stripes is investigated. Short voltage pulses causing in-plane current-injection across transverse contacts in the heavy metal trigger a localized horizontal boundary-nucleated reverse AFM domain that propagates throughout the width to the opposite boundary, defining a locally written DW pair without affecting information in other parts of the device. The nucleation mechanism is examined, indicating exchange torque governing. A diagram of the number of DW-pairs written as a function of applied writing pulse amplitude and pulse duration is shown for a generic antiferromagnet, illustrating the degree of control required of the excitation protocol. Simulations of write and drive pulses are also presented, showing that the slight current bending around the writing contacts does not impose any significant pinning nor nucleation of unwanted textures for a typical driving amplitude. The advantages of this simple scheme are that it does not require any component for vertical spin-polarized current injection nor lasers for writing as in previous proposals.

Current-driven transverse domain wall oscillations in perpendicular spin-valve structures

Spin-transfer-driven oscillations of a transverse domain wall confined to a perpendicular spin-valve structure are investigated using a one-dimensional model. The stack consists of a polarizer, nonmagnetic spacer, soft free layer, and pinned magnetic layer. It is found that the domain-wall oscillation frequency is a nonmonotonic, highly asymmetrical function of applied electric current, showing a strong dependence on the current direction and the relative strengths of the interfacial and bulk spin-transfer torques. Micromagnetic analysis reveals that the surprising and atypical oscillator response is due to an interplay between the interfacial spin-transfer torque, the bulk spin-transfer torque, the exchange torque, and the damping torque. The underlying physical and material responses are examined, including the important role of the domain-wall twist. The competitions between the involved torques under different operating conditions suggest that the oscillator could serve as a model system to investigate magnetic and spintronic phenomena at the nanoscale. The observed current-dependent twisting of the free-layer magnetization about the axis of precession may further be found interesting for investigations of the interaction between spin-polarized current and chiral spin structures.

A novel three-axis attitude stabilization method using in-plane internal mass-shifting

This paper investigates the feasibility of using four movable masses distributed in a plane to realize three-axis attitude stabilization. With the proposed distribution and moving the paired masses in the same or opposite direction simultaneously, aerodynamic torque or internal momentum exchange torque is acted on the spacecraft. Then the spacecraft is gradually stabilized under a three-phase control strategy. Each of the three control phases is designed based on optimal control, nonlinear and sliding mode control, respectively. The stability of the proposed controller is given. Furthermore, numerical simulation matches the analytical results presented in this paper. Results show that three-axis attitude stabilization is possible using only in-plane movable masses which weigh less than 10 percent of spacecraft mass. Finally, the proposed control system can be a viable alternative for three-axis attitude stabilization of spacecraft orbiting in low Earth orbit.

Hydrodynamic description of long-distance spin transport through noncollinear magnetization states: Role of dispersion, nonlinearity, and damping

Nonlocal compensation of magnetic damping by spin injection has been theoretically shown to establish dynamic, noncollinear magnetization states that carry spin currents over micrometer distances. Such states can be generically referred to as dissipative exchange flows (DEFs) because spatially diffusing spin currents are established by the mutual exchange torque exerted by neighboring spins. Analytical studies to date have been limited to the weak spin injection assumption whereby the equation of motion for the magnetization is mapped to hydrodynamic equations describing spin flow and then linearized. Here, we analytically and numerically study easy-plane ferromagnetic channels subject to spin injection of arbitrary strength at one extremum under a unified hydrodynamic framework. We find that DEFs generally exhibit a nonlinear profile along the channel accompanied by a nonlinear frequency tuneability. At large injection strengths, we fully characterize a novel magnetization state we call a contact-soliton DEF (CS-DEF) composed of a stationary soliton at the injection site, which smoothly transitions into a DEF and exhibits a negative frequency tuneability. The transition between a DEF and a CS-DEF occurs at the maximum precessional frequency and coincides with the Landau criterion: a subsonic to supersonic flow transition. Leveraging the hydraulic-electrical analogy, the current-voltage characteristics of a nonlinear DEF circuit are presented. Micromagnetic simulations of nanowires that include magnetocrystalline anisotropy and non-local dipole fields are in qualitative agreement with the analytical results. The magnetization states found here along with their characteristic profile and spectral features provide quantitative guidelines to pursue an experimental demonstration of DEFs in ferromagnetic materials and establishes a unified description for long-distance spin transport.

Exchange-torque-induced excitation of perpendicular standing spin waves in nanometer-thick YIG films

Spin waves in ferrimagnetic yttrium iron garnet (YIG) films with ultralow magnetic damping are relevant for magnon-based spintronics and low-power wave-like computing. The excitation frequency of spin waves in YIG is rather low in weak external magnetic fields because of its small saturation magnetization, which limits the potential of YIG films for high-frequency applications. Here, we demonstrate how exchange-coupling to a CoFeB film enables efficient excitation of high-frequency perpendicular standing spin waves (PSSWs) in nanometer-thick (80 nm and 295 nm) YIG films using uniform microwave magnetic fields. In the 295-nm-thick YIG film, we measure intense PSSW modes up to 10th order. Strong hybridization between the PSSW modes and the ferromagnetic resonance mode of CoFeB leads to characteristic anti-crossing behavior in broadband spin-wave spectra. We explain the excitation of PSSWs by exchange coupling between forced magnetization precessions in the YIG and CoFeB layers. If the amplitudes of these precessions are different, a dynamic exchange torque is generated, causing the emission of spin waves from the interface. PSSWs form when the wave vector of the spin waves matches a perpendicular confinement condition. PSSWs are not excited if exchange coupling between YIG and CoFeB is eliminated by a 10 nm Ta spacer layer. Micromagnetic simulations confirm the exchange-torque-driven mechanism.

Role of RKKY torque on domain wall motion in synthetic antiferromagnetic nanowires with opposite spin Hall angles

We experimentally show the effect of enhanced spin-orbit and RKKY induced torques on the current-induced motion of a pair of domain walls (DWs), which are coupled antiferromagnetically in synthetic antiferromagnetic (SAF) nanowires. The torque from the spin Hall effect (SHE) rotates the Néel DWs pair into the transverse direction, which is due to the fact that heavy metals of opposite spin Hall angles are deposited at the top and the bottom ferromagnetic interfaces. The rotation of both DWs in non-collinear fashion largely perturbs the antiferromagnetic coupling, which in turn stimulates an enhanced interlayer RKKY exchange torque that improved the DW velocity. The interplay between the SHE-induced torque and the RKKY exchange torque is validated via micromagnetic simulations. In addition, the DW velocity can be further improved by increasing the RKKY exchange strength.

Spin torque driven dynamics of a coupled two-layer structure: Interplay between conservative and dissipative coupling

In this manuscript the general concepts of spin wave theory are adapted to the dynamics of a self-polarized system based on two layers coupled via interlayer exchange (conservative coupling) and mutual spin torque (dissipative coupling). An analytical description of the non-linear dynamics is proposed and validated through numerical simulations. In contrast to the single layer model, the phase equation of the coupled system has a contribution coming from the dissipative part of the LLGS equation. It is shown that this is a major contribution to the frequency mandatory to describe well the most basic features of the dynamics of coupled systems. Using the proposed model a specific feature of coupled dynamics is addressed: the redshift to blueshift transition observed in the frequency current dependence of this kind of exchange coupled systems upon increasing the applied field. It is found that the blueshift regime can only occur in a region of field where the two linear eigenmodes contribute equally to the steady state mode (i.e. high mode hybridization). Finally, a general perturbed Hamiltonian equation for the coupled system is proposed.

Swift thermal steering of domain walls in ferromagnetic MnBi stripes.

We predict a fast domain wall (DW) motion induced by a thermal gradient across a nanoscopic ferromagnetic stripe of MnBi. The driving mechanism is an exchange torque fueled by magnon accumulation at the DWs. Depending on the thickness of the sample, both hot-to-cold and cold-to-hot DW motion directions are possible. The finding unveils an energy efficient way to manipulate DWs as an essential element in magnetic information processing such as racetrack memory.

Spin transfer torque in antiferromagnetic spin valves: From clean to disordered regimes

Current-driven spin torques in metallic spin valves composed of antiferromagnets are theoretically studied using the nonequilibrium Green's function method implemented on a tight-binding model. We focus our attention on G-type and L-type antiferromagnets in both clean and disordered regimes. In such structures, spin torques can either rotate the magnetic order parameter coherently (coherent torque) or compete with the internal antiferromagnetic exchange (exchange torque). We show that, depending on the symmetry of the spin valve, the coherent and exchange torques can either be in the plane, $\ensuremath{\propto}\mathbf{n}\ifmmode\times\else\texttimes\fi{}(\mathbf{q}\ifmmode\times\else\texttimes\fi{}\mathbf{n})$ or out of the plane $\ensuremath{\propto}\mathbf{n}\ifmmode\times\else\texttimes\fi{}\mathbf{q}$, where $\mathbf{q}$ and $\mathbf{n}$ are the directions of the order parameter of the polarizer and the free antiferromagnetic layers, respectively. Although disorder conserves the symmetry of the torques, it strongly reduces the torque magnitude, pointing out the need for momentum conservation to ensure strong spin torque in antiferromagnetic spin valves.

Anomalous domain wall velocity and Walker breakdown in hybrid systems with anisotropic exchange

It has recently been proposed that spin-transfer torques in magnetic systems with anisotropic exchange can be strongly enhanced, reducing the characteristic current density with up to four orders of magnitude compared to conventional setups. Motivated by this, we analytically solve the equations of motion in a collective-coordinate framework for this type of anisotropic exchange system, to investigate the domain wall dynamics in detail. In particular, we obtain analytical expressions for the maximum attainable domain wall velocity of such a setup and also for the occurrence of Walker breakdown. Surprisingly, we find that, in contrast to the standard case with domain wall motion driven by the nonadiabatic torque, the maximum velocity obtained via the anisotropic exchange torque is completely independent of the nonadiabaticity parameter beta, in spite of the torque itself being very large for small beta. Moreover, the Walker breakdown threshold has an opposite dependence on beta in these two cases; i.e., for the anisotropic exchange torque scenario, the threshold value decreases monotonically with beta. These findings are of importance to any practical application of the proposed giant spin-transfer torque in anisotropic exchange systems.

Spin-Transfer and Exchange Torques in Ferromagnetic Superconductors

We consider how superconducting correlations influence spin-transfer torques in ferromagnetic superconductors. It is demonstrated that there is a novel torque arising from particle-hole interference that depends on the U(1) phase associated with the superconducting order parameter. We also show that there is an equilibrium exchange torque between two ferromagnetic superconductors in contact via a normal metal mediated by Andreev states. The latter equilibrium magnetic torque is also sensitive to spin-resolved phase differences in the superconducting order parameters as well as to an externally applied phase difference.

Fluxmetric-magnetooptical approach to broadband energy losses in amorphous ribbons

The magnetization process in field annealed amorphous ribbons has been investigated from dc to 10 MHz. Loss and permeability measurements, carried out both on single strips and ring samples by means of a broadband fluxmetric setup, have been associated with observations of the domain wall dynamics by high-speed stroboscopic Kerr apparatus. Transverse anisotropy Co-based ribbons exhibit a combination of rotational and domain wall processes, the latter being observed to progressively damp with frequency and coming to a halt on approaching the megahertz range. Given the vanishing direct contribution of the domain walls to the high-frequency magnetization process, the so-called classical loss formulation, associated with the rotational magnetization processes, is expected to correspondingly hold for the energy loss W(f). Under these conditions, W(f) tends to increase linearly with f, which, in view of the expected surge of the skin effect, does not agree with the f1/2 behavior accordingly predicted by standard formulas. This points to the specific properties of the rotational process and the role played by the exchange torque in connection with incomplete flux penetration.

Viscous Spin Exchange Torque on Precessional Magnetization in(LaMnO3)2n/(SrMnO3)nSuperlattices

Photoinduced magnetization dynamics is investigated in chemically ordered (LaMnO3)2n/(SrMnO3)n superlattices using the time-resolved magneto-optic Kerr effect. A monotonic frequency-field dependence is observed for the n=1 superlattice, indicating a single spin population consistent with a homogeneous hole distribution. In contrast, for n> or =2 superlattices, a large precession frequency is observed at low fields indicating the presence of an exchange torque in the dynamic regime. We attribute the emergence of exchange torque to the coupling between two spin populations-viscous and fast spins.

Spin transfer by spin injection between both interfaces of a Ni nanowire

Magnetization switching provoked by spin injection is studied in Ni nanowires of various sizes and morphologies. The response of the magnetization to current injection is measured as a function of the amplitude of the current, the temperature, and the symmetry of the interfaces. The efficiency of the response of the magnetization of spin injection is a decreasing function of the temperature, does not depend on the current sign, and occurs only in the case of asymmetric interfaces. It is shown that the switching provoked by spin injection is not affected by the presence of a magnetic domain inside the layer. Some consequences in terms of spin transfer or exchange torque are discussed.

Exchange torque and spin transfer between spin polarized current and ferromagnetic layers

Magnetization reversal triggered by spin injection is measured in electrodeposited Co/Cu/Co pillars (diameter about 60 nm). Two protocols are used. (i) switching of magnetization after a current pulse is monitored as a function of applied field. The maximum offset from the switching field at which irreversible switching occurs is a measure of the strength of the effect; and (ii) irreversible and reversible magnetization changes are observed while the current is ramped at fixed applied field. (i) and (ii) show that irreversible transitions occur only from antiparallel to parallel magnetic configurations and for electrons flow from the polarizer to the analyzer.