Gate-Tunable Spin-Charge Conversion and the Role of Spin-Orbit Interaction in Graphene

The small spin-orbit interaction of carbon atoms in graphene promises a long spin diffusion length and the potential to create a spin field-effect transistor. However, for this reason, graphene was largely overlooked as a possible spin-charge conversion material. We report electric gate tuning of the spin-charge conversion voltage signal in single-layer graphene. Using spin pumping from an yttrium iron garnet ferrimagnetic insulator and ionic liquid top gate, we determined that the inverse spin Hall effect is the dominant spin-charge conversion mechanism in single-layer graphene. From the gate dependence of the electromotive force we showed the dominance of the intrinsic over Rashba spin-orbit interaction, a long-standing question in graphene research.

Fast Magnetic Domain-Wall Motion in a Ring-Shaped Nanowire Driven by a Voltage

Magnetic domain-wall motion driven by a voltage dissipates much less heat than by a current, but none of the existing reports have achieved speeds exceeding 100 m/s. Here phase-field and finite-element simulations were combined to study the dynamics of strain-mediated voltage-driven magnetic domain-wall motion in curved nanowires. Using a ring-shaped, rough-edged magnetic nanowire on top of a piezoelectric disk, we demonstrate a fast voltage-driven magnetic domain-wall motion with average velocity up to 550 m/s, which is comparable to current-driven wall velocity. An analytical theory is derived to describe the strain dependence of average magnetic domain-wall velocity. Moreover, one 180° domain-wall cycle around the ring dissipates an ultrasmall amount of heat, as small as 0.2 fJ, approximately 3 orders of magnitude smaller than those in current-driven cases. These findings suggest a new route toward developing high-speed, low-power-dissipation domain-wall spintronics.

Competing effect of spin-orbit torque terms on perpendicular magnetization switching in structures with multiple inversion asymmetries

Current-induced spin-orbit torques (SOTs) in structurally asymmetric multilayers have been used to efficiently manipulate magnetization. In a structure with vertical symmetry breaking, a damping-like SOT can deterministically switch a perpendicular magnet, provided an in-plane magnetic field is applied. Recently, it has been further demonstrated that the in-plane magnetic field can be eliminated by introducing a new type of perpendicular field-like SOT via incorporating a lateral structural asymmetry into the device. Typically, however, when a current is applied to such devices with combined vertical and lateral asymmetries, both the perpendicular field-like torque and the damping-like torque coexist, hence jointly affecting the magnetization switching behavior. Here, we study perpendicular magnetization switching driven by the combination of the perpendicular field-like and the damping-like SOTs, which exhibits deterministic switching mediated through domain wall propagation. It is demonstrated that the role of the damping-like SOT in the deterministic switching is highly dependent on the magnetization direction in the domain wall. By contrast, the perpendicular field-like SOT is solely determined by the relative orientation between the lateral structural asymmetry and the current direction, regardless of the magnetization direction in the domain wall. The experimental results further the understanding of SOTs-induced switching, with implications for spintronic devices.

Electric-field control of spin-orbit torque in a magnetically doped topological insulator

Electric-field manipulation of magnetic order has proved of both fundamental and technological importance in spintronic devices. So far, electric-field control of ferromagnetism, magnetization and magnetic anisotropy has been explored in various magnetic materials, but the efficient electric-field control of spin-orbit torque (SOT) still remains elusive. Here, we report the effective electric-field control of a giant SOT in a Cr-doped topological insulator (TI) thin film using a top-gate field-effect transistor structure. The SOT strength can be modulated by a factor of four within the accessible gate voltage range, and it shows strong correlation with the spin-polarized surface current in the film. Furthermore, we demonstrate the magnetization switching by scanning gate voltage with constant current and in-plane magnetic field applied in the film. The effective electric-field control of SOT and the giant spin-torque efficiency in Cr-doped TI may lead to the development of energy-efficient gate-controlled spin-torque devices compatible with modern field-effect semiconductor technologies.

Spin-torque resonant expulsion of the vortex core for an efficient radiofrequency detection scheme

It has been proposed that high-frequency detectors based on the so-called spin-torque diode effect in spin transfer oscillators could eventually replace conventional Schottky diodes due to their nanoscale size, frequency tunability and large output sensitivity. Although a promising candidate for information and communications technology applications, the output voltage generated from this effect has still to be improved and, more pertinently, reduces drastically with decreasing radiofrequency (RF) current. Here we present a scheme for a new type of spintronics-based high-frequency detector based on the expulsion of the vortex core in a magnetic tunnel junction (MTJ). The resonant expulsion of the core leads to a large and sharp change in resistance associated with the difference in magnetoresistance between the vortex ground state and the final C-state configuration. Interestingly, this reversible effect is independent of the incoming RF current amplitude, offering a fast real-time RF threshold detector.

Nonlocal Anomalous Hall Effect

The anomalous Hall (AH) effect is deemed to be a unique transport property of ferromagnetic metals, caused by the concerted action of spin polarization and spin-orbit coupling. Nevertheless, recent experiments have shown that the effect also occurs in a nonmagnetic metal (Pt) in contact with a magnetic insulator [yttrium iron garnet (YIG)], even when precautions are taken to ensure that there is no induced magnetization in the metal. We propose a theory of this effect based on the combined action of spin-dependent scattering from the magnetic interface and the spin-Hall effect in the bulk of the metal. At variance with previous theories, we predict the effect to be of first order in the spin-orbit coupling, just as the conventional anomalous Hall effect-the only difference being the spatial separation of the spin-orbit interaction and the magnetization. For this reason we name this effect the nonlocal anomalous Hall effect and predict that its sign will be determined by the sign of the spin-Hall angle in the metal. The AH conductivity that we calculate from our theory is in order of magnitude agreement with the measured values in Pt/YIG structures.

Phase-resolved ferromagnetic resonance using heterodyne detection method

This paper describes a phase-resolved ferromagnetic resonance (FMR) measurement using a heterodyne method. Spin precession is driven by microwave fields and detected by 1550 nm laser light that is modulated at a frequency slightly shifted with respected to the FMR driving frequency. The evolving phase difference between the spin precession and the modulated light produces a slowly oscillating Kerr rotation signal with a phase equal to the precession phase plus a phase due to the path length difference between the excitation microwave signal and the optical signal. We estimate the accuracy of the precession phase measurement to be 0.1 rad. This heterodyne FMR detection method eliminates the need for field modulation and allows a stronger detection signal at higher intermediate frequency where the 1/f noise floor is reduced.

Spin Torque Study of the Spin Hall Conductivity and Spin Diffusion Length in Platinum Thin Films with Varying Resistivity

We report measurements of the spin torque efficiencies in perpendicularly magnetized Pt/Co bilayers where the Pt resistivity ρ_{Pt} is strongly dependent on thickness t_{Pt}. The dampinglike spin Hall torque efficiency per unit current density ξ_{DL}^{j} varies significantly with t_{Pt}, exhibiting a peak value ξ_{DL}^{j}=0.12 at t_{Pt}=2.8-3.9  nm. In contrast, ξ_{DL}^{j}/ρ_{Pt} increases monotonically with t_{Pt} and saturates for t_{Pt}>5  nm, consistent with an intrinsic spin Hall effect mechanism, in which ξ_{DL}^{j} is enhanced by an increase in ρ_{Pt}. Assuming the Elliott-Yafet spin scattering mechanism dominates, we estimate that the spin diffusion length λ_{s}=(0.77±0.08)×10^{-15}  Ω·m^{2}/ρ_{Pt}.

Theory of spin Hall magnetoresistance (SMR) and related phenomena

We review the so-called spin Hall magnetoresistance (SMR) in bilayers of a magnetic insulator and a metal, in which spin currents are generated in the normal metal by the spin Hall effect. The associated angular momentum transfer to the ferromagnetic layer and thereby the electrical resistance is modulated by the angle between the applied current and the magnetization direction. The SMR provides a convenient tool to non-invasively measure the magnetization direction and spin-transfer torque to an insulator. We introduce the minimal theoretical instruments to calculate the SMR, i.e. spin diffusion theory and quantum mechanical boundary conditions. This leads to a small set of parameters that can be fitted to experiments. We discuss the limitations of the theory as well as alternative mechanisms such as the ferromagnetic proximity effect and Rashba spin-orbit torques, and point out new developments.

Room-Temperature Creation and Spin-Orbit Torque Manipulation of Skyrmions in Thin Films with Engineered Asymmetry

Magnetic skyrmions, which are topologically protected spin textures, are promising candidates for ultralow-energy and ultrahigh-density magnetic data storage and computing applications. To date, most experiments on skyrmions have been carried out at low temperatures. The choice of available materials is limited, and there is a lack of electrical means to control skyrmions in devices. In this work, we demonstrate a new method for creating a stable skyrmion bubble phase in the CoFeB-MgO material system at room temperature, by engineering the interfacial perpendicular magnetic anisotropy of the ferromagnetic layer. Importantly, we also demonstrate that artificially engineered symmetry breaking gives rise to a force acting on the skyrmions, in addition to the current-induced spin-orbit torque, which can be used to drive their motion. This room-temperature creation and manipulation of skyrmions offers new possibilities to engineer skyrmionic devices. The results bring skyrmionic memory and logic concepts closer to realization in industrially relevant and manufacturable thin film material systems.

Field-free magnetization reversal by spin-Hall effect and exchange bias

As the first magnetic random access memories are finding their way onto the market, an important issue remains to be solved: the current density required to write magnetic bits becomes prohibitively high as bit dimensions are reduced. Recently, spin–orbit torques and the spin-Hall effect in particular have attracted significant interest, as they enable magnetization reversal without high current densities running through the tunnel barrier. For perpendicularly magnetized layers, however, the technological implementation of the spin-Hall effect is hampered by the necessity of an in-plane magnetic field for deterministic switching. Here we interface a thin ferromagnetic layer with an anti-ferromagnetic material. An in-plane exchange bias is created and shown to enable field-free S HE-driven magnetization reversal of a perpendicularly magnetized Pt/Co/IrMn structure. Aside from the potential technological implications, our experiment provides additional insight into the local spin structure at the ferromagnetic/anti-ferromagnetic interface.

Future information storage technology may exploit electrical currents to write the states of ferromagnetic nanoelements via spin torque effects. Here, the authors demonstrate such behaviour promoted by exchange bias from an interfaced antiferromagnet, which may help overcome practical device limitations.

Spin Hall Magnetoresistance in Metallic Bilayers

Spin Hall magnetoresistance (SMR) is studied in metallic bilayers that consist of a heavy metal (HM) layer and a ferromagnetic metal (FM) layer. We find a nearly tenfold increase of SMR in W/CoFeB compared to previously studied HM/ferromagnetic insulator systems. The SMR increases with decreasing temperature despite the negligible change in the W layer resistivity. A model is developed to account for the absorption of the longitudinal spin current to the FM layer, one of the key characteristics of a metallic ferromagnet. We find that the model not only quantitatively describes the HM layer thickness dependence of SMR, allowing accurate estimation of the spin Hall angle and the spin diffusion length of the HM layer, but also can account for the temperature dependence of SMR by assuming a temperature dependent spin polarization of the FM layer. These results illustrate the unique role a metallic ferromagnetic layer plays in defining spin transmission across the HM/FM interface.

Observation of magnon-mediated current drag in Pt/yttrium iron garnet/Pt(Ta) trilayers

Pure spin current, a flow of spin angular momentum without flow of any accompanying net charge, is generated in two common ways. One makes use of the spin Hall effect in normal metals (NM) with strong spin-orbit coupling, such as Pt or Ta. The other utilizes the collective motion of magnetic moments or spin waves with the quasi-particle excitations called magnons. A popular material for the latter is yttrium iron garnet, a magnetic insulator (MI). Here we demonstrate in NM/MI/NM trilayers that these two types of spin currents are interconvertible across the interfaces, predicated as the magnon-mediated current drag phenomenon. The transmitted signal scales linearly with the driving current without a threshold and follows the power-law T(n) with n ranging from 1.5 to 2.5. Our results indicate that the NM/MI/NM trilayer structure can serve as a scalable pure spin current valve device which is an essential ingredient in spintronics.

Chiral damping of magnetic domain walls

Structural symmetry breaking in magnetic materials is responsible for the existence of multiferroics, current-induced spin-orbit torques and some topological magnetic structures. In this Letter we report that the structural inversion asymmetry (SIA) gives rise to a chiral damping mechanism, which is evidenced by measuring the field-driven domain-wall (DW) motion in perpendicularly magnetized asymmetric Pt/Co/Pt trilayers. The DW dynamics associated with the chiral damping and those with Dzyaloshinskii-Moriya interaction (DMI) exhibit identical spatial symmetry. However, both scenarios are differentiated by their time reversal properties: whereas DMI is a conservative effect that can be modelled by an effective field, the chiral damping is purely dissipative and has no influence on the equilibrium magnetic texture. When the DW motion is modulated by an in-plane magnetic field, it reveals the structure of the internal fields experienced by the DWs, allowing one to distinguish the physical mechanism. The chiral damping enriches the spectrum of physical phenomena engendered by the SIA, and is essential for conceiving DW and skyrmion devices owing to its coexistence with DMI (ref. ).

Antiferromagnetic spintronics

Antiferromagnetic materials are internally magnetic, but the direction of their ordered microscopic moments alternates between individual atomic sites. The resulting zero net magnetic moment makes magnetism in antiferromagnets externally invisible. This implies that information stored in antiferromagnetic moments would be invisible to common magnetic probes, insensitive to disturbing magnetic fields, and the antiferromagnetic element would not magnetically affect its neighbours, regardless of how densely the elements are arranged in the device. The intrinsic high frequencies of antiferromagnetic dynamics represent another property that makes antiferromagnets distinct from ferromagnets. Among the outstanding questions is how to manipulate and detect the magnetic state of an antiferromagnet efficiently. In this Review we focus on recent works that have addressed this question. The field of antiferromagnetic spintronics can also be viewed from the general perspectives of spin transport, magnetic textures and dynamics, and materials research. We briefly mention this broader context, together with an outlook of future research and applications of antiferromagnetic spintronics.

Enhanced spin-orbit torques by oxygen incorporation in tungsten films

The origin of spin-orbit torques, which are generated by the conversion of charge-to-spin currents in non-magnetic materials, is of considerable debate. One of the most interesting materials is tungsten, for which large spin-orbit torques have been found in thin films that are stabilized in the A15 (β-phase) structure. Here we report large spin Hall angles of up to approximately -0.5 by incorporating oxygen into tungsten. While the incorporation of oxygen into the tungsten films leads to significant changes in their microstructure and electrical resistivity, the large spin Hall angles measured are found to be remarkably insensitive to the oxygen-doping level (12-44%). The invariance of the spin Hall angle for higher oxygen concentrations with the bulk properties of the films suggests that the spin-orbit torques in this system may originate dominantly from the interface rather than from the interior of the films.

Experimental Clocking of Nanomagnets with Strain for Ultralow Power Boolean Logic

Nanomagnetic implementations of Boolean logic have attracted attention because of their nonvolatility and the potential for unprecedented overall energy-efficiency. Unfortunately, the large dissipative losses that occur when nanomagnets are switched with a magnetic field or spin-transfer-torque severely compromise the energy-efficiency. Recently, there have been experimental reports of utilizing the Spin Hall effect for switching magnets, and theoretical proposals for strain induced switching of single-domain magnetostrictive nanomagnets, that might reduce the dissipative losses significantly. Here, we experimentally demonstrate, for the first time that strain-induced switching of single-domain magnetostrictive nanomagnets of lateral dimensions ∼200 nm fabricated on a piezoelectric substrate can implement a nanomagnetic Boolean NOT gate and steer bit information unidirectionally in dipole-coupled nanomagnet chains. On the basis of the experimental results with bulk PMN-PT substrates, we estimate that the energy dissipation for logic operations in a reasonably scaled system using thin films will be a mere ∼1 aJ/bit.

Spin-orbit torque in Pt/CoNiCo/Pt symmetric devices

Current induced magnetization switching by spin-orbit torques offers an energy-efficient means of writing information in heavy metal/ferromagnet (FM) multilayer systems. The relative contributions of field-like torques and damping-like torques to the magnetization switching induced by the electrical current are still under debate. Here, we describe a device based on a symmetric Pt/FM/Pt structure, in which we demonstrate a strong damping-like torque from the spin Hall effect and unmeasurable field-like torque from Rashba effect. The spin-orbit effective fields due to the spin Hall effect were investigated quantitatively and were found to be consistent with the switching effective fields after accounting for the switching current reduction due to thermal fluctuations from the current pulse. A non-linear dependence of deterministic switching of average M_z on the in-plane magnetic field was revealed, which could be explained and understood by micromagnetic simulation.

Spin-orbit torque magnetization switching controlled by geometry

Magnetization reversal by an electric current is essential for future magnetic data storage technology, such as magnetic random access memories. Typically, an electric current is injected into a pillar-shaped magnetic element, and switching relies on the transfer of spin momentum from a ferromagnetic reference layer (an approach known as spin-transfer torque). Recently, an alternative technique has emerged that uses spin-orbit torque (SOT) and allows the magnetization to be reversed without a polarizing layer by transferring angular momentum directly from the crystal lattice. With spin-orbit torque, the current is no longer applied perpendicularly, but is in the plane of the magnetic thin film. Therefore, the current flow is no longer restricted to a single direction and can have any orientation within the film plane. Here, we use Kerr microscopy to examine spin-orbit torque-driven domain wall motion in Co/AlOx wires with different shapes and orientations on top of a current-carrying Pt layer. The displacement of the domain walls is found to be highly dependent on the angle between the direction of the current and domain wall motion, and asymmetric and nonlinear with respect to the current polarity. Using these insights, devices are fabricated in which magnetization switching is determined entirely by the geometry of the device.

Nonvolatile modulation of electronic structure and correlative magnetism of L10-FePt films using significant strain induced by shape memory substrates

Tuning the lattice strain (εL) is a novel approach to manipulate the magnetic, electronic, and transport properties of spintronic materials. Achievable εL in thin film samples induced by traditional ferroelectric or flexible substrates is usually volatile and well below 1%. Such limits in the tuning capability cannot meet the requirements for nonvolatile applications of spintronic materials. This study answers to the challenge of introducing significant amount of elastic strain in deposited thin films so that noticeable tuning of the spintronic characteristics can be realized. Based on subtle elastic strain engineering of depositing L10-FePt films on pre-stretched NiTi(Nb) shape memory alloy substrates, steerable and nonvolatile lattice strain up to 2.18% has been achieved in the L10-FePt films by thermally controlling the shape memory effect of the substrates. Introduced strains at this level significantly modify the electronic density of state, orbital overlap, and spin-orbit coupling (SOC) strength in the FePt film, leading to nonvolatile modulation of magnetic anisotropy and magnetization reversal characteristics. This finding not only opens an efficient avenue for the nonvolatile tuning of SOC based magnetism and spintronic effects, but also helps to clarify the physical nature of pure strain effect.

Nonlinear dynamics induced anomalous Hall effect in topological insulators

We uncover an alternative mechanism for anomalous Hall effect. In particular, we investigate the magnetisation dynamics of an insulating ferromagnet (FM) deposited on the surface of a three-dimensional topological insulator (TI), subject to an external voltage. The spin-polarised current on the TI surface induces a spin-transfer torque on the magnetisation of the top FM while its dynamics can change the transmission probability of the surface electrons through the exchange coupling and hence the current. We find a host of nonlinear dynamical behaviors including multistability, chaos, and phase synchronisation. Strikingly, a dynamics mediated Hall-like current can arise, which exhibits a nontrivial dependence on the channel conductance. We develop a physical understanding of the mechanism that leads to the anomalous Hall effect. The nonlinear dynamical origin of the effect stipulates that a rich variety of final states exist, implying that the associated Hall current can be controlled to yield desirable behaviors. The phenomenon can find applications in Dirac-material based spintronics.

Low energy consumption spintronics using multiferroic heterostructures

We review the recent progress in the field of multiferroic magnetoelectric heterostructures. The lack of single phase multiferroic candidates exhibiting simultaneously strong and coupled magnetic and ferroelectric orders led to an increased effort into the development of artificial multiferroic heterostructures in which these orders are combined by assembling different materials. The magnetoelectric coupling emerging from the created interface between the ferroelectric and ferromagnetic layers can result in electrically tunable magnetic transition temperature, magnetic anisotropy or magnetization reversal. The full potential of low energy consumption magnetic based devices for spintronics lies in our understanding of the magnetoelectric coupling at the scale of the ferroic domains. Although the thin film synthesis progresses resulted into the complete control of ferroic domain ordering using epitaxial strain, the local observation of magnetoelectric coupling remains challenging. The ability to imprint ferroelectric domains into ferromagnets and to manipulate those solely using electric fields suggests new technological advances for spintronics such as magnetoelectric memories or memristors.

Anomalous anti-damping in sputtered β-Ta/Py bilayer system

Anomalous decrease in effective damping parameter α_eff in sputtered Ni₈₁Fe₁₉ (Py) thin films in contact with a very thin β-Ta layer without necessitating the flow of DC-current is observed. This reduction in α_eff, which is also referred to as anti-damping effect, is found to be critically dependent on the thickness of β-Ta layer; α_eff being highest, i.e., 0.0093 ± 0.0003 for bare Ni₈₁Fe₁₉(18 nm)/SiO₂/Si compared to the smallest value of 0.0077 ± 0.0001 for β-Ta(6 nm)/Py(18 nm)/SiO₂/Si. This anomalous anti-damping effect is understood in terms of interfacial Rashba effect associated with the formation of a thin protective Ta₂O₅ barrier layer and also the spin pumping induced non-equilibrium diffusive spin-accumulation effect in β-Ta layer near the Ta/Py interface which induces additional spin orbit torque (SOT) on the moments in Py leading to reduction in . The fitting of (t_Ta) revealed an anomalous negative interfacial spin mixing conductance, and spin diffusion length,. The increase in α_eff observed above t_Ta = 6 nm is attributed to the weakening of SOT at higher t_Ta. The study highlights the potential of employing β-Ta based nanostructures in developing low power spintronic devices having tunable as well as low value of α.

Lithium-Ion Battery Cycling for Magnetism Control

Magnetization and electric-field coupling is fundamentally interesting and important. Specifically, current- or voltage-driven magnetization switching at room temperature is highly desirable from scientific and technological viewpoints. Herein, we demonstrate that magnetization can be controlled via the discharge-charge cycling of a lithium-ion battery (LIB) with rationally designed electrode nanomaterials. Reversible manipulation of magnetism over 3 orders of magnitude was achieved by controlling the lithiation/delithiation of a nanoscale α-Fe2O3-based electrode. The process was completed rapidly under room-temperature conditions. Our results indicate that in addition to energy storage LIBs, which have been under continuous development for several decades, provide exciting opportunities for the multireversible magnetization of magnetic fields.

Logic circuit prototypes for three-terminal magnetic tunnel junctions with mobile domain walls

Spintronic computing promises superior energy efficiency and nonvolatility compared to conventional field-effect transistor logic. But, it has proven difficult to realize spintronic circuits with a versatile, scalable device design that is adaptable to emerging material physics. Here we present prototypes of a logic device that encode information in the position of a magnetic domain wall in a ferromagnetic wire. We show that a single three-terminal device can perform inverter and buffer operations. We demonstrate one device can drive two subsequent gates and logic propagation in a circuit of three inverters. This prototype demonstration shows that magnetic domain wall logic devices have the necessary characteristics for future computing, including nonlinearity, gain, cascadability, and room temperature operation.

Hanle Magnetoresistance in Thin Metal Films with Strong Spin-Orbit Coupling

We report measurements of a new type of magnetoresistance in Pt and Ta thin films. The spin accumulation created at the surfaces of the film by the spin Hall effect decreases in a magnetic field because of the Hanle effect, resulting in an increase of the electrical resistance as predicted by Dyakonov [Phys. Rev. Lett. 99, 126601 (2007)]. The angular dependence of this magnetoresistance resembles the recently discovered spin Hall magnetoresistance in Pt/Y(3)Fe(5)O(12) bilayers, although the presence of a ferromagnetic insulator is not required. We show that this Hanle magnetoresistance is an alternative simple way to quantitatively study the coupling between charge and spin currents in metals with strong spin-orbit coupling.

Magnetization switching by combining electric field and spin-transfer torque effects in a perpendicular magnetic tunnel junction

Effective manipulation of magnetization orientation driven by electric field in a perpendicularly magnetized tunnel junction introduces technologically relevant possibility for developing low power magnetic memories. However, the bipolar orientation characteristic of toggle-like magnetization switching possesses intrinsic difficulties for practical applications. By including both the in-plane (T//) and field-like (T⊥) spin-transfer torque terms in the Landau-Lifshitz-Gilbert simulation, reliable and deterministic magnetization reversal can be achieved at a significantly reduced current density of 5×10(9) A/m(2) under the co-action of electric field and spin-polarized current, provided that the electric-field pulse duration exceeds a certain critical value τc. The required critical τc decreases with the increase of T⊥ strength because stronger T⊥ can make the finally stabilized out-of-plane component of magnetization stay in a larger negative value. The power consumption for such kind of deterministic magnetization switching is found to be two orders of magnitude lower than that of the switching driven by current only.

Anatomy of Dzyaloshinskii-Moriya Interaction at Co/Pt Interfaces

The Dzyaloshinskii-Moriya interaction (DMI) has been recently recognized to play a crucial role in allowing fast domain wall dynamics driven by spin-orbit torques and the generation of magnetic Skyrmions. Here, we unveil the main features and microscopic mechanisms of DMI in Co/Pt bilayers via first principles calculations. We find that the large DMI of the bilayers has a dominant contribution from the spins of the interfacial Co layer. This DMI between the interfacical Co spins extends very weakly away from the interface and is associated with a spin-orbit coupling in the adjacent atomic layer of Pt. Furthermore, no direct correlation is found between DMI and proximity induced magnetism in Pt. These results clarify the underlying mechanisms of DMI at interfaces between ferromagnetic and heavy metals and should help optimizing material combinations for domain wall and Skyrmion-based devices.

Electric field control of magnetic properties and electron transport in BaTiO₃-based multiferroic heterostructures

In this paper, we report on a purely electric mechanism for achieving the electric control of the interfacial spin polarization and magnetoresistance in multiferroic tunneling junctions. We investigate micrometric devices based on the Co/Fe/BaTiO3/La0.7Sr0.3MnO3 heterostructure, where Co/Fe and La0.7Sr0.3MnO3 are the magnetic electrodes and BaTiO3 acts both as a ferroelectric element and tunneling barrier. We show that, at 20 K, devices with a 2 nm thick BaTiO3 barrier present both tunneling electroresistance (TER = 12   ±   0.1%) and tunneling magnetoresistance (TMR). The latter depends on the direction of the BaTiO3 polarization, displaying a sizable change of the TMR from  -0.32   ±   0.05% for the polarization pointing towards Fe, to  -0.12   ±   0.05% for the opposite direction. This is consistent with the on-off switching of the Fe magnetization at the Fe/BaTiO3 interface, driven by the BaTiO3 polarization, we have previously demonstrated in x-ray magnetic circular dichroism experiments.

Reversible strain-induced magnetization switching in FeGa nanomagnets: Pathway to a rewritable, non-volatile, non-toggle, extremely low energy straintronic memory

We report reversible strain-induced magnetization switching between two stable/metastable states in ~300 nm sized FeGa nanomagnets delineated on a piezoelectric PMN-PT substrate. Voltage of one polarity applied across the substrate generates compressive strain in a nanomagnet and switches its magnetization to one state, while voltage of the opposite polarity generates tensile strain and switches the magnetization back to the original state. The two states can encode the two binary bits, and, using the right voltage polarity, one can write either bit deterministically. This portends an ultra-energy-efficient non-volatile "non-toggle" memory.

Ferromagnetic Resonance Spin Pumping and Electrical Spin Injection in Silicon-Based Metal-Oxide-Semiconductor Heterostructures

We present the measurement of ferromagnetic resonance (FMR-)driven spin pumping and three-terminal electrical spin injection within the same silicon-based device. Both effects manifest in a dc spin accumulation voltage V_{s} that is suppressed as an applied field is rotated to the out-of-plane direction, i.e., the oblique Hanle geometry. Comparison of V_{s} between these two spin injection mechanisms reveals an anomalously strong suppression of FMR-driven spin pumping with increasing out-of-plane field H_{app}^{z}. We propose that the presence of the large ac component to the spin current generated by the spin pumping approach, expected to exceed the dc value by 2 orders of magnitude, is the origin of this discrepancy through its influence on the spin dynamics at the oxide-silicon interface. This convolution, wherein the dynamics of both the injector and the interface play a significant role in the spin accumulation, represents a new regime for spin injection that is not well described by existing models of either FMR-driven spin pumping or electrical spin injection.

Manipulating quantum information with spin torque

The use of spin torque as a substitute for magnetic fields is now well established for classical operations like the switching of a nanomagnet. What we are describing here could be viewed as an application of spin torque like effects to quantum processes involving single qubit rotations as well as two qubit entanglement. A key ingredient of this scheme is the use of a large number of itinerant electrons whose cumulative effect is to produce the desired qubit operations on static spins. Each interaction involves entanglement and collapse of wavefunctions so that the operation is only approximately unitary. However, we show that the non-unitary component of the operations can be kept below tolerable limits with proper design. As a capstone example, we present the implementation of a complete CNOT gate using the proposed spin potential based architecture, and show that the fidelity under ideal conditions can be made acceptably close to one.

Magneto-optical investigation of spin-orbit torques in metallic and insulating magnetic heterostructures

Manipulating magnetism by electric current is of great interest for both fundamental and technological reasons. Much effort has been dedicated to spin–orbit torques (SOTs) in metallic structures, while quantitative investigation of analogous phenomena in magnetic insulators remains challenging due to their low electrical conductivity. Here we address this challenge by exploiting the interaction of light with magnetic order, to directly measure SOTs in both metallic and insulating structures. The equivalency of optical and transport measurements is established by investigating a heavy-metal/ferromagnetic-metal device (Ta/CoFeB/MgO). Subsequently, SOTs are measured optically in the contrasting case of a magnetic-insulator/heavy-metal (YIG/Pt) heterostructure, where analogous transport measurements are not viable. We observe a large anti-damping torque in the YIG/Pt system, revealing its promise for spintronic device applications. Moreover, our results demonstrate that SOT physics is directly accessible by optical means in a range of materials, where transport measurements may not be possible.

The study of spin orbit torques in insulating materials via conventional transport methods is restricted due to low electrical conductivity. Here, the authors use magneto-optical methods to measure spin orbit torques in ferromagnetic-insulator/heavy-metal heterostructures.

Reciprocal spin Hall effects in conductors with strong spin-orbit coupling: a review

Spin Hall effect and its inverse provide essential means to convert charge to spin currents and vice versa, which serve as a primary function for spintronic phenomena such as the spin-torque ferromagnetic resonance and the spin Seebeck effect. These effects can oscillate magnetization or detect a thermally generated spin splitting in the chemical potential. Importantly this conversion process occurs via the spin-orbit interaction, and requires neither magnetic materials nor external magnetic fields. However, the spin Hall angle, i.e. the conversion yield between the charge and spin currents, depends severely on the experimental methods. Here we discuss the spin Hall angle and the spin diffusion length for a variety of materials including pure metals such as Pt and Ta, alloys and oxides determined by the spin absorption method in a lateral spin valve structure.

Intrinsic spin torque without spin-orbit coupling

We derive an intrinsic contribution to the non-adiabatic spin torque for non-uniform magnetic textures. It differs from previously considered contributions in several ways and can be the dominant contribution in some models. It does not depend on the change in occupation of the electron states due to the current flow but rather is due to the perturbation of the electronic states when an electric field is applied. Therefore it should be viewed as electric-field-induced rather than current-induced. Unlike previously reported non-adiabatic spin torques, it does not originate from extrinsic relaxation mechanisms nor spin-orbit coupling. This intrinsic non-adiabatic spin torque is related by a chiral connection to the intrinsic spin-orbit torque that has been calculated from the Berry phase for Rashba systems.

Reduction of phase noise in nanowire spin orbit torque oscillators

Spin torque oscillators (STOs) are compact, tunable sources of microwave radiation that serve as a test bed for studies of nonlinear magnetization dynamics at the nanometer length scale. The spin torque in an STO can be created by spin-orbit interaction, but low spectral purity of the microwave signals generated by spin orbit torque oscillators hinders practical applications of these magnetic nanodevices. Here we demonstrate a method for decreasing the phase noise of spin orbit torque oscillators based on Pt/Ni80Fe20 nanowires. We experimentally demonstrate that tapering of the nanowire, which serves as the STO active region, significantly decreases the spectral linewidth of the generated signal. We explain the observed linewidth narrowing in the framework of the Ginzburg-Landau auto-oscillator model. The model reveals that spatial non-uniformity of the spin current density in the tapered nanowire geometry hinders the excitation of higher order spin-wave modes, thus stabilizing the single-mode generation regime. This non-uniformity also generates a restoring force acting on the excited self-oscillatory mode, which reduces thermal fluctuations of the mode spatial position along the wire. Both these effects improve the STO spectral purity.

Minimal Model of Spin-Transfer Torque and Spin Pumping Caused by the Spin Hall Effect

In the normal-metal-ferromagnetic-insulator bilayer (such as Pt/Y_{3}Fe_{5}O_{12}) and the normal-metal-ferromagnetic-metal-oxide trilayer (such as Pt/Co/AlO_{x}) where spin injection and ejection are achieved by the spin Hall effect in the normal metal, we propose a minimal model based on quantum tunneling of spins to explain the spin-transfer torque and spin pumping caused by the spin Hall effect. The ratio of their dampinglike to fieldlike component depends on the tunneling wave function that is strongly influenced by generic material properties such as interface s-d coupling, insulating gap, and layer thickness, yet the spin relaxation plays a minor role. The quantified result renders our minimal model an inexpensive tool for searching for appropriate materials.

Imaging and Tailoring the Chirality of Domain Walls in Magnetic Films

Electric-current-induced magnetization switching is a keystone concept in the development of spintronics devices. In the last few years this field has experienced a significant boost with the discovery of ultrafast domain wall motions and very low threshold currents in structures designed to stabilize chiral spin textures. Imaging domain-wall spin textures in situ, while fabricating magnetic multilayer structures, is a powerful way to investigate the forces stabilizing this type of chirality, and informs strategies to engineer structures with controlled spin textures. Here, recent results applying spin-polarized low-energy electron microscopy to image chiral domain walls in magnetic multilayer films are summarized. Providing a way to measure the strength of the asymmetric exchange interaction that causes the chirality, this approach can be used to tailor the texture and handedness of magnetic domain walls by interface engineering. These results advance understanding of the underlying physics and offer new insights toward the design of spintronic devices.

Enhanced orbital magnetic moments in magnetic heterostructures with interface perpendicular magnetic anisotropy

We have studied the magnetic layer thickness dependence of the orbital magnetic moment in magnetic heterostructures to identify contributions from interfaces. Three different heterostructures, Ta/CoFeB/MgO, Pt/Co/AlO_x and Pt/Co/Pt, which possess significant interface contribution to the perpendicular magnetic anisotropy, are studied as model systems. X-ray magnetic circular dichroism spectroscopy is used to evaluate the relative orbital moment, i.e. the ratio of the orbital to spin moments, of the magnetic elements constituting the heterostructures. We find that the relative orbital moment of Co in Pt/Co/Pt remains constant against its thickness whereas the moment increases with decreasing Co layer thickness for Pt/Co/AlO_x, suggesting that a non-zero interface orbital moment exists for the latter system. For Ta/CoFeB/MgO, a non-zero interface orbital moment is found only for Fe. X-ray absorption spectra shows that a particular oxidized Co state in Pt/Co/AlO_x, absent in other heterosturctures, may give rise to the interface orbital moment in this system. These results show element specific contributions to the interface orbital magnetic moments in ultrathin magnetic heterostructures.

Large spin Hall magnetoresistance and its correlation to the spin-orbit torque in W/CoFeB/MgO structures

The phenomena based on spin-orbit interaction in heavy metal/ferromagnet/oxide structures have been investigated extensively due to their applicability to the manipulation of the magnetization direction via the in-plane current. This implies the existence of an inverse effect, in which the conductivity in such structures should depend on the magnetization orientation. In this work, we report a systematic study of the magnetoresistance (MR) of W/CoFeB/MgO structures and its correlation with the current-induced torque to the magnetization. We observe that the MR is independent of the angle between the magnetization and current direction but is determined by the relative magnetization orientation with respect to the spin direction accumulated by the spin Hall effect, for which the symmetry is identical to that of so-called the spin Hall magnetoresistance. The MR of ~1% in W/CoFeB/MgO samples is considerably larger than those in other structures of Ta/CoFeB/MgO or Pt/Co/AlOx, which indicates a larger spin Hall angle of W. Moreover, the similar W thickness dependence of the MR and the current-induced magnetization switching efficiency demonstrates that MR in a non-magnet/ferromagnet structure can be utilized to understand other closely correlated spin-orbit coupling effects such as the inverse spin Hall effect or the spin-orbit spin transfer torques.

Proposal for a Domain Wall Nano-Oscillator driven by Non-uniform Spin Currents

We propose a new mechanism and a related device concept for a robust, magnetic field tunable radio-frequency (rf) oscillator using the self oscillation of a magnetic domain wall subject to a uniform static magnetic field and a spatially non-uniform vertical dc spin current. The self oscillation of the domain wall is created as it translates periodically between two unstable positions, one being in the region where both the dc spin current and the magnetic field are present, and the other, being where only the magnetic field is present. The vertical dc spin current pushes it away from one unstable position while the magnetic field pushes it away from the other. We show that such oscillations are stable under noise and can exhibit a quality factor of over 1000. A domain wall under dynamic translation, not only being a source for rich physics, is also a promising candidate for advancements in nanoelectronics with the actively researched racetrack memory architecture, digital and analog switching paradigms as candidate examples. Devising a stable rf oscillator using a domain wall is hence another step towards the realization of an all domain wall logic scheme.

X-rays and magnetism

Magnetism is among the most active and attractive areas in modern solid state physics because of intriguing phenomena interesting to fundamental research and a manifold of technological applications. State-of-the-art synthesis of advanced magnetic materials, e.g. in hybrid structures paves the way to new functionalities. To characterize modern magnetic materials and the associated magnetic phenomena, polarized x-rays have emerged as unique probes due to their specific interaction with magnetic materials. A large variety of spectroscopic and microscopic techniques have been developed to quantify in an element, valence and site-sensitive way properties of ferro-, ferri-, and antiferromagnetic systems, such as spin and orbital moments, and to image nanoscale spin textures and their dynamics with sub-ns time and almost 10 nm spatial resolution. The enormous intensity of x-rays and their degree of coherence at next generation x-ray facilities will open the fsec time window to magnetic studies addressing fundamental time scales in magnetism with nanometer spatial resolution. This review will give an introduction into contemporary topics of nanoscale magnetic materials and provide an overview of analytical spectroscopy and microscopy tools based on x-ray dichroism effects. Selected examples of current research will demonstrate the potential and future directions of these techniques.

New perspectives for Rashba spin-orbit coupling

In 1984, Bychkov and Rashba introduced a simple form of spin-orbit coupling to explain the peculiarities of electron spin resonance in two-dimensional semiconductors. Over the past 30 years, Rashba spin-orbit coupling has inspired a vast number of predictions, discoveries and innovative concepts far beyond semiconductors. The past decade has been particularly creative, with the realizations of manipulating spin orientation by moving electrons in space, controlling electron trajectories using spin as a steering wheel, and the discovery of new topological classes of materials. This progress has reinvigorated the interest of physicists and materials scientists in the development of inversion asymmetric structures, ranging from layered graphene-like materials to cold atoms. This Review discusses relevant recent and ongoing realizations of Rashba physics in condensed matter.

Spin Hall Effects Due to Phonon Skew Scattering

A diversity of spin Hall effects in metallic systems is known to rely on Mott skew scattering. In this work its high-temperature counterpart, phonon skew scattering, which is expected to be of foremost experimental relevance, is investigated. In particular, the phonon skew scattering spin Hall conductivity is found to be practically T independent for temperatures above the Debye temperature T_{D}. As a consequence, in Rashba-like systems a high-T linear behavior of the spin Hall angle demonstrates the dominance of extrinsic spin-orbit scattering only if the intrinsic spin splitting is smaller than the temperature.

Switching of perpendicularly polarized nanomagnets with spin orbit torque without an external magnetic field by engineering a tilted anisotropy

Spin orbit torque (SOT) provides an efficient way to significantly reduce the current required for switching nanomagnets. However, SOT generated by an in-plane current 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 ultrascaled dimensions. Here, we show that it is possible to switch a perpendicularly polarized magnet by SOT without needing an external magnetic field. This is accomplished by engineering an anisotropy in the magnets such that the magnetic easy axis slightly tilts away from the direction, normal to the film plane. Such a tilted anisotropy breaks the symmetry of the problem and makes it possible to switch the magnet deterministically. Using a simple Ta/CoFeB/MgO/Ta heterostructure, we demonstrate reversible switching of the magnetization by reversing the polarity of the applied current. This demonstration presents a previously unidentified approach for controlling nanomagnets with SOT.

The straintronic spin-neuron

In artificial neural networks, neurons are usually implemented with highly dissipative CMOS-based operational amplifiers. A more energy-efficient implementation is a 'spin-neuron' realized with a magneto-tunneling junction (MTJ) that is switched with a spin-polarized current (representing weighted sum of input currents) that either delivers a spin transfer torque or induces domain wall motion in the soft layer of the MTJ to mimic neuron firing. Here, we propose and analyze a different type of spin-neuron in which the soft layer of the MTJ is switched with mechanical strain generated by a voltage (representing weighted sum of input voltages) and term it straintronic spin-neuron. It dissipates orders of magnitude less energy in threshold operations than the traditional current-driven spin neuron at 0 K temperature and may even be faster. We have also studied the room-temperature firing behaviors of both types of spin neurons and find that thermal noise degrades the performance of both types, but the current-driven type is degraded much more than the straintronic type if both are optimized for maximum energy-efficiency. On the other hand, if both are designed to have the same level of thermal degradation, then the current-driven version will dissipate orders of magnitude more energy than the straintronic version. Thus, the straintronic spin-neuron is superior to current-driven spin neurons.