Spin Hall Magnetoresistance in Metallic Bilayers

Theory of spin and orbital Edelstein effects

In systems with broken spatial inversion symmetry, such as surfaces, interfaces, or bulk systems lacking an inversion center, the application of a charge current can generate finite spin and orbital densities associated with a nonequilibrium magnetization, which is known as spin and orbital Edelstein effect (SEE and OEE), respectively. Early reports on this current-induced magnetization focus on two-dimensional Rashba systems, in which an in-plane nonequilibrium spin density is generated perpendicular to the applied charge current. However, until today, a large variety of materials have been theoretically predicted and experimentally demonstrated to exhibit a sizeable Edelstein effect, which comprises contributions from the spin as well as the orbital degrees of freedom, and whose associated magnetization may be out of plane, nonorthogonal, and even parallel to the applied charge current, depending on the system's particular symmetries. In this review, we give an overview on the most commonly used theoretical approaches for the discussion and prediction of the SEE and OEE. Further, we introduce a selection of the most intensely discussed materials exhibiting a finite Edelstein effect, and give a brief summary of common experimental techniques.

Influence of ferromagnetic interlayer exchange coupling on current-induced magnetization switching and Dzyaloshinskii-Moriya interaction in Co/Pt/Co multilayer system

This paper investigates the relationship among interlayer exchange coupling (IEC), Dzyaloshinskii-Moriya interaction (DMI), and multilevel magnetization switching within a Co/Pt/Co heterostructure, where varying Pt thicknesses enable control over the coupling strength. Employing Brillouin Light Scattering to quantify the effective DMI, we explore its potential role in magnetization dynamics and multilevel magnetization switching. Experimental findings show four distinct resistance states under an external magnetic field and spin Hall effect related spin current. We explain this phenomenon based on the asymmetry between Pt/Co and Co/Pt interfaces and the interlayer coupling, which, in turn, influences the DMI and subsequently impacts the magnetization dynamics. Numerical simulations, including macrospin, 1D domain wall, and simple spin wave models, further support the experimental observations of multilevel switching and help uncover the underlying mechanisms. Our proposed explanation, supported by magnetic domain observation using polar-magnetooptical Kerr microscopy, offers insights into both the spatial distribution of magnetization and its dynamics for different IECs, thereby shedding light on its interplay with DMI, which may lead to potential applications in storage devices.

Thermally generated spin current in the topological insulator Bi2Se3

We present measurements of thermally generated transverse spin currents in the topological insulator Bi2Se3, thereby completing measurements of interconversions among the full triad of thermal gradients, charge currents, and spin currents. We accomplish this by comparing the spin Nernst magneto-thermopower to the spin Hall magnetoresistance for bilayers of Bi2Se3/CoFeB. We find that Bi2Se3 does generate substantial thermally driven spin currents. A lower bound for the ratio of spin current density to thermal gradient is [Formula: see text] = (4.9 ± 0.9) × 106 [Formula: see text], and a lower bound for the magnitude of the spin Nernst ratio is -0.61 ± 0.11. The spin Nernst ratio for Bi2Se3 is the largest among all materials measured to date, two to three times larger compared to previous measurements for the heavy metals Pt and W. Strong thermally generated spin currents in Bi2Se3 can be understood via Mott relations to be due to an overall large spin Hall conductivity and its dependence on electron energy.

Manipulation of Spin-Orbit Torque in Tungsten Oxide/Manganite Heterostructure by Ionic Liquid Gating and Orbit Engineering

Spin-orbit coupling (SOC) is the interaction between electron's spin and orbital motion, which could realize a charge-to-spin current conversion and enable an innovative method to switch the magnetization by spin-orbit torque (SOT). Varied techniques have been developed to manipulate and improve the SOT, but the role of the orbit degree of freedom, which should have a crucial bearing on the SOC and SOT, is still confusing. Here, we find that the charge-to-spin current conversion and SOT in W3O8-δ/(La, Sr)MnO3 could be produced or eliminated by ionic liquid gating. Through tuning the preferential occupancy of Mn/W-d electrons from the in-plane (dx2-y2) to out-of-plane (d3z2-r2) orbit, the SOT damping-like field efficiency is nearly doubled due to the enhanced spin Hall effect and interfacial Rashba-Edelstein effect. These findings not only offer intriguing opportunities to control the SOT for high-efficient spintronic devices but also could be a fundamental step toward spin-orbitronics in the future.

Spin-Orbit Torques and Spin Hall Magnetoresistance Generated by Twin-Free and Amorphous Bi0.9 Sb0.1 Topological Insulator Films

Topological insulators have attracted great interest as generators of spin-orbit torques (SOTs) in spintronic devices. Bi1-x Sbx is a prominent topological insulator that has a high charge-to-spin conversion efficiency. However, the origin and magnitude of the SOTs induced by current-injection in Bi1-x Sbx remain controversial. Here, the investigation of the SOTs and spin Hall magnetoresistance resulting from charge-to-spin conversion in twin-free epitaxial layers of Bi0.9 Sb0.1 (0001) coupled to FeCo are investigated, and compared with those of amorphous Bi0.9 Sb0.1 . A large charge-to-spin conversion efficiency of 1 in the first case and less than 0.1 in the second is found, confirming crystalline Bi0.9 Sb0.1 as a strong spin-injector material. The SOTs and spin Hall magnetoresistance are independent of the direction of the electric current, indicating that charge-to-spin conversion in single-crystal Bi0.9 Sb0.1 (0001) is isotropic despite the strong anisotropy of the topological surface states. Further, it is found that the damping-like SOT has a non-monotonic temperature dependence with a minimum at 20 K. By correlating the SOT with resistivity and weak antilocalization measurements, charge-spin conversion is concluded to occur via thermally excited holes from the bulk states above 20 K, and conduction through the isotropic surface states with increasing spin polarization due to decreasing electron-electron scattering below 20 K.

Orbital Hanle Magnetoresistance in a 3d Transition Metal

The Hanle magnetoresistance is a telltale signature of spin precession in nonmagnetic conductors, in which strong spin-orbit coupling generates edge spin accumulation via the spin Hall effect. Here, we report the existence of a large Hanle magnetoresistance in single layers of Mn with weak spin-orbit coupling, which we attribute to the orbital Hall effect. The simultaneous observation of a sizable Hanle magnetoresistance and vanishing small spin Hall magnetoresistance in BiYIG/Mn bilayers corroborates the orbital origin of both effects. We estimate an orbital Hall angle of 0.016, an orbital relaxation time of 2 ps and diffusion length of the order of 2 nm in disordered Mn. Our findings indicate that current-induced orbital moments are responsible for magnetoresistance effects comparable to or even larger than those determined by spin moments, and provide a tool to investigate nonequilibrium orbital transport phenomena.

Proximity-Induced Interfacial Room-Temperature Ferromagnetism in Semiconducting Fe3GeTe2

The discoveries of two-dimensional ferromagnetism and magnetic semiconductors highly enrich the magnetic material family for constructing spin-based electronic devices, but with an acknowledged challenge that the Curie temperature (Tc) is usually far below room temperature. Many efforts such as voltage control and magnetic ion doping are currently underway to enhance the functional temperature, in which the involvement of additional electrodes or extra magnetic ions limits their application in practical devices. Here we demonstrate that the magnetic proximity, a robust effect but with elusive mechanisms, can induce room-temperature ferromagnetism at the interface between sputtered Pt and semiconducting Fe3GeTe2, both of which do not show ferromagnetism at 300 K. The independent electrical and magnetization measurements, structure analysis, and control samples with Ta highlighting the role of Pt confirm that the ferromagnetism with the Tc of above 400 K arises from the Fe3GeTe2/Pt interfaces, rather than Fe aggregation or other artificial effects. Moreover, contrary to conventional ferromagnet/Pt structures, the spin current generated by the Pt layer is enhanced more than two times at the Fe3GeTe2/Pt interfaces, indicating the potential applications of the unique proximity effect in building highly efficient spintronic devices. These results may pave a new avenue to create room-temperature functional spin devices based on low-Tc materials and provide clear evidence of magnetic proximity effects by using nonferromagnetic materials.

Gate-Tunable Spin Hall Effect in an All-Light-Element Heterostructure: Graphene with Copper Oxide

Graphene is a light material for long-distance spin transport due to its low spin-orbit coupling, which at the same time is the main drawback for exhibiting a sizable spin Hall effect. Decoration by light atoms has been predicted to enhance the spin Hall angle in graphene while retaining a long spin diffusion length. Here, we combine a light metal oxide (oxidized Cu) with graphene to induce the spin Hall effect. Its efficiency, given by the product of the spin Hall angle and the spin diffusion length, can be tuned with the Fermi level position, exhibiting a maximum (1.8 ± 0.6 nm at 100 K) around the charge neutrality point. This all-light-element heterostructure shows a larger efficiency than conventional spin Hall materials. The gate-tunable spin Hall effect is observed up to room temperature. Our experimental demonstration provides an efficient spin-to-charge conversion system free from heavy metals and compatible with large-scale fabrication.

Bulk Rashba-Type Spin Splitting in Non-Centrosymmetric Artificial Superlattices

Spin current, converted from charge current via spin Hall or Rashba effects, can transfer its angular momentum to local moments in a ferromagnetic layer. In this regard, the high charge-to-spin conversion efficiency is required for magnetization manipulation for developing future memory or logic devices including magnetic random-access memory. Here, the bulk Rashba-type charge-to-spin conversion is demonstrated in an artificial superlattice without centrosymmetry. The charge-to-spin conversion in [Pt/Co/W] superlattice with sub-nm scale thickness shows strong W thickness dependence. When the W thickness becomes 0.6 nm, the observed field-like torque efficiency is about 0.6, which is an order larger than other metallic heterostructures. First-principles calculation suggests that such large field-like torque arises from bulk-type Rashba effect due to the vertically broken inversion symmetry inherent from W layers. The result implies that the spin splitting in a band of such an ABC-type artificial SL can be an additional degree of freedom for the large charge-to-spin conversion.

Maximizing spin Hall magnetoresistance in heavy metal/crystalline metallic ferromagnet multilayers with opposite spin Hall angles

Interconversion between charge and spin through spin-orbit coupling at a heavy metal (HM)/ferromagnet (FM) interface plays a key role in determining the amplitude of spin Hall magnetoresistance (SMR), which might maximally facilitate its applications in novel electronics. In this study, annealed NiFe films grown on MgO (100) substrates capped with Pt and Ta are reported to exhibit a maximum SMR. When the measuring temperature is reduced, the SMR rises and is significantly larger in crystalline NiFe than in amorphous NiFe. Another physical process for the negative SMR in Ta(d_Ta)/Pt(3 nm)/annealed NiFe samples is attributed to the interfacial spin-orbit coupling (ISOC) driven spin current (J_s) generation and its reciprocal effects. Moreover, spin accumulation is enhanced at Pt(3 nm)/annealed NiFe interfaces after capping with a Ta layer, which functions as a spin sink in a certain thinner thickness range. With the cooperative interaction of choosing the proper Ta's thickness and annealing NiFe layers, the maximum SMR is obtained. Our results pave the way for rational interface engineering to enhance SMR for developing high-efficiency spintronic devices.

Significant Role of Interfacial Spin-Orbit Coupling in the Spin-to-Charge Conversion in Pt/NiFe Heterostructure

For the spin-to-charge conversion (SCC) in heavy metal/ferromagnet (HM/FM) heterostructure, the contribution of interfacial spin-orbit coupling (SOC) remains controversial. Here, we investigate the SCC process of the Pt/NiFe heterostructure by the spin pumping in YIG/Pt/NiFe/IrMn multilayers. Due to the exchange bias of NiFe/IrMn structure, the NiFe magnetization can be switched between magnetically unsaturated and saturated states by opposite resonance fields of YIG layer. The spin-pumping signal is found to decrease significantly when the NiFe magnetization is changed from the saturated state to the unsaturated state. Theoretical analysis indicates that the interfacial spin absorption is enhanced for the above-mentioned NiFe magnetic state change, which results in the increased and decreased spin flow in the Pt layer and across the Pt/NiFe interface, respectively. These results demonstrate that in our case the interfacial SOC effect at the Pt/NiFe interface is dominant over the bulk inverse spin Hall effect in the Pt layer. Our work reveals a significant role of interfacial SOC in the SCC in HM/FM heterostructure, which can promote the development of high-efficiency spintronic devices through interfacial engineering.

Observation of the Orbital Rashba-Edelstein Magnetoresistance

We report the observation of magnetoresistance (MR) that could originate from the orbital angular momentum (OAM) transport in a permalloy (Py)/oxidized Cu (Cu^{*}) heterostructure: the orbital Rashba-Edelstein magnetoresistance. The angular dependence of the MR depends on the relative angle between the induced OAM and the magnetization in a similar fashion as the spin Hall magnetoresistance. Despite the absence of elements with large spin-orbit coupling, we find a sizable MR ratio, which is in contrast to the conventional spin Hall magnetoresistance which requires heavy elements. Through Py thickness-dependence studies, we conclude another mechanism beyond the conventional spin-based scenario is responsible for the MR observed in Py/Cu^{*} structures-originated in a sizable transport of OAM. Our findings not only suggest the current-induced torques without using any heavy elements via the OAM channel but also provide an important clue towards the microscopic understanding of the role that OAM transport can play for magnetization dynamics.

A review on magnetic and spintronic neurostimulation: challenges and prospects

In the treatment of neurodegenerative, sensory and cardiovascular diseases, electrical probes and arrays have shown quite a promising success rate. However, despite the outstanding clinical outcomes, their operation is significantly hindered by non-selective control of electric fields. A promising alternative is micromagnetic stimulation (μMS) due to the high permeability of magnetic field through biological tissues. The induced electric field from the time-varying magnetic field generated by magnetic neurostimulators is used to remotely stimulate neighboring neurons. Due to the spatial asymmetry of the induced electric field, high spatial selectivity of neurostimulation has been realized. Herein, some popular choices of magnetic neurostimulators such as microcoils (μcoils) and spintronic nanodevices are reviewed. The neurostimulator features such as power consumption and resolution (aiming at cellular level) are discussed. In addition, the chronic stability and biocompatibility of these implantable neurostimulator are commented in favor of further translation to clinical settings. Furthermore, magnetic nanoparticles (MNPs), as another invaluable neurostimulation material, has emerged in recent years. Thus, in this review we have also included MNPs as a remote neurostimulation solution that overcomes physical limitations of invasive implants. Overall, this review provides peers with the recent development of ultra-low power, cellular-level, spatially selective magnetic neurostimulators of dimensions within micro- to nano-range for treating chronic neurological disorders. At the end of this review, some potential applications of next generation neuro-devices have also been discussed.

Magnonic Unidirectional Spin Hall Magnetoresistance in a Heavy-Metal-Ferromagnetic-Insulator Bilayer

We report the observation of the unidirectional spin Hall magnetoresistance (USMR), which depends on the current or magnetization direction, in heavy-metal-ferromagnetic-insulator bilayer, Pt-Y_{3}Fe_{5}O_{12} (YIG). This USMR is apparently not caused by the mechanisms established in metallic bilayer, in which the ferromagnetic layer is required to be electrically conductive. From the magnetic field, current, temperature, and YIG thickness dependent measurements, the USMR is attributed to the asymmetric magnon creation and annihilation induced by the spin-orbit torque. This asymmetry and the resultant USMR are further revealed by the micromagnetic simulations combined with the spin-orbit torque and the spin drift-diffusion model. Our finding exhibits a nonlinear manipulation of magnons with the charge current.

Theory of unidirectional magnetoresistance and nonlinear Hall effect

We study the unidirectional magnetoresistance (UMR) and the nonlinear Hall effect (NLHE) in the ferromagnetic Rashba model. For this purpose we derive expressions to describe the response of the electric current quadratic in the applied electric field. We compare two different formalisms, namely the standard Keldysh nonequilibrium formalism and the Moyal-Keldysh formalism, to derive the nonlinear conductivities of UMR and NLHE. We find that both formalisms lead to identical numerical results when applied to the ferromagnetic Rashba model. The UMR and the NLHE nonlinear conductivities tend to be comparable in magnitude according to our calculations. Additionally, their dependencies on the Rashba parameter and on the quasiparticle broadening are similar. The nonlinear zero-frequency response considered here is several orders of magnitude higher than the one at optical frequencies that describes the photocurrent generation in the ferromagnetic Rashba model. Additionally, we compare our Keldysh nonequilibrium expression in the independent-particle approximation to literature expressions of the UMR that have been obtained within the constant relaxation time approximation of the Boltzmann formalism. We find that both formalisms converge to the same analytical formula in the limit of infinite relaxation time. However, remarkably, we find that the Boltzmann result does not correspond to the intraband term of the Keldysh expression. Instead, the Boltzmann result corresponds to the sum of the intraband term and an interband term that can be brought into the form of an effective intraband term due to thef-sum rule.

Study of Spin-Orbit Interactions and Interlayer Ferromagnetic Coupling in Co/Pt/Co Trilayers in a Wide Range of Heavy-Metal Thickness

The spin-orbit torque, a torque induced by a charge current flowing through the heavy-metal-conducting layer with strong spin-orbit interactions, provides an efficient way to control the magnetization direction in heavy-metal/ferromagnet nanostructures, required for applications in the emergent magnetic technologies like random access memories, high-frequency nano-oscillators, or bioinspired neuromorphic computations. We study the interface properties, magnetization dynamics, magnetostatic features, and spin-orbit interactions within the multilayer system Ti(2)/Co(1)/Pt(0-4)/Co(1)/MgO(2)/Ti(2) (thicknesses in nanometers) patterned by optical lithography on micrometer-sized bars. In the investigated devices, Pt is used as a source of the spin current and as a nonmagnetic spacer with variable thickness, which enables the magnitude of the interlayer ferromagnetic exchange coupling to be effectively tuned. We also find the Pt thickness-dependent changes in magnetic anisotropies, magnetoresistances, effective Hall angles, and, eventually, spin-orbit torque fields at interfaces. The experimental findings are supported by the relevant interface structure-related simulations, micromagnetic, macrospin, as well as the spin drift-diffusion models. Finally, the contribution of the spin-orbital Edelstein-Rashba interfacial fields is also briefly discussed in the analysis.

Spin-orbit torque driven magnetization switching in W/CoFeB/MgO-based type-Y three terminal magnetic tunnel junctions

We have studied current induced magnetization switching in W/CoFeB/MgO based three terminal magnetic tunnel junctions. The switching driven by spin—orbit torque (SOT) is evaluated in the so-called type-Y structure, in which the magnetic easy-axis of the CoFeB layer lies in the film plane and is orthogonal to the current flow. The effective spin Hall angle estimated from the bias field dependence of critical current (I_c) is ~ 0.07. The field and current dependence of the switching probability are studied. The field and DC current induced switching can be described using a model based on thermally assisted magnetization switching. In contrast, the 50 ns long pulse current dependence of the switching probability shows significant deviation from the model, even if contribution from the field-like torque is included. The deviation is particularly evident when the threshold switching current is larger. These results show that conventional thermally assisted magnetization switching model cannot be used to describe SOT induced switching using short current pulses.

Spin-to-charge conversion and interface-induced spin Hall magnetoresistance in yttrium iron garnet/metallic bilayers

We report the investigation of spin-to-charge current interconversion process in hybrid structures of yttrium iron garnet (YIG)/metallic bilayers by means of two different experimental techniques: spin pumping effect (SPE) and spin Hall magnetoresistance (SMR). We demonstrate the evidence of a correlation between spin-to-charge conversion and SMR in bilayers of YIG/Pd, YIG/Pt, and YIG/IrMn. The correlation was verified directly in the spin Hall angles and the amplitudes of the voltage signals measured by the SPE and SMR techniques. The detection of SMR was carried out using the modulated magnetoresistance technique and lock-in amplifier detection. For these measurements, we present a simple model for the interpretation of the results. The results allow us to conclude that indeed the interface in the YIG/metallic bilayers has a dominant role in the spin-to-charge current conversion and SMR.

Structural Phase-Dependent Giant Interfacial Spin Transparency in W/CoFeB Thin-Film Heterostructures

Pure spin current has transformed the research field of conventional spintronics due to its various advantages, including energy efficiency. An efficient mechanism for generation of pure spin current is spin pumping, and high effective spin-mixing conductance (G_eff) and interfacial spin transparency (T) are essential for its higher efficiency. By employing the time-resolved magneto-optical Kerr effect technique, we report here a giant value of T in substrate/W (t)/Co₂₀Fe₆₀B₂₀ (d)/SiO₂ (2 nm) thin-film heterostructures in the beta-tungsten (β-W) phase. We extract the spin diffusion length of W and spin-mixing conductance of the W/CoFeB interface from the variation of damping as a function of W and CoFeB thickness. This leads to a value of T = 0.81 ± 0.03 for the β-W/CoFeB interface. A stark variation of G_eff and T with the thickness of the W layer is obtained in accordance with the structural phase transition and resistivity variation of W with its thickness. Effects such as spin memory loss and two-magnon scattering are found to have minor contributions to damping modulation in comparison to the spin pumping effect which is reconfirmed from the unchanged damping constant with the variation of Cu spacer layer thickness inserted between W and CoFeB. The giant interfacial spin transparency and its strong dependence on crystal structures of W will be important for future spin-orbitronic devices based on pure spin current.

Large Magnetic Moment in Flexoelectronic Silicon at Room Temperature

Time-dependent rotational electric polarizations have been proposed to generate temporally varying magnetic moments, for example, through a combination of ferroelectric polarization and optical phonons. This phenomenon has been called dynamical multiferroicity, but explicit experimental demonstrations have been elusive to date. Here, we report the detection of a temporal magnetic moment as high as 1.2 μ_B/atom in a charge-doped thin film of silicon under flexural strain. We demonstrate that the magnetic moment is generated by a combination of electric polarization arising from a flexoelectronic charge separation along the strain gradient and the deformation potential of phonons. The effect can be controlled by adjusting the external strain gradient, doping concentration, and dopant and can be regarded as a dynamical multiferroic effect involving flexoelectronic polarization instead of ferroelectricity. The discovery of a large magnetic moment in silicon may enable the use of nonmagnetic and nonferroelectric semiconductors in various multiferroic and spintronic applications.

Acoustic spin Hall effect in strong spin-orbit metals

We report on the observation of the acoustic spin Hall effect that facilitates lattice motion-induced spin current via spin-orbit interaction (SOI). Under excitation of surface acoustic wave (SAW), we find that a spin current flows orthogonal to the SAW propagation in nonmagnetic metals (NMs). The acoustic spin Hall effect manifests itself in a field-dependent acoustic voltage in NM/ferromagnetic metal bilayers. The acoustic voltage takes a maximum when the NM layer thickness is close to its spin diffusion length, vanishes for NM layers with weak SOI, and increases linearly with the SAW frequency. To account for these results, we find that the spin current must scale with the SOI and the time derivative of the lattice displacement. These results, which imply the strong coupling of electron spins with rotating lattices via the SOI, show the potential of lattice dynamics to supply spin current in strong spin-orbit metals.

Modulation of field-like spin orbit torque in heavy metal/ferromagnet heterostructures

Spin orbit torque (SOT) has drawn widespread attention in the emerging field of magnetic memory devices, such as magnetic random access memory (MRAM). To promote the performance of SOT-MRAM, most efforts have been devoted to enhance the SOT switching efficiency by improving the damping-like torque. Recently, some studies noted that the field-like torque also plays a crucial role in the nanosecond-timescale SOT dynamics. However, there is not yet an effective way to tune its relative amplitude. Here, we experimentally modulate the field-like SOT in W/CoFeB/MgO trilayers through tuning the interfacial spin accumulation. By performing spin Hall magnetoresistance measurement, we find that the CoFeB with enhanced spin dephasing, either generated from larger layer thickness or from proper annealing, can distinctly boost the spin absorption and enhance the interfacial spin mixing conductance Gr. While the damping-like torque efficiency increases with Gr, the field-like torque efficiency is found to decrease with it. The results suggest that the interfacial spin accumulation, which largely contributes to the field-like torque, is reduced by higher interfacial spin transparency. Our work shows a new path to further improve the performance of SOT-based ultrafast magnetic devices.

Negative spin Hall magnetoresistance of normal metal/ferromagnet bilayers

Interconversion between charge and spin through spin-orbit coupling lies at the heart of condensed-matter physics. In normal metal/ferromagnet bilayers, a concerted action of the interconversions, the spin Hall effect and its inverse effect of normal metals, results in spin Hall magnetoresistance, whose sign is always positive regardless of the sign of spin Hall conductivity of normal metals. Here we report that the spin Hall magnetoresistance of Ta/NiFe bilayers is negative, necessitating an additional interconversion process. Our theory shows that the interconversion owing to interfacial spin-orbit coupling at normal metal/ferromagnet interfaces can give rise to negative spin Hall magnetoresistance. Given that recent studies found the conversion from charge currents to spin currents at normal metal/ferromagnet interfaces, our work provides a missing proof of its reciprocal spin-current-to-charge-current conversion at same interface. Our result suggests that interfacial spin-orbit coupling effect can dominate over bulk effects, thereby demanding interface engineering for advanced spintronics devices.

Optimization of spin Hall magnetoresistance in heavy-metal/ferromagnetic-metal bilayers

We present experimental data and their theoretical description on spin Hall magnetoresistance (SMR) in bilayers consisting of a heavy metal (H) coupled to in-plane magnetized ferromagnetic metal (F), and determine contributions to the magnetoresistance due to SMR and anisotropic magnetoresistance (AMR) in five different bilayer systems: [Formula: see text], [Formula: see text], [Formula: see text], W/Co, and Co/Pt. The devices used for experiments have different interfacial properties due to either amorphous or crystalline structures of constitutent layers. To determine magnetoresistance contributions and to allow for optimization, the AMR is explicitly included in the diffusion transport equations in the ferromagnets. The results allow determination of different contributions to the magnetoresistance, which can play an important role in optimizing prospective magnetic stray field sensors. They also may be useful in the determination of spin transport properties of metallic magnetic heterostructures in other experiments based on magnetoresistance measurements.

Planar Hall Driven Torque in a Ferromagnet/Nonmagnet/Ferromagnet System

An important goal of spintronics is to covert a charge current into a spin current with a controlled spin polarization that can exert torques on an adjacent magnetic layer. Here we demonstrate such torques in a two ferromagnet system. A CoNi multilayer is used as a spin current source in a sample with structure CoNi/Au/CoFeB. Spin torque ferromagnetic resonance is used to measure the torque on the CoFeB layer. The response as a function of the applied field angle and current is consistent with the symmetry expected for a torque produced by the planar Hall effect originating in CoNi. We find the strength of this effect to be comparable to that of the spin Hall effect in platinum, indicating that the planar Hall effect holds potential as a spin current source with a controllable polarization direction.

The spin Hall effect of Bi-Sb alloys driven by thermally excited Dirac-like electrons

We have studied the charge to spin conversion in Bi_1-x Sb _x /CoFeB heterostructures. The spin Hall conductivity (SHC) of the sputter-deposited heterostructures exhibits a high plateau at Bi-rich compositions, corresponding to the topological insulator phase, followed by a decrease of SHC for Sb-richer alloys, in agreement with the calculated intrinsic spin Hall effect of Bi_1-x Sb _x . The SHC increases with increasing Bi_1-x Sb _x thickness before it saturates, indicating that it is the bulk of the alloy that predominantly contributes to the generation of spin current; the topological surface states, if present, play little role. Unexpectedly, the SHC is found to increase with increasing temperature, following the trend of carrier density. These results suggest that the large SHC at room temperature, with a spin Hall efficiency exceeding 1 and an extremely large spin current mobility, is due to increased number of thermally excited Dirac-like electrons in the L valley of the narrow gap Bi_1-x Sb _x alloy.

Spin-Momentum-Locking Inhomogeneities as a Source of Bilinear Magnetoresistance in Topological Insulators

A new mechanism of bilinear magnetoresistance (BMR) is proposed and studied theoretically within the minimal model describing surface electronic states in topological insulators. The BMR appears as a consequence of the second-order response to electric field, and depends linearly on both magnetic field and current (electric field). The mechanism is based on the interplay of current-induced spin polarization and scattering processes due to inhomogeneities of spin-momentum locking, that unavoidably appear as a result of structural defects in topological insulators. The proposed mechanism leads to the BMR even if the electronic band structure is isotropic (e.g., absence of hexagonal warping), and is shown to be dominant at lower Fermi energies.

Observation of Large Unidirectional Rashba Magnetoresistance in Ge(111)

Relating magnetotransport properties to specific spin textures at surfaces or interfaces is an intense field of research nowadays. Here, we investigate the variation of the electrical resistance of Ge(111) grown epitaxially on semi-insulating Si(111) under the application of an external magnetic field. We find a magnetoresistance term that is linear in current density j and magnetic field B, hence, odd in j and B, corresponding to a unidirectional magnetoresistance. At 15 K, for I=10  μA (or j=0.33  A m^{-1}) and B=1  T, it represents 0.5% of the zero field resistance, a much higher value compared to previous reports on unidirectional magnetoresistance (UMR). We ascribe the origin of this magnetoresistance to the interplay between the externally applied magnetic field and the pseudomagnetic field generated by the current applied in the spin-splitted subsurface states of Ge(111). This unidirectional magnetoresistance is independent of the current direction with respect to the Ge crystal axes. It progressively vanishes, either using a negative gate voltage due to carrier activation into the bulk (without spin-splitted bands), or by increasing the temperature due to the Rashba energy splitting of the subsurface states lower than ∼58k_{B}. We believe that UMR could be used as a powerful probe of the spin-orbit interaction in a wide range of materials.

Impact of Symmetry on Anisotropic Magnetoresistance in Textured Ferromagnetic Thin Films

We report on the magnetoresistance of textured films consisting of 3d-ferromagnetic layers sandwiched by Pt. While the conventional cos^{2}φ behavior of the anisotropic magnetoresistance (AMR) is found when the magnetization M is varied in the film plane, cos^{2n}θ contributions (2n≤6) exist for rotating M in the plane perpendicular to the current. This finding is explained by the symmetry-adapted modeling of AMR of textured films demonstrating that the cos^{2}θ behavior cannot be used as a fingerprint for the presence of spin Hall magnetoresistance (SMR). Further, the interfacial MR contributions for Pt/Ni/Pt contradict the SMR behavior confirming the dominant role of AMR in all-metallic systems.

Free Field Electric Switching of Perpendicularly Magnetized Thin Film by Spin Current Gradient

To realize high-speed nonvolatile magnetic memory with low energy consumption, electric switching of perpendicular magnetization by spin-orbit torque in the heavy metal/ferromagnetic (HM/FM) structure has recently attracted intensive attention. Conventionally, an external in-plane magnetic field for breaking the symmetry is required for achieving electric switching of perpendicular magnetization. However, electric switching without external field is the prerequisite for the integration of magnetic functionality into the integrated circuit devices. Here, we propose a new method of utilizing a W wedge in the Pt/W/FM structure to induce a spin current gradient, which can result in an in-plane equivalent field along the wedge thickness gradient direction. We experimentally demonstrate the deterministic magnetization switching of perpendicular Co/Ni multilayers without external magnetic field when the electric current is along the wedge thickness gradient direction. Our findings shed light on free field electric switching of magnetization by a new physical parameter-an asymmetric spin current induced by a bilayer wedge structure.

Effective Spin-Mixing Conductance of Heavy-Metal-Ferromagnet Interfaces

The effective spin-mixing conductance (G_{eff}^{↑↓}) of a heavy-metal-ferromagnet (HM-FM) interface characterizes the efficiency of the interfacial spin transport. Accurately determining G_{eff}^{↑↓} is critical to the quantitative understanding of measurements of direct and inverse spin Hall effects. G_{eff}^{↑↓} is typically ascertained from the inverse dependence of magnetic damping on the FM thickness under the assumption that spin pumping is the dominant mechanism affecting this dependence. We report that this assumption fails badly in many in-plane magnetized prototypical HM-FM systems in the nanometer-scale thickness regime. Instead, the majority of the damping is from two-magnon scattering at the FM interface, while spin-memory-loss scattering at the interface can also be significant. If these two effects are neglected, the results will be an unphysical "giant" apparent G_{eff}^{↑↓} and hence considerable underestimation of both the spin Hall ratio and the spin Hall conductivity in inverse or direct spin Hall experiments.

Unidirectional Magneto-Resistance in Modulation-Doped Magnetic Topological Insulators

Nonlinear unidirectional spin Hall magnetoresistance (USMR) has been reported in heavy metal/ferromagnet bilayers, which could be employed as an effective method in detecting the magnetization orientation in spintronic devices with two-terminal geometry. Recently, another unidirectional magnetoresistance (UMR) was reported in magnetic topological insulator (TI)-based heterostructures at cryogenic temperature, whose amplitude is orders of magnitude larger than the USMR measured in heavy metal-based magnetic heterostructures at room temperature. Here, we report the UMR effect in the modulation-doped magnetic TI structures. This UMR arises due to the interplay between the magnetic dopant's magnetization and the current-induced surface spin polarization, when they are parallel or antiparallel to each other in the TI material. By varying the dopant's position in the structure, we reveal that the UMR is mainly originating from the interaction between the magnetization and the surface spin-polarized carriers (not bulk carriers). Furthermore, from the magnetic field-, the angular rotation-, and the temperature-dependence, we highlight the correlation between the UMR effect and the magnetism in the structures. The large UMR versus current ratio in TI-based magnetic bilayers promises the easy readout in TI-based spintronic devices with two-terminal geometry.

Interface Engineering and Emergent Phenomena in Oxide Heterostructures

Complex oxide interfaces have mesmerized the scientific community in the last decade due to the possibility of creating tunable novel multifunctionalities, which are possible owing to the strong interaction among charge, spin, orbital, and structural degrees of freedom. Artificial interfacial modifications, which include defects, formal polarization, structural symmetry breaking, and interlayer interaction, have led to novel properties in various complex oxide heterostructures. These emergent phenomena not only serve as a platform for investigating strong electronic correlations in low-dimensional systems but also provide potentials for exploring next-generation electronic devices with high functionality. Herein, some recently developed strategies in engineering functional oxide interfaces and their emergent properties are reviewed.

Interface morphology effect on the spin mixing conductance of Pt/Fe3O4 bilayers

Non-magnetic (NM) metals with strong spin-orbit coupling have been recently explored as a probe of interface magnetism on ferromagnetic insulators (FMI) by means of the spin Hall magnetoresistance (SMR) effect. In NM/FMI heterostructures, increasing the spin mixing conductance (SMC) at the interface comes as an important step towards devices with maximized SMR. Here we report on the study of SMR in Pt/Fe₃O₄ bilayers at cryogenic temperature, and identify a strong dependence of the determined real part of the complex SMC on the interface roughness. We tune the roughness of the Pt/Fe₃O₄ interface by controlling the growth conditions of the Fe₃O₄ films, namely by varying the thickness, growth technique, and post-annealing processes. Field-dependent and angular-dependent magnetoresistance measurements sustain the clear observation of SMR. The determined real part of the complex SMC of the Pt/Fe₃O₄ bilayers ranges from 4.96 × 10¹⁴ Ω⁻¹ m⁻² to 7.16 × 10¹⁴ Ω⁻¹ m⁻² and increases with the roughness of the Fe₃O₄ underlayer. We demonstrate experimentally that the interface morphology, acting as an effective interlayer potential, leads to an enhancement of the spin mixing conductance.

Origins of the Unidirectional Spin Hall Magnetoresistance in Metallic Bilayers

Recent studies evidenced the emergence of asymmetric electron transport in layered conductors owing to the interplay between electrical conductivity, magnetization, and the spin Hall or Rashba-Edelstein effects. Here, we investigate the unidirectional magnetoresistance (UMR) caused by the current-induced spin accumulation in Co/Pt and CoCr/Pt bilayers. We identify three competing mechanisms underpinning the resistance asymmetry, namely, interface and bulk spin-dependent electron scattering and electron-magnon scattering. Our measurements provide a consistent description of the current, magnetic field, and temperature dependence of the UMR and show that both positive and negative UMR can be obtained by tuning the interface and bulk spin-dependent scattering.

Anomalous Hall magnetoresistance in a ferromagnet

The anomalous Hall effect, observed in conducting ferromagnets with broken time-reversal symmetry, offers the possibility to couple spin and orbital degrees of freedom of electrons in ferromagnets. In addition to charge, the anomalous Hall effect also leads to spin accumulation at the surfaces perpendicular to both the current and magnetization direction. Here, we experimentally demonstrate that the spin accumulation, subsequent spin backflow, and spin-charge conversion can give rise to a different type of spin current-related spin current related magnetoresistance, dubbed here as the anomalous Hall magnetoresistance, which has the same angular dependence as the recently discovered spin Hall magnetoresistance. The anomalous Hall magnetoresistance is observed in four types of samples: co-sputtered (Fe1-xMn x )0.6Pt0.4, Fe1-xMn x /Pt multilayer, Fe1-xMn x with x = 0.17-0.65 and Fe, and analyzed using the drift-diffusion model. Our results provide an alternative route to study charge-spin conversion in ferromagnets and to exploit it for potential spintronic applications.

Spin-orbit torque magnetometry by wide-field magneto-optical Kerr effect

Magneto-optical Kerr effect (MOKE) is an efficient approach to probe surface magnetization in thin film samples. Here we present a wide-field MOKE technique that adopts a Köhler illumination scheme to characterize the current-induced damping-like spin-orbit torque (DL-SOT) in micron-sized and unpatterned magnetic heterostructures with perpendicular magnetic anisotropy. Through a current-induced hysteresis loop shift analysis, we quantify the DL-SOT efficiency of a Ta-based heterostructure with bar-shaped geometry, Hall-cross geometry, and unpatterned geometry to be |ξ_DL| ≈ 0.08. The proposed wide-field MOKE approach therefore provides an instant and direct characterization of DL-SOT, without the need of any further interpretation on electrical signals.

Unidirectional spin-Hall and Rashba-Edelstein magnetoresistance in topological insulator-ferromagnet layer heterostructures

The large spin−orbit coupling in topological insulators results in helical spin-textured Dirac surface states that are attractive for topological spintronics. These states generate an efficient spin−orbit torque on proximal magnetic moments. However, memory or logic spin devices based upon such switching require a non-optimal three-terminal geometry, with two terminals for the writing current and one for reading the state of the device. An alternative two-terminal device geometry is now possible by exploiting the recent discovery of the unidirectional spin Hall magnetoresistance in heavy metal/ferromagnet bilayers and unidirectional magnetoresistance in magnetic topological insulators. Here, we report the observation of such unidirectional magnetoresistance in a technologically relevant device geometry that combines a topological insulator with a conventional ferromagnetic metal. Our devices show a figure of merit (magnetoresistance per current density per total resistance) that is more than twice as large as the highest reported values in all-metal Ta/Co bilayers.

Unidirectional spin Hall magnetoresistance enables the new spintronic devices but is limited by the low amplitude or working temperature. Here, the authors report the large unidirectional spin Hall magnetoresistance in a topological insulator and ferromagnetic metal bilayer system at relatively higher temperature.

Interface-induced spin Hall magnetoresistance enhancement in Pt-based tri-layer structure

In this study, we integrated bilayer structure of covered Pt on nickel zinc ferrite (NZFO) and CoFe/Pt/NZFO tri-layer structure by pulsed laser deposition system for a spin Hall magnetoresistance (SMR) study. In the bilayer structure, the angular-dependent magnetoresistance (MR) results indicate that Pt/NZFO has a well-defined SMR behavior. Moreover, the spin Hall angle and the spin diffusion length, which were 0.0648 and 1.31 nm, respectively, can be fitted by changing the Pt thickness in the longitudinal SMR function. Particularly, the MR ratio of the bilayer structure (Pt/NZFO) has the highest changing ratio (about 0.135%), compared to the prototype structure Pt/Y₃Fe₅O₁₂ (YIG) because the NZFO has higher magnetization. Meanwhile, the tri-layer samples (CoFe/Pt/NZFO) indicate that the MR behavior is related with CoFe thickness as revealed in angular-dependent MR measurement. Additionally, comparison between the tri-layer structure with Pt/NZFO and CoFe/Pt bilayer systems suggests that the SMR ratio can be enhanced by more than 70%, indicating that additional spin current should be injected into Pt layer.

Observation of spin-orbit magnetoresistance in metallic thin films on magnetic insulators

A magnetoresistance (MR) effect induced by the Rashba spin-orbit interaction was predicted, but not yet observed, in bilayers consisting of normal metal and ferromagnetic insulator. We present an experimental observation of this new type of spin-orbit MR (SOMR) effect in the Cu[Pt]/Y₃Fe₅O₁₂ (YIG) bilayer structure, where the Cu/YIG interface is decorated with nanosize Pt islands. This new MR is apparently not caused by the bulk spin-orbit interaction because of the negligible spin-orbit interaction in Cu and the discontinuity of the Pt islands. This SOMR disappears when the Pt islands are absent or located away from the Cu/YIG interface; therefore, we can unambiguously ascribe it to the Rashba spin-orbit interaction at the interface enhanced by the Pt decoration. The numerical Boltzmann simulations are consistent with the experimental SOMR results in the angular dependence of magnetic field and the Cu thickness dependence. Our finding demonstrates the realization of the spin manipulation by interface engineering.

Observation of transverse spin Nernst magnetoresistance induced by thermal spin current in ferromagnet/non-magnet bilayers

Electric generation of spin current via spin Hall effect is of great interest as it allows an efficient manipulation of magnetization in spintronic devices. Theoretically, pure spin current can be also created by a temperature gradient, which is known as spin Nernst effect. Here, we report spin Nernst effect-induced transverse magnetoresistance in ferromagnet/non-magnetic heavy metal bilayers. We observe that the magnitude of transverse magnetoresistance in the bilayers is significantly modified by heavy metal and its thickness. This strong dependence of transverse magnetoresistance on heavy metal evidences the generation of thermally induced pure spin current in heavy metal. Our analysis shows that spin Nernst angles of W and Pt have the opposite sign to their spin Hall angles. Moreover, our estimate implies that the magnitude of spin Nernst angle would be comparable to that of spin Hall angle, suggesting an efficient generation of spin current by the spin Nernst effect.

The spin Nernst effect in tungsten

The spin Hall effect allows the generation of spin current when charge current is passed along materials with large spin-orbit coupling. It has been recently predicted that heat current in a nonmagnetic metal can be converted into spin current via a process referred to as the spin Nernst effect. We report the observation of the spin Nernst effect in W. In W/CoFeB/MgO heterostructures, we find changes in the longitudinal and transverse voltages with magnetic field when temperature gradient is applied across the film. The field dependence of the voltage resembles that of the spin Hall magnetoresistance. A comparison of the temperature gradient-induced voltage and the spin Hall magnetoresistance allows direct estimation of the spin Nernst angle. We find the spin Nernst angle of W to be similar in magnitude but opposite in sign to its spin Hall angle. Under an open-circuit condition, this sign difference results in the spin current generation larger than otherwise. These results highlight the distinct characteristics of the spin Nernst and spin Hall effects, providing pathways to explore materials with unique band structures that may generate large spin current with high efficiency.

Spin-orbit torques from interfacial spin-orbit coupling for various interfaces

We use a perturbative approach to study the effects of interfacial spin-orbit coupling in magnetic multilayers by treating the two-dimensional Rashba model in a fully three-dimensional description of electron transport near an interface. This formalism provides a compact analytic expression for current-induced spin-orbit torques in terms of unperturbed scattering coefficients, allowing computation of spin-orbit torques for various contexts, by simply substituting scattering coefficients into the formulas. It applies to calculations of spin-orbit torques for magnetic bilayers with bulk magnetism, those with interface magnetism, a normal metal/ferromagnetic insulator junction, and a topological insulator/ferromagnet junction. It predicts a dampinglike component of spin-orbit torque that is distinct from any intrinsic contribution or those that arise from particular spin relaxation mechanisms. We discuss the effects of proximity-induced magnetism and insertion of an additional layer and provide formulas for in-plane current, which is induced by a perpendicular bias, anisotropic magnetoresistance, and spin memory loss in the same formalism.

Observation of Room-Temperature Magnetoresistance in Monolayer MoS2 by Ferromagnetic Gating

Room-temperature magnetoresistance (MR) effect is observed in heterostructures of wafer-scale MoS₂ layers and ferromagnetic dielectric CoFe₂O₄ (CFO) thin films. Through the ferromagnetic gating, an MR ratio of -12.7% is experimentally achieved in monolayer MoS₂ under 90 kOe magnetic field at room temperature (RT). The observed MR ratio is much higher than that in previously reported nonmagnetic metal coupled with ferromagnetic insulator, which generally exhibited MR ratio of less than 1%. The enhanced MR is attributed to the spin accumulation at the heterostructure interface and spin injection to the MoS₂ layers by the strong spin-orbit coupling effect. The injected spin can contribute to the spin current and give rise to the MR by changing the resistance of MoS₂ layers. Furthermore, the MR effect decreases as the thickness of MoS₂ increases, and the MR ratio becomes negligible in MoS₂ with thickness more than 10 layers. Besides, it is interesting to find a magnetic field direction dependent spin Hall magnetoresistance that stems from a combination of the spin Hall and the inverse spin Hall effects. Our research provides an insight into exploring RT MR in monolayer materials, which should be helpful for developing ultrathin magnetic storage devices in the atomically thin limit.

Dynamical amplification of magnetoresistances and Hall currents up to the THz regime

Spin-orbit-related effects offer a highly promising route for reading and writing information in magnetic units of future devices. These phenomena rely not only on the static magnetization orientation but also on its dynamics to achieve fast switchings that can reach the THz range. In this work, we consider Co/Pt and Fe/W bilayers to show that accounting for the phase difference between different processes is crucial to the correct description of the dynamical currents. By tuning each system towards its ferromagnetic resonance, we reveal that dynamical spin Hall angles can non-trivially change sign and be boosted by over 500%, reaching giant values. We demonstrate that charge and spin pumping mechanisms can greatly magnify or dwindle the currents flowing through the system, influencing all kinds of magnetoresistive and Hall effects, thus impacting also dc and second harmonic experimental measurements.

Influence of intermixing at the Ta/CoFeB interface on spin Hall angle in Ta/CoFeB/MgO heterostructures

When a current is passed through a non-magnetic metal with strong spin-orbit coupling, an orthogonal spin current is generated. This spin current can be used to switch the magnetization of an adjacent ferromagnetic layer or drive its magnetization into continuous precession. The interface, which is not necessarily sharp, and the crystallographic structure of the nonmagnetic metal can both affect the strength of current-induced spin-orbit torques. Here, we investigate the effects of interface intermixing and film microstructure on spin-orbit torques in perpendicularly magnetized Ta/Co₄₀Fe₄₀B₂₀/MgO trilayers with different Ta layer thickness (5 nm, 10 nm, 15 nm), greater than the spin diffusion length. Effective spin-orbit torques are determined from harmonic Hall voltage measurements performed at temperatures ranging from 20 K to 300 K. We account for the temperature dependence of damping-like and field-like torques by including an additional contribution from the Ta/CoFeB interface in the spin diffusion model. Using this approach, the temperature variations of the spin Hall angle in the Ta underlayer and at the Ta/CoFeB interface are determined separately. Our results indicate an almost temperature-independent spin Hall angle of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{\theta }}}_{{\boldsymbol{SH}}}^{{\boldsymbol{N}}}\approx -{\bf{0.2}}$$\end{document}θSHN≈−0.2 in Ta and a strongly temperature-dependent \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{\theta }}}_{{\boldsymbol{SH}}}^{{\boldsymbol{N}}}$$\end{document}θSHN for the intermixed Ta/CoFeB interface.

Effect of quantum tunneling on spin Hall magnetoresistance

We present a formalism that simultaneously incorporates the effect of quantum tunneling and spin diffusion on the spin Hall magnetoresistance observed in normal metal/ferromagnetic insulator bilayers (such as Pt/Y₃Fe₅O₁₂) and normal metal/ferromagnetic metal bilayers (such as Pt/Co), in which the angle of magnetization influences the magnetoresistance of the normal metal. In the normal metal side the spin diffusion is known to affect the landscape of the spin accumulation caused by spin Hall effect and subsequently the magnetoresistance, while on the ferromagnet side the quantum tunneling effect is detrimental to the interface spin current which also affects the spin accumulation. The influence of generic material properties such as spin diffusion length, layer thickness, interface coupling, and insulating gap can be quantified in a unified manner, and experiments that reveal the quantum feature of the magnetoresistance are suggested.

Modulated switching current density and spin-orbit torques in MnGa/Ta films with inserting ferromagnetic layers

We report modulated switching current density and spin-orbit torques (SOT) in MnGa/Ta films with inserting very thin Co₂FeAl and Co layers. Ferromagnetic coupling has been found in MnGa/Co₂FeAl/Ta, resulting in a decreased effective anisotropy field. On the contrary, in MnGa/Co/Ta, antiferromagnetic coupling plays a dominant role. The switching current density J_c in MnGa/Ta is 8.5 × 10⁷ A/cm². After inserting 0.8-nm-thick Co₂FeAl and Co, theJ_c becomes 5 × 10⁷ A/cm² and 9 × 10⁷ A/cm², respectively. By performing adiabatic harmonic Hall voltage measurements, it is demonstrated that the inserted Co₂FeAl layer has mainly enhanced the field-like torques, while in MnGa/Co/Ta the damping-like torques have been enhanced. Finally, the enhanced spin Hall effect (SHE) has also been studied using the spin Hall magnetoresistance measurement. The modulated J_c and SOT are ascribed to the combination of magnetic coupling, Rashba effect and SHE at the interfaces.

Tunable inertia of chiral magnetic domain walls

The time it takes to accelerate an object from zero to a given velocity depends on the applied force and the environment. If the force ceases, it takes exactly the same time to completely decelerate. A magnetic domain wall is a topological object that has been observed to follow this behaviour. Here we show that acceleration and deceleration times of chiral Neel walls driven by current are different in a system with low damping and moderate Dzyaloshinskii–Moriya exchange constant. The time needed to accelerate a domain wall with current via the spin Hall torque is much faster than the time it needs to decelerate once the current is turned off. The deceleration time is defined by the Dzyaloshinskii–Moriya exchange constant whereas the acceleration time depends on the spin Hall torque, enabling tunable inertia of chiral domain walls. Such unique feature of chiral domain walls can be utilized to move and position domain walls with lower current, key to the development of storage class memory devices.

The controlled motion of magnetic domain walls in nanowire conduits forms the basis of emerging memory and information processing devices. Here, the authors report a pulse-length dependent quasi-static velocity of current-driven chiral domain walls, showing that their inertia is tunable.