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Electric manipulation of magnetization is essential for the integration of magnetic functionalities in integrated circuits. Spin-orbit torque (SOT), originating from the coupling of electron spin and orbital motion through spin-orbital interaction, can effectively manipulate magnetization. Symmetry breaking plays an important role in spintronics based on SOT. SOT requires inversion asymmetry in order to have a net effect on magnetic materials, which is commonly realized by spatial asymmetry: a thin magnetic layer sandwiched between two dissimilar layers. This kind of structure restricts the SOT by mirror and rotational symmetries to have a particular form: an “antidamping-like” component oriented in the film plane even upon reversal of the magnetization direction. Consequently, magnetization perpendicular to the film plane cannot be deterministically switched with pure electric current. To achieve all-electric switching of perpendicular magnetization, it is necessary to break the mirror and rotational symmetries of the sandwiched structure.

The long fascination antiferromagnetic materials have exerted on the scientific community over about a century has been entirely renewed recently with the discovery of several unexpected phenomena including various classes of anomalous spin and charge Hall effects and unconventional magnonic transport, but also homochiral magnetic entities such as skyrmions. With these breakthroughs, antiferromagnets standout as a rich playground for the investigation of novel topological behaviors, and as promising candidate materials for disruptive low-power microelectronic applications. Remarkably, the newly discovered phenomena are all related to the topology of the magnetic, electronic or magnonic ground state of the antiferromagnets. This review exposes how non-trivial topology emerges at different levels in antiferromagnets and explores the novel mechanisms that have been discovered recently. We also discuss how novel classes of quantum magnets could enrich the currently expanding field of antiferromagnetic spintronics and how spin transport can in turn favor a better understanding of exotic quantum excitations., Comment: 77 pages, 47 figures

In this work, we discuss the nature of Dzyaloshinskii-Moriya interaction (DMI) in transition metal heterostructures. We first derive the expression of DMI in the small spatial gradient limit using Keldysh formalism. This derivation provides us with a Green's function formula that is well adapted to tight-binding Hamiltonians. With this tool, we first uncover the role of orbital mixing: using both a toy model and a realistic multi-orbital Hamiltonian representing transition metal heterostructures, we show that symmetry breaking enables the onset of interfacial orbital momentum that is at the origin of the DMI. We then investigate the contribution of the different layers to the DMI and reveal that it can expand over several nonmagnetic metal layers depending on the Fermi energy, thereby revealing the complex orbital texture of the band structure. Finally, we examine the thickness dependence of DMI on both ferromagnetic and nonmagnetic metal thicknesses and we find that whereas the former remains very weak, the latter can be substantial., 11 pages, 11 figures

International audience; Magnetic chirality is an important knob in spintronics and can be engineered through structural symmetry breaking of magnetic thin-film multilayers. The dynamics of chiral domain walls is determined by the synergy of chiral contributions in the magnetic energy functional as well as in the dissipation tensor, which need to be better controlled for the sake of device applications. In this work, we performed a systematic study of magnetic field-induced magnetic bubble expansion in structural inversion asymmetric multilayers with different Pt thicknesses using polar magneto-optical Kerr microscopy. Asymmetric expansion of a magnetic bubble is investigated in the creep regime as a function of in-plane and out-of-plane magnetic fields. The results reveal the competition between two key mechanisms governing the asymmetry in the field-driven domain wall expansion, namely, the Dzyaloshinskii–Moriya interaction and the chiral magnetic damping. The interplay between these two effects leads to a seemingly counterintuitive experimental signature, depending on the strength of the external magnetic field. An effective control on bubble expansion asymmetry can be of great importance for future memory and multiplexer-based applications

We compute the spin-orbit torque in a transition metal heterostructure using Slater-Koster parameterization in the two-center tight-binding approximation and accounting for d-orbitals only. In this method, the spin-orbit coupling is modeled within Russel-Saunders scheme, which enables us to treat interfacial and bulk spin-orbit transport on equal footing. The two components of the spin-orbit torque, dissipative (damping-like) and reactive (field-like), are computed within Kubo linear response theory. By systematically studying their thickness and angular dependence, we were able to accurately characterize these components beyond the traditional "inverse spin galvanic" and "spin Hall" effects. Whereas the conventional field-like torque is purely interfacial, we unambiguously demonstrate that the conventional the damping-like torque possesses both an interfacial and a bulk contribution. In addition, both field-like and damping-like torques display substantial angular dependence with strikingly different thickness behavior. While the planar contribution of the field-like torque decreases smoothly with the nonmagnetic metal thickness, the planar contribution of the damping-like torque increases dramatically with the nonmagnetic metal thickness. Finally, we investigate the self-torque exerted on the ferromagnet when the spin-orbit coupling of the nonmagnetic metal is turned off. Our results suggest that the spin accumulation that builds up inside the ferromagnet can be large enough to induce magnetic excitations., 13 pages, 11 figures

The Rashba effect plays important roles in emerging quantum materials physics and potential spintronic applications, entailing both the spin orbit interaction (SOI) and broken inversion symmetry. In this work, we devise asymmetric oxide heterostructures of LaAlO3//SrTiO3/LaAlO3 (LAO//STO/LAO) to study the Rashba effect in STO with an initial centrosymmetric structure, and broken inversion symmetry is created by the inequivalent bottom and top interfaces due to their opposite polar discontinuities. Furthermore, we report the observation of a transition from the cubic Rashba effect to the coexistence of linear and cubic Rashba effects in the oxide heterostructures, which is controlled by the filling of Ti orbitals. Such asymmetric oxide heterostructures with initially centrosymmetric materials provide a general strategy for tuning the Rashba SOI in artificial quantum materials., The two-dimensional electron gases that form at LaAlO3/SrTiO3 heterostructure interfaces feature strong spin-orbit interactions, leading to proposed spintronic applications. Lin et al. show that the design of asymmetric heterostructures enables the Rashba spin-orbit interaction to be tuned between two regimes.

International audience; It has been predicted that transverse spin current can propagate coherently (without dephasing) over a long distance in antiferromagnetically ordered metals. Here, we estimate the dephasing length of transverse spin current in ferrimagnetic CoGd alloys by spin pumping measurements across the compensation point. A modified drift-diffusion model, which accounts for spin-current transmission through the ferrimagnet, reveals that the dephasing length is about 4-5 times longer in nearly compensated CoGd than in ferromagnetic metals. This finding suggests that antiferromagnetic order can mitigate spin dephasingin a manner analogous to spin echo rephasing for nuclear and qubit spin systemseven in structurally disordered alloys at room temperature. We also find evidence that transverse spin current interacts more strongly with the Co sublattice than the Gd sublattice. Our results provide fundamental insights into the interplay between spin current and antiferromagnetic order, which are crucial for engineering spin torque effects in ferrimagnetic and antiferromagnetic metals.

In recent years, the notion of Quantum Materials has emerged as a powerful unifying concept across diverse fields of science and engineering, from condensed-matter and cold atom physics to materials science and quantum computing. Beyond traditional quantum materials such as unconventional superconductors, heavy fermions, and multiferroics, the field has significantly expanded to encompass topological quantum matter, two-dimensional materials and their van der Waals heterostructures, Moire materials, Floquet time crystals, as well as materials and devices for quantum computation with Majorana fermions. In this Roadmap collection we aim to capture a snapshot of the most recent developments in the field, and to identify outstanding challenges and emerging opportunities. The format of the Roadmap, whereby experts in each discipline share their viewpoint and articulate their vision for quantum materials, reflects the dynamic and multifaceted nature of this research area, and is meant to encourage exchanges and discussions across traditional disciplinary boundaries. It is our hope that this collective vision will contribute to sparking new fascinating questions and activities at the intersection of materials science, condensed matter physics, device engineering, and quantum information, and to shaping a clearer landscape of quantum materials science as a new frontier of interdisciplinary scientific inquiry., Comment: 93 pages, 27 figures

We investigate the spin transport across the magnetic phase diagram of a frustrated antiferromagnetic insulator and uncover a drastic modification of the transport regime from spin diffusion to spin superfluidity. Adopting a triangular lattice accounting for both nearest neighbor and next-nearest neighbor exchange interactions with easy-plane anisotropy, we perform atomistic spin simulations on a two-terminal configuration across the full magnetic phase diagram. We found that as long as the ground state magnetic moments remain in-plane, irrespective of whether the magnetic configuration is ferromagnetic, collinear or non-collinear antiferromagnetic, the system exhibits spin superfluid behavior with a device output that is independent on the value of the exchange interactions. When the magnetic frustration is large enough to compete with the easy-plane anisotropy and cant the magnetic moments out of the plane, the spin transport progressively evolves towards the diffusive regime. The robustness of spin superfluidity close to magnetic phase boundaries is investigated and we uncover the possibility for {\em proximate} spin superfluidity close to the ferromagnetic transition., 9 pages, 7 figures

The Smrcka-Streda version of Kubo's linear response formula is widely used in the literature to compute non-equilibrium transport properties of heterostructures. It is particularly useful for the evaluation of intrinsic transport properties associated with the Berry curvature of the Bloch states, such as anomalous and spin Hall currents as well as the damping-like component of the spin-orbit torque. Here, we demonstrate in a very general way that the widely used decomposition of the Kubo-Bastin formula introduced by Smrcka and Streda contains an overlap, which has lead to widespread confusion in the literature regarding the Fermi surface and Fermi sea contributions. To remedy this pathology, we propose a new decomposition of the Kubo-Bastin formula based on the permutation properties of the correlation function and derive a new set of formulas, without an overlap, that provides direct access to the transport effects of interest. We apply these new formulas to selected cases and demonstrate that the Fermi sea and Fermi surface contributions can be uniquely addressed with our symmetrized approach.

Using symmetry analysis and density functional theory calculations, we uncover the nature of the Dzyaloshinskii-Moriya interaction in monolayer ${\mathrm{Fe}}_{3}{\mathrm{GeTe}}_{2}$. We show that while such an interaction might result in small distortions of the magnetic texture in the short range, in the long range it favors in-plane N\'eel spin spirals along equivalent directions of the crystal structure. Whereas our results show that the observed N\'eel skyrmions cannot be explained by the Dzyaloshinskii-Moriya interaction at the monolayer level, they suggest that a canted magnetic texture shall arise at the boundary of ${\mathrm{Fe}}_{3}{\mathrm{GeTe}}_{2}$ nanoflakes or nanoribbons and, most interestingly, that homochiral planar magnetic textures could be stabilized.

While some of the most elegant applications of topological insulators, such as quantum anomalous Hall effect, require the preservation of Dirac surface states in the presence of time-reversal symmetry breaking, other phenomena such as spin-charge conversion rather rely on the ability for these surface states to imprint their spin texture on adjacent magnetic layers. In this work, we investigate the spin-momentum locking of the surface states of a wide range of monolayer transition metals (3$d$-TM) deposited on top of Bi$_{2}$Se$_{3}$ topological insulators using first principles calculations. We find an anticorrelation between the magnetic moment of the 3$d$-TM and the magnitude of the spin-momentum locking {\em induced} by the Dirac surface states. While the magnetic moment is large in the first half of the 3$d$ series, following Hund's rule, the spin-momentum locking is maximum in the second half of the series. We explain this trend as arising from a compromise between intra-atomic magnetic exchange and covalent bonding between the 3$d$-TM overlayer and the Dirac surface states. As a result, while Cr and Mn overlayers can be used successfully for the observation of quantum anomalous Hall effect or the realization of axion insulators, Co and Ni are substantially more efficient for spin-charge conversion effects, e.g. spin-orbit torque and charge pumping., Comment: 5 pages, 7 figures

International audience; While antiferromagnetic skyrmions display appealing properties, their lateral expansion in the high-velocity regime hinders their potential for applications. In this work, we study the impact of spin Hall torque, spin transfer torque, and topological torque on the velocity-current relation of antiferromagnetic skyrmions with the aim of reducing this deformation. Using a combination of micromagnetic simulations and analytical derivations, we demonstrate that the lateral expansion of the antiferromagnetic skyrmion is reminiscent of the well-known Lorentz contraction identified in one-dimensional antiferromagnetic domain walls. We also show that in the flow regime the lateral expansion is accompanied by a progressive saturation of the skyrmion velocity when driven by spin Hall and topological torques. This saturation occurs at much smaller velocities when driven by the topological torque, while the lateral expansion is reduced, preventing the skyrmion size from diverging at large current densities. We extend this study toward synthetic antiferromagnets, where the weaker antiferromagnetic exchange leads to much larger lateral expansion at smaller current densities in all cases. This study suggests that a compromise must be made between skyrmion velocity and lateral expansion during the device design. In this respect, exploiting the topological torque could lead to better control of the skyrmion velocity in antiferromagnetic racetracks.

International audience; An analysis of magnetic symmetry groups in antiferromagnets points to a new class of materials that will be useful for spintronics.

The various aspects of spin transport in two-dimensional electron gases (2DEG) in the presence of Rashba spin–orbit coupling are reviewed. We start with a brief introduction on the origin of spin–orbit splitting in asymmetrically grown 2DEG, extended to metallic interfaces, and topological surfaces. We then discuss how Rashba spin–orbit coupling can be detected via magnetic field-induced quantum oscillations, electric-dipole spin resonance, and weak antilocalization. In the third part, spin transport properties are addressed, including the spin-charge conversion processes, quenched spin relaxation in the spin helix state, as well as the Zitterbewegung effect, quantum anomalous and magnetoelectric effects, and Floquet physics. Finally, we close this chapter with a review on device concepts, covering the spin interferometer, and the spin field-effect transistor, as well as the spin–orbit torque magnetic memory device, and the spin–orbit Qubit.

The spin-orbit torque (SOT) arising from materials with large spin-orbit coupling promises a path for ultra-low power and fast magnetic-based storage and computational devices. We investigated the SOT from magnetron-sputtered BixSe(1-x) thin films in BixSe(1-x)/CoFeB heterostructures by using a dc planar Hall method. Remarkably, the spin Hall angle (SHA) was found to be as large as 18.83, which is the largest ever reported at room temperature (RT). Moreover, switching of a perpendicular CoFeB multilayer using SOT from the BixSe(1-x) has been observed with the lowest-ever switching current density reported in a bilayer system: 2.3 * 105 A/cm2 at RT. The giant SHA, smooth surface, ease of growth of the films on silicon substrate, successful growth and switching of a perpendicular CoFeB multilayer on BixSe(1-x) film opens a path for use of BixSe(1-x) topological insulator (TI) material as a spin-current generator in SOT-based memory and logic devices.

The work reported in this publication was supported by King Abdullah University of Science and Technology (KAUST) through the Office of Sponsored Research (OSR) (Grant No. OSR-2015-CRG4-2626).

Spin-orbit coupling in inversion-asymmetric magnetic crystals and structures has emerged as a powerful tool to generate complex magnetic textures, interconvert charge and spin under applied current, and control magnetization dynamics. Current-induced spin-orbit torques mediate the transfer of angular momentum from the lattice to the spin system, leading to sustained magnetic oscillations or switching of ferromagnetic as well as antiferromagnetic structures. The manipulation of magnetic order, domain walls and skyrmions by spin-orbit torques provides evidence of the microscopic interactions between charge and spin in a variety of materials and opens novel strategies to design spintronic devices with potentially high impact in data storage, nonvolatile logic, and magnonic applications. This paper reviews recent progress in the field of spin-orbitronics, focusing on theoretical models, material properties, and experimental results obtained on bulk noncentrosymmetric conductors and multilayer heterostructures, including metals, semiconductors, and topological insulator systems. Relevant aspects for improving the understanding and optimizing the efficiency of nonequilibrium spin-orbit phenomena in future nanoscale devices are also discussed., Comment: 90 pages, 50 figures

We study the behavior of non-equilibrium spin density and spin-orbit torque in a topological insulator - antiferromagnet heterostructure. Unlike ferromagnetic heterostructures where Dirac cone is gapped due to time-reversal symmetry breaking, here the Dirac cone is preserved. We demonstrate the existence of a staggered spin density corresponding to a damping like torque, which is quite robust against the scalar impurity, when the transport energy is in the topological insulator surface energy regime. We show the contribution to the non-equilibrium spin density due to both surface and bulk topological insulator bands. Finally, we show that the torques in topological insulator-antiferromagnet heterostructure exhibit an angular dependence that is consistent with the standard spin-orbit torque obtained in Rashba system with some additional nonlinear effects arising from the interfacial coupling., Comment: 9 pages, 11 figures

The direct imaging of inhomogeneous current distribution was demonstrated by using the polar magneto-optical Kerr microscopy., The direct imaging of current density vector distributions in thin films has remained a daring challenge. Here, we report that an inhomogeneous current distribution can be mapped directly by the trajectories of magnetic half-skyrmions driven by an electrical current in Pt/Co/Ta trilayer, using polar magneto-optical Kerr microscopy. The half-skyrmion carries a topological charge of 0.5 due to the presence of Dzyaloshinskii-Moriya interaction, which leads to the half-skyrmion Hall effect. The Hall angle of half-skyrmions is independent of current density and can be reduced to as small as 4° by tuning the thickness of the Co layer. The Hall angle is so small that the elongation path of half-skyrmion approximately delineates the invisible current flow as demonstrated in both a continuous film and a curved track. Our work provides a practical technique to directly map inhomogeneous current distribution even in complex geometries for both fundamental research and industrial applications.

Manipulating the magnetization direction of a magnetic layer with-out the use of an external magnetic field represents an outstanding opportunity and a challenge for spintronic applications. This chapter provides a coherent theoretical description of the topic for various phenomena involving the interplay between spin transport and magnetization dynamics. The spin transport in heterogeneous magnetic structures with a collinear magnetization configuration gives rise to a longitudinal spin density. In magnetic tunnel junctions, the spacer layer that separates the two ferromagnetic layers is a thin insulator in contrast with the metallic spacer in spin valves. The inelastic scattering of tunneling electrons by phonons or magnons is known to be detrimental to the tunneling magnetoresistance in magnetic tunnel junctions. Spin transport becomes even more intriguing in two- and three-dimensional textures such as vortices and skyrmions. Investigating the stability diagrams out of the stability regions reveals a rich variety of magnetization regimes, including in-plane precessions, out-of-plane precessions, and inhomogeneous magnetic excitations.

Recent experiments on switching antiferromagnetic domains by electric current pulses have attracted a lot of attention to spin-orbit torques in antiferromagnets. In this work, we employ the tight-binding model solver, kwant, to compute spin-orbit torques in a two-dimensional antiferromagnet on a honeycomb lattice with strong spin-orbit interaction of Rashba type. Our model combines spin-orbit interaction, local s-d-like exchange, and scattering of conduction electrons on on-site disorder potential to provide a microscopic mechanism for angular momentum relaxation. We consider two versions of the model: one with preserved and one with broken sublattice symmetry. A non-equilibrium staggered polarization, that is responsible for the so-called Neel spin-orbit torque, is shown to vanish identically in the symmetric model but may become finite if sublattice symmetry is broken. Similarly, anti-damping spin-orbit torques vanish in the symmetric model but become finite and anisotropic in a model with broken sublattice symmetry. As expected, anti-damping torques also reveal a sizable dependence on impurity concentration. Our numerical analysis also confirms symmetry classification of spin-orbit torques and strong torque anisotropy due to in-plane confinement of electron momenta., 14 pages, 12 figures

The CoRoT and Kepler missions have provided high-quality measurements of the frequency spectra of solar-like pulsators, enabling us to probe stellar interiors with a very high degree of accuracy by comparing the observed and modeled frequencies. However, the frequencies computed with 1D models suffer from systematic errors related to the poor modeling of the uppermost layers of stars. These biases are what is commonly named the near surface effect. The dominant effect is related to the turbulent pressure that modifies the hydrostatic equilibrium and thus the frequencies. This has already been investigated using grids of 3D RMHD simulations, which also were used to constrain the parameters of the empirical correction models. However, the effect of metallicity has not been considered so far. We study the impact of metallicity on the surface effect across the HR diagram, and provide a method for accounting for it when using the empirical correction models. We computed a grid of patched 1D stellar models with the stellar evolution code CESTAM in which poorly modeled surface layers have been replaced by averaged stratification computed with the 3D RMHD code CO5BOLD. We found that metallicity has a strong impact on the surface effect: keeping T_eff and log g constant, the frequency residuals can vary by up to a factor two. Therefore, the influence of metallicity cannot be neglected. We found that a correct way of accounting for it is to consider the surface Rosseland mean opacity. It allowed us to give a physically-grounded justification as well as a scaling relation for the frequency differences at nu_max as a function of T_eff, log g and kappa. Finally, we provide prescriptions for the fitting parameters of the correction functions. We show that the impact of metallicity through the Rosseland mean opacity must be taken into account when studying and correcting the surface effect., Comment: 15 pages, 7 figures. Accepted for publication in A&A

The spin field-effect transistor, an essential building block for spin information processing, shows promise for energy-efficient computing. Despite steady progress, it suffers from a low-output signal because of low spin injection and detection efficiencies. We demonstrate that this low-output obstacle can be overcome by utilizing direct and inverse spin Hall effects for spin injection and detection, respectively, without a ferromagnetic component. The output voltage of our all-electric spin Hall transistor is about two orders of magnitude larger than that of previously reported spin transistors based on ferromagnets or quantum point contacts. Moreover, the symmetry of the spin Hall effect allows all-electric spin Hall transistors to effectively mimic n-type and p-type devices, opening a way of realizing the complementary functionality.

Spin–orbit torque has recently been intensively investigated for the purposes of manipulating the magnetization in magnetic nano-devices and understanding fundamental physics. Therefore, the search for novel materials or material combinations that exhibit a strong enough spin-torque effect has become one of the top priorities in this field of spintronics. Weyl semimetal, a new topological material that features open Fermi arc with strong spin–orbit coupling and spin–momentum locking effect, is naturally expected to exhibit an enhanced spin-torque effect in magnetic nano-devices. Here we observe a significantly enhanced spin conductivity, which is associated with the field-like torque at low temperatures. The enhancement is obtained in the b-axis WTe2/Py bilayers of nano-devices but not observed in the a-axis of WTe2/Py nano-devices, which can be ascribed to the enhanced spin accumulation by the spin–momentum locking effect of the Fermi arcs of the Weyl semimetal WTe2., The Fermi arcs, topological surface states of Weyl semimetals can enable the intriguing spin control and facilitate topological spintronics. Here the authors report the spin-orbit torque at the interface of WTe2/Py and attribute it to the enhanced spin accumulation by the spin-momentum locking effect of the Fermi arcs of WTe2.

Spin-related phenomena, such as the giant magnetoresistance and the spin-transfer torque, have led to a new era of nano-spintronics in last two decades. The discovery of these physical phenomena has contributed to a substantial increase in the data storage capacity of computers. Another revolutionary phenomenon, the interfacial Dzyaloshinskii-Moriya interaction (DMI), was recently discovered in ultra-thin ferromagnet/heavy-metal bilayers. The DMI stabilizes nanometre-sized chiral spin textures such as Neel domain walls and hedgehog skyrmions. These chiral objects find the potential for applications in ultra-high density, low-energy, and high-speed memory devices because they are stable due to topological protection and easy to move with high efficiency. As both stability and current-driven speed of chiral spin textures are proportional to the DMI strength [A. Thiaville et al., Europhys Lett. 100, 57002 (2012); A. Fert, V. Cros, and J. Sampiao, Nat. Nanotechnol. 8, 152 (2013)], tremendous efforts are being devoted to finding high-DMI materials. In this respect, understanding the microscopic origin of DMI is of critical importance. Here we discuss the microscopic origin of the interfacial DMI with experimental and theoretical studies as follows: First, we show the temperature dependence of the DMI for a Pt/Co/MgO trilayer; the DMI increases with decreasing temperature in a range from 300 to 100 K. To discuss this temperature dependence of the DMI, that of the spin and orbital magnetic moments of Co and Pt is studied by X-ray magnetic circular dichroism (XMCD) spectroscopy. We find that spin moment values of Co and Pt show temperature dependences due to change in Heisenberg exchange. Furthermore, the intra-atomic magnetic dipole moment, which is due to the asymmetric spin-density distribution, shows strong temperature dependence, suggesting a sizable modification of the charge distribution between the in-plane and the out-of-plane d-orbitals under temperature variation. We also find that the out-of-plane orbital moment shows large temperature dependence while in-plane orbital moment does not, revealing a close connection between the anisotropy of orbital moment and the DMI. The ab-initio and the tight-binding model calculations suggest that the ISB-dependent electron hopping, which gives rise to the asymmetric charge distribution at the interface of the FM/HM, is a possible microscopic origin of the correlation between the orbital anisotropy and the DMI.

We consider current-driven motion of magnetic skyrmions in granular magnetic films. The study uses micromagnetic modeling and phenomenological analysis based on the Thiele formalism. Remarkably, disorder enhances the effective skyrmion Hall effect that depends on the magnitude of the driving force (current density and non-adiabaticity parameter). The origin is sliding motion of the skyrmion along the grain boundaries, followed by pinning and depinning at the grain junctions. A side-jump can occur during this depinning process. In addition, the critical current that triggers the skyrmion motion depends on the relative size of the crystallites with respect to the skyrmion size. Finally, when the skyrmion trajectory is confined along an edge by the non-adiabatic Magnus force, the critical current density can be significantly reduced. Our results imply that narrow nanowires have higher skyrmion mobilities., 8 pages, 7 figures

A complete set of the generalized drift-diffusion equations for a coupled charge and spin dynamics in ferromagnets in the presence of extrinsic spin-orbit coupling is derived from the quantum kinetic approach, covering major transport phenomena, such as the spin and anomalous Hall effects, spin swapping, spin precession, and relaxation processes. We argue that the spin swapping effect in ferromagnets is enhanced due to spin polarization, while the overall spin texture induced by the interplay of spin-orbital and spin precession effects displays a complex spatial dependence that can be exploited to generate torques and nucleate or propagate domain walls in centrosymmetric geometries without the use of external polarizers, as opposed to the conventional understanding of spin-orbit mediated torques. © 2018 American Physical Society.

International audience; It is well known that moving magnetic textures may pump spin and charge currents along the direction ofmotion, a phenomenon called electronic pumping. Here, the electronic pumping arising from the steadymotion of ferromagnetic skyrmions is investigated by solving the time evolution of the Schrödingerequation implemented on a tight-binding model with the statistical physics of the many-body problem. Incontrast with rigid one-dimensional magnetic textures, we show that steadily moving magnetic skyrmionsare able to pump large dc currents. This ability arises from their nontrivial magnetic topology, i.e., thecoexistence of the spin-motive force and the topological Hall effect. Based on an adiabatic scatteringtheory, we compute the pumped current and demonstrate that it scales with the reflection coefficient of theconduction electrons against the skyrmion. In other words, in the semiclassical limit, reducing the size ofthe skyrmion and the width of the nanowire enhances this effect, making it scalable. We propose that such aphenomenon can be exploited in the context of racetrack devices, where the electronic pumping enhancesthe collective motion of the train of skyrmions.

Current-driven spin-orbit torques are investigated in a heterostructure composed of a ferromagnet deposited on top of a three-dimensional topological insulator using the linear response formalism. We develop a tight-binding model of the heterostructure adopting a minimal interfacial hybridization scheme that promotes induced magnetic exchange on the topological surface states, as well as induced Rashba-like spin-orbit coupling in the ferromagnet. Therefore our model accounts for the spin Hall effect from bulk states together with inverse spin galvanic and magnetoelectric effects at the interface on equal footing. By varying the transport energy across the band structure, we uncover a crossover from surface-dominated to bulk-dominated transport regimes. We show that the spin density profile and the nature of the spin-orbit torques differ substantially in both regimes. Our results, which compare favorably with experimental observations, demonstrate that the large dampinglike torque reported recently is more likely attributed to the Berry curvature of interfacial states, while spin Hall torque remains small even in the bulk-dominated regime.

International audience; Antiferromagnetic materials could represent the future of spintronic applications thanks to the numerous interesting features they combine: they are robust against perturbation due to magnetic fields, produce no stray fields, display ultrafast dynamics and are capable of generating large magneto-transport effects. Intense research efforts over the past decade have been invested in unraveling spin transport properties in antiferromagnetic materials. Whether spin transport can be used to drive the antiferromagnetic order and how subsequent variations can be detected are some of the thrilling challenges currently being addressed. Antiferromagnetic spintronics started out with studies on spin transfer, and has undergone a definite revival in the last few years with the publication of pioneering articles on the use of spin-orbit interactions in antiferromagnets. This paradigm shift offers possibilities for radically new concepts for spin manipulation in electronics. Central to these endeavors are the need for predictive models, relevant disruptive materials and new experimental designs. This paper reviews the most prominent spintronic effects described based on theoretical and experimental analysis of antiferromagnetic materials. It also details some of the remaining bottlenecks and suggests possible avenues for future research. Our review covers both spin-transfer-related effects, such as spin transfer torque, spin penetration length, domain wall motion and ‘magnetization’ dynamics; and spin-orbit related phenomena, such as (tunnel) anisotropic magnetoresistance, spin Hall and inverse spin galvanic effects. Effects related to spin-caloritronics, such as the spin Seebeck effect, are linked to the transport of magnons in antiferromagnets. The propagation of spin waves and spin superfluids in antiferromagnets are also covered.

We investigate the emergence of both quantum anomalous Hall and disorder-induced Anderson Chern insulating phases in two dimensional hexagonal lattices, with antiferromagnetically ordered 3Q state and in the absence of spin-orbit coupling. Using tight-binding modeling, we show that such systems display not only a spin-polarized edge-localized current, the chirality of which is energy dependent but also an impurity-induced transition from trivial metallic to topological insulating regimes, through one edge mode plateau. We compute the gaps' phase diagrams, and demonstrate the robustness of the edge channel against deformation and disorder. Our study hints at the 3Q state as a promising building block for dissipationless spintronics based on antiferromagnets., Comment: 7 pages, 8 figures

We demonstrate a unidirectional motion of a quasiparticle without an explicit symmetry breaking along the space-time coordinate of the particle motion. This counterintuitive behavior originates from a combined action of two intrinsic asymmetries in the other two directions. We realize this idea with the magnon-driven motion of a magnetic domain wall in thin films with interfacial asymmetry. Contrary to previous studies, the domain wall moves along the same direction regardless of the magnon-flow direction. Our general symmetry analysis and numerical simulation reveal that the odd order contributions from the interfacial asymmetry is unidirectional, which is dominant over bidirectional contributions in the realistic regime. We develop a simple analytic theory on the unidirectional motion, which provides an insightful description of this counterintuitive phenomenon., Comment: 5 pages, 3 figures, 3 pages SM

New developments in spintronics based on antiferromagnetic materials show promise for improved fundamental understanding and applications in technology.

This chapter focuses on the theory of current-driven Rashba torque, a special type of spin–orbit mediated spin torque that requires broken spatial-inversion symmetry. This specific form of spin-orbit interaction enables the electrical generation of a non-equilibrium spin density that yields both damping-like and field-like torques on the local magnetic moments. We review the recent results obtained in (ferromagnetic and antiferromagnetic) two-dimensional electron gases, bulk magnetic semiconductors, and at the surface of topological insulators. We conclude by summarizing recent experimental results that support the emergence of Rashba torques in magnets lacking inversion symmetry.

We demonstrate that the nontrivial magnetic texture of antiferromagnetic skyrmions (AFM-Sks) promotes a non-vanishing topological spin Hall effect (TSHE) on the flowing electrons. This results in a substantial enhancement of the non-adiabatic torque and hence improves the skyrmion mobility. This non-adiabatic torque increases when decreasing the skyrmion size, and therefore scaling down results in a much higher torque efficiency. In clean AFM-Sks, we find a significant boost of the TSHE close to van Hove singularity. Interestingly, this effect is enhanced away from the band gap in the presence of non-magnetic interstitial defects. Furthermore, unlike their ferromagnetic counterpart, TSHE in AFM-Sks increases with increase in disorder strength thus opening promising avenues for materials engineering of this effect., 6 pages, 4 figures

We address the nature of spin-orbit torques at the magnetic surfaces of topological insulators using the linear-response theory. We find that the so-called Dirac torques in such systems possess a different symmetry compared to their Rashba counterpart, as well as a high anisotropy as a function of the magnetization direction. In particular, the damping torque vanishes when the magnetization lies in the plane of the topological-insulator surface. We also show that the Onsager reciprocal of the spin-orbit torque, the charge pumping, induces an enhanced anisotropic damping. Via a macrospin model, we numerically demonstrate that these features have important consequences in terms of magnetization switching.

Chiral spin textures of a ferromagnetic layer in contact to a heavy non-magnetic metal, such as Néel-type domain walls and skyrmions, have been studied intensively because of their potential for future nanomagnetic devices. The Dyzaloshinskii–Moriya interaction (DMI) is an essential phenomenon for the formation of such chiral spin textures. In spite of recent theoretical progress aiming at understanding the microscopic origin of the DMI, an experimental investigation unravelling the physics at stake is still required. Here we experimentally demonstrate the close correlation of the DMI with the anisotropy of the orbital magnetic moment and with the magnetic dipole moment of the ferromagnetic metal in addition to Heisenberg exchange. The density functional theory and the tight-binding model calculations reveal that inversion symmetry breaking with spin–orbit coupling gives rise to the orbital-related correlation. Our study provides the experimental connection between the orbital physics and the spin–orbit-related phenomena, such as DMI., 原子磁石どうしが捻れて並ぶ現象のミクロな起源を解明 --新原理の情報記録技術をめざして--. 京都大学プレスリリース. 2018-05-01.

We theoretically study the current-induced spin torque in antiferromagnetic tunnel junctions, composed of two semi-infinite antiferromagnetic layers separated by a tunnel barrier, in both clean and disordered regimes. We find that the torque enabling the electrical manipulation of the N\'eel antiferromagnetic order parameter is out of plane $\sim {\bf n}\times{\bf p}$, while the torque competing with the antiferromagnetic exchange is in-plane $\sim {\bf n}\times({\bf p}\times{\bf n})$. Here, ${\bf { p}}$ and ${\bf { n}}$ are the N\'eel order parameter direction of the reference and free layers, respectively. Their bias dependence shows similar behavior as in ferromagnetic tunnel junctions, the in-plane torque being mostly linear in bias while the out-of-plane torque is quadratic. Most importantly, we find that the spin transfer torque in antiferromagnetic tunnel junctions is much more robust against disorder than in antiferromagnetic metallic spin-valves due to the tunneling nature of spin transport., Comment: 7 pages, 7 figures

We explore the role of the spin diffusion of conducting electrons in two-dimensional magnetic textures (domain walls and skyrmions) with spatial variation of the order of the spin precession length ${\ensuremath{\lambda}}_{\text{ex}}$. The effect of diffusion reflects in four additional torques that are third order in spatial derivatives of magnetization and bilinear in ${\ensuremath{\lambda}}_{\text{ex}}$ and in the nonadiabatic parameter ${\ensuremath{\beta}}^{\ensuremath{'}}$. In order to study the dynamics of the solitons when these diffusive torques are present, we derive the Thiele equation in the limit of steady motion and we compare the results with the nondiffusive limit. When considering a homogenous current these torques increase the longitudinal velocity of transverse domain walls of width $\mathrm{\ensuremath{\Delta}}$ by a factor ${({\ensuremath{\lambda}}_{\text{ex}}/\mathrm{\ensuremath{\Delta}})}^{2}(\ensuremath{\alpha}/3), \ensuremath{\alpha}$ being the magnetic damping constant. In the case of single skyrmions with core radius ${r}_{0}$ these new contributions tend to increase the Magnus effect in an amount proportional to ${({\ensuremath{\lambda}}_{\text{ex}}/{r}_{0})}^{2}(1+2\ensuremath{\alpha}{\ensuremath{\beta}}^{\ensuremath{'}})$.

We investigated current driven spin-orbit torques in $\mathrm{C}{\mathrm{u}}_{40}\mathrm{A}{\mathrm{u}}_{60}/\mathrm{N}{\mathrm{i}}_{80}\mathrm{F}{\mathrm{e}}_{20}/\mathrm{Ti}$ layered structures with in-plane magnetization. We have demonstrated a reliable and convenient method to separate dampinglike torque and fieldlike torque by using the second harmonic technique. It is found that the dampinglike torque and fieldlike torque depend on temperature very differently. Dampinglike torque increases with temperature, while fieldlike torque decreases with temperature, which are different from results obtained previously in other material systems. We observed a nearly linear dependence between the spin Hall angle and longitudinal resistivity, suggesting that skew scattering may be the dominant mechanism of spin-orbit torques.

We propose that topological spin currents flowing in topologically non-trivial magnetic textures, such as magnetic skyrmions and vortices, produce an intrinsic non-adiabatic torque of the form ${\bf T}_t\sim [(\partial_x{\bf m}\times\partial_y{\bf m})\cdot{\bf m}]\partial_y{\bf m}$. We show that this torque, which is absent in one-dimensional domain walls and/or non-topological textures, is responsible for the enhanced non-adiabaticity parameter observed in magnetic vortices compared to one-dimensional textures. The impact of this torque on the motion of magnetic skyrmions is expected to be crucial, especially to determine their robustness against defects and pinning centers., Comment: 7 pages, 4 figures

We carry out a throughout study of the topological Hall and topological spin Hall effects in disordered skyrmionic systems: the dimensionless (spin) Hall angles are evaluated across the energy band structure in the multiprobe Landauer-B\"uttiker formalism and their link to the effective magnetic field emerging from the real space topology of the spin texture is highlighted. We discuss these results for an optimal skyrmion size and for various sizes of the sample and found that the adiabatic approximation still holds for large skyrmions as well as for few atomic size-nanoskyrmions. Finally, we test the robustness of the topological signals against disorder strength and show that topological Hall effect is highly sensitive to momentum scattering., Comment: 7 pages, 6 figures

We have developed a drift-diffusion equation of spin transport in collinear bipartite metallic antiferromagnets. Starting from a model tight-binding Hamiltonian, we obtain the quantum kinetic equation within Keldysh formalism and expand it to the lowest order in spatial gradient using Wigner expansion method. In the diffusive limit, these equations track the spatio-temporal evolution of the spin accumulations and spin currents on each sublattice of the antiferromagnet. We use these equations to address the nature of spin transfer torque in (i) a spin-valve composed of a ferromagnet and an antiferromagnet, (ii) a metallic bilayer consisting in an antiferromagnet adjacent to a heavy metal possessing spin Hall effect, and in (ii) a single antiferromagnet possessing spin Hall effect. We show that the latter can experience a self-torque thanks to the non-vanishing spin Hall effect in the antiferromagnet., 15 pages, 2 Figures