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Recent Submissions

  • Spin-orbit coupling induced ultrahigh-harmonic generation from magnetic dynamics

    Ly, Ousmane; Manchon, Aurelien (Physical Review B, American Physical Society (APS), 2022-05-31) [Article]
    The generation of a nonlinear high-frequency response in solids from powerful optical pumps has gained momentum over the past decade. High-harmonic generation (HHG) in solids can be obtained from strong-field laser excitation, usually restricted to optical frequencies and limited both in amplitude and in harmonic order. Here, we demonstrate that high-harmonic emission can be achieved by exploiting conventional spin pumping, without the need for optical excitation. Considering a noncentrosymmetric (ferro- or antiferro-)magnet excited at a frequency ω, we demonstrate the emergence of HHG in two main regimes: (i) In the perturbative regime, where a weak spin-orbit interaction is considered, the carrier pumping features a number of harmonics with a cutoff order nmax<10. (ii) When the spin-orbit coupling strength is close to, or higher than, the s−d exchange energy, a strongly nonlinear regime resulting from resonantlike spin-flip scattering occurs leading to the emission of a large number of harmonics. This is in sharp contrast to conventional pumping, where the corresponding time-dependent currents simply oscillate with the frequency of the magnetic drive ω. Our proposal enables the enhancement of both spin and charge dynamics by orders of magnitude. This effect could be used to trigger high-frequency emission deep in the terahertz regime.
  • Competition between chiral energy and chiral damping in the asymmetric expansion of magnetic bubbles

    Ganguly, Arnab; Zhang, Senfu; Mibhaimiron, Loan; Kosel, Jürgen; Zhang, Xixiang; Manchon, Aurelien; Singh, Nirpendra; Anjum, Dalaver; Das, Gobind (ACS Applied Electronic Materials., 2021-10) [Article]
    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 cooperation 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 the 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 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 the seemingly counterintuitive experimental signature, depending on the strength of the external magnetic field. The effective control on the bubble asymmetry expansion can be of great importance for future memory and multiplexer-based applications.
  • Skyrmion battery effect via inhomogeneous magnetic anisotropy

    Hao, Xiawei; Zhuo, Fengjun; Manchon, Aurelien; Wang, Xiaolin; Li, Hang; Cheng, Zhenxiang (Applied Physics Reviews, AIP Publishing, 2021-04-14) [Article]
    Magnetic skyrmions are considered a promising candidate for the next-generation information processing technology. Being topologically robust, magnetic skyrmions are swirling spin textures that can be used in a broad range of applications from memory devices and logic circuits to neuromorphic computing. In a magnetic medium lacking inversion symmetry, magnetic skyrmion arises as a result of the interplay among magnetic exchange interaction, Dzyaloshinskii-Moriya interaction, and magnetic anisotropy. Instrumental to the integrated skyrmion-based applications are the creation and manipulation of magnetic skyrmions at a designated location, absent any need of a magnetic field. In this paper, we propose a generic design strategy to achieve that goal and a model system to demonstrate its feasibility. By implementing a disk-shaped thin film heterostructure with an inhomogeneous perpendicular magnetic anisotropy, stable sub-100-nm size skyrmions can be generated without magnetic field. This structure can be etched out via, for example, focused ion beam microscope. Using micromagnetic simulation, we show that such heterostructure not only stabilizes the edge spins of the skyrmion but also protects its rotation symmetry. Furthermore, we may switch the spin texture between skyrmionic and vortex-like ones by tuning the slope of perpendicular anisotropy using a bias voltage. When embedded into a magnetic conductor and under a spin polarized current, such heterostructure emits skyrmions continuously and may function as a skyrmion source. This unique phenomenon is dubbed a skyrmion battery effect. Our proposal may open a novel venue for the realization of all-electric skyrmion-based devices.
  • Nonreciprocal charge transport up to room temperature in bulk Rashba semiconductor α-GeTe

    Li, Yan; Li, Yang; Li, Peng; Fang, Bin; Yang, Xu; Wen, Yan; Zheng, Dong-xing; Zhang, Chenhui; He, Xin; Manchon, Aurelien; Cheng, Zhao-Hua; Zhang, Xixiang (Nature Communications, Springer Nature, 2021-01-22) [Article]
    AbstractNonmagnetic Rashba systems with broken inversion symmetry are expected to exhibit nonreciprocal charge transport, a new paradigm of unidirectional magnetoresistance in the absence of ferromagnetic layer. So far, most work on nonreciprocal transport has been solely limited to cryogenic temperatures, which is a major obstacle for exploiting the room-temperature two-terminal devices based on such a nonreciprocal response. Here, we report a nonreciprocal charge transport behavior up to room temperature in semiconductor α-GeTe with coexisting the surface and bulk Rashba states. The combination of the band structure measurements and theoretical calculations strongly suggest that the nonreciprocal response is ascribed to the giant bulk Rashba spin splitting rather than the surface Rashba states. Remarkably, we find that the magnitude of the nonreciprocal response shows an unexpected non-monotonical dependence on temperature. The extended theoretical model based on the second-order spin–orbit coupled magnetotransport enables us to establish the correlation between the nonlinear magnetoresistance and the spin textures in the Rashba system. Our findings offer significant fundamental insight into the physics underlying the nonreciprocity and may pave a route for future rectification devices.
  • Symmetry-dependent field-free switching of perpendicular magnetization

    Liu, Liang; Zhou, Chenghang; Shu, Xinyu; Li, Changjian; Zhao, Tieyang; Lin, Weinan; Deng, Jinyu; Xie, Qidong; Chen, Shaohai; Zhou, Jing; Guo, Rui; Wang, Han; Yu, Jihang; Shi, Shu; Yang, Ping; Pennycook, S. J.; Manchon, Aurelien; Chen, Jingsheng (Nature Nanotechnology, Springer Nature, 2021-01-18) [Article]
    Modern magnetic-memory technology requires all-electric control of perpendicular magnetization with low energy consumption. While spin–orbit torque (SOT) in heavy metal/ferromagnet (HM/FM) heterostructures1,2,3,4,5 holds promise for applications in magnetic random access memory, until today, it has been limited to the in-plane direction. Such in-plane torque can switch perpendicular magnetization only deterministically with the help of additional symmetry breaking, for example, through the application of an external magnetic field2,4, an interlayer/exchange coupling6,7,8,9 or an asymmetric design10,11,12,13,14. Instead, an out-of-plane SOT15 could directly switch perpendicular magnetization. Here we observe an out-of-plane SOT in an HM/FM bilayer of L11-ordered CuPt/CoPt and demonstrate field-free switching of the perpendicular magnetization of the CoPt layer. The low-symmetry point group (3m1) at the CuPt/CoPt interface gives rise to this spin torque, hereinafter referred to as 3m torque, which strongly depends on the relative orientation of the current flow and the crystal symmetry. We observe a three-fold angular dependence in both the field-free switching and the current-induced out-of-plane effective field. Because of the intrinsic nature of the 3m torque, the field-free switching in CuPt/CoPt shows good endurance in cycling experiments. Experiments involving a wide variety of SOT bilayers with low-symmetry point groups16,17 at the interface may reveal further unconventional spin torques in the future.
  • Spin transport in multilayer graphene away from the charge neutrality point

    He, Xin; Wen, Yan; Zhang, Chenhui; Li, Peng; Zheng, Dongxing; Chen, Aitian; Manchon, Aurelien; Zhang, Xixiang (Carbon, Elsevier BV, 2020-10-17) [Article]
    Graphene is considered as a promising material in spintronics due to its long spin relaxation time and long spin relaxation length. However, its spin transport properties have been studied at low carrier density only, beyond which much is still unknown. In this study, we explore the spin transport and spin precession properties in multilayer graphene at high carrier density using ionic liquid gating. We find that the spin relaxation time is directly proportional to the momentum relaxation time, indicating that the Elliott-Yafet mechanism still dominates the spin relaxation in multilayer graphene away from the charge neutrality point.
  • Two-Dimensional Electron Gas at the Spinel/Perovskite Interface: Suppression of Polar Catastrophe by an Ultrathin Layer of Interfacial Defects.

    Ding, Junfeng; Cheng, Jianli; Dogan, Fatih; Li, Yangyang; Lin, Weinan; Yao, Yingbang; Manchon, Aurelien; Yang, Kesong; Wu, Tao (ACS applied materials & interfaces, American Chemical Society (ACS), 2020-08-24) [Article]
    Two-dimensional electron gas (2DEG) at the interface between two insulating perovskite oxides has attracted much interest for both fundamental physics and potential applications. Here, we report the discovery of a new 2DEG formed at the interface between spinel MgAl2O4 and perovskite SrTiO3. Transport measurements, electron microscopy imaging, and first-principles calculations reveal that the interfacial 2DEG is closely related to the symmetry breaking at the MgAl2O4/SrTiO3 interface. The critical film thickness for the insulator-to-metal transition is approximately 32 Å, which is twice as thick as that reported on the widely studied LaAlO3/SrTiO3 system. Scanning transmission electron microscopy imaging indicates the formation of interfacial Ti-Al antisite defects with a thickness of ∼4 Å. First-principles density functional theory calculations indicate that the coexistence of the antisite defects and surface oxygen vacancies may explain the formation of interfacial 2DEG as well as the observed critical film thickness. The discovery of 2DEG at the spinel/perovskite interface introduces a new material platform for designing oxide interfaces with desired characteristics.
  • Symmetrized decomposition of the Kubo-Bastin formula

    Bonbien, Varga; Manchon, Aurelien (Physical Review B, American Physical Society (APS), 2020-08-06) [Article]
    The Smrcka-Streda version of Kubo's linear response formula is widely used in the literature to compute nonequilibrium 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 dampinglike 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 decomposition of the Kubo-Bastin formula based on the permutation properties of the correlation function and derive a set of formulas, without an overlap, that provides direct access to the transport effects of interest. We apply these formulas to selected cases and demonstrate that the Fermi sea and Fermi surface contributions can be uniquely addressed with our symmetrized approach.
  • Elusive Dzyaloshinskii-Moriya interaction in monolayer Fe3GeTe2

    Laref, Slimane; Kim, Kyoung-Whan; Manchon, Aurelien (Physical Review B, American Physical Society (APS), 2020-08-05) [Article]
    Using symmetry analysis and density functional theory calculations, we uncover the nature of the Dzyaloshinskii-Moriya interaction in monolayer Fe3GeTe2. 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 Néel spin spirals along equivalent directions of the crystal structure. Whereas our results show that the observed Néel 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 Fe3GeTe2 nanoflakes or nanoribbons and, most interestingly, that homochiral planar magnetic textures could be stabilized.
  • Bulk Spin Torque-Driven Perpendicular Magnetization Switching in L10 FePt Single Layer.

    Tang, Meng; Shen, Ka; Xu, Shijie; Yang, Huanglin; Hu, Shuai; Lü, Weiming; Li, Changjian; Li, Mengsha; Yuan, Zhe; Pennycook, Stephen J; Xia, Ke; Manchon, Aurelien; Zhou, Shiming; Qiu, Xuepeng (Advanced Materials, Wiley, 2020-06-28) [Article]
    Due to its inherent superior perpendicular magnetocrystalline anisotropy, the FePt in L10 phase enables magnetic storage and memory devices with ultrahigh capacity. However, reversing the FePt magnetic state, and therefore encoding information, has proven to be extremely difficult. Here, it is demonstrated that an electric current can exert a large spin torque on an L10 FePt magnet, ultimately leading to reversible magnetization switching. The spin torque monotonically increases with increasing FePt thickness, exhibiting a bulk characteristic. Meanwhile, the spin torque effective fields and switching efficiency increase as the FePt approaches higher chemical ordering with stronger spin-orbit coupling. The symmetry breaking that generates spin torque within L10 FePt is shown to arise from an inherent structural gradient along the film normal direction. By artificially reversing the structural gradient, an opposite spin torque effect in L10 FePt is demonstrated. At last, the role of the disorder gradient in generating a substantial torque in a single ferromagnet is supported by theoretical calculations. These results will push forward the frontier of material systems for generating spin torques and will have a transformative impact on magnetic storage and spin memory devices with simple architecture, ultrahigh density, and readily application.
  • Induced spin textures at 3d transition metal–topological insulator interfaces

    Laref, Slimane; Ghosh, Sumit; Tsymbal, Evgeny Y.; Manchon, Aurelien (Physical Review B, American Physical Society (APS), 2020-06-25) [Article]
    While some of the most elegant applications of topological insulators, such as the 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 Rapid Communication, we investigate the spin-momentum locking of the surface states of a wide range of monolayer transition metals (3d-TM) deposited on top of Bi2Se3 topological insulators using first-principles calculations. We find an anticorrelation between the magnetic moment of the 3d-TM and the magnitude of the spin-momentum locking induced by the Dirac surface states. While the magnetic moment is large in the first half of the 3d 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 3d-TM overlayer and the Dirac surface states. As a result, while Cr and Mn overlayers can be used successfully for the observation of the 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.
  • Tunable magnetic anisotropy in Cr–trihalide Janus monolayers

    Albaridy, Rehab; Manchon, Aurelien; Schwingenschlögl, Udo (Journal of Physics: Condensed Matter, IOP Publishing, 2020-05-29) [Article]
    Achieving a two-dimensional material with tunable magnetic anisotropy is highly desirable, especially if it is complemented with out-of-plane electric polarization, as this could provide a versatile platform for spintronic and multifunctional devices. Using first principles calculations, we demonstrate that the magnetic anisotropy of Cr-trihalides become highly sensitive to mechanical strain upon structural inversion symmetry breaking through the realization of Janus monolayers. This remarkable feature, absent in pristine Cr-trihalide monolayers, enables mechanical control of the direction of the easy axis: biaxial compressive/tensile strain supports in-plane/out-of-plane orientation of the easy axis. The magnetic exchange itself shows higher sensitivity to compressive than to tensile strain, while in general the Janus monolayers maintain ferromagnetic ordering in the studied range of strain.
  • Semirealistic tight-binding model for spin-orbit torques

    Manchon, Guilhem; Ghosh, Sumit; Barreteau, Cyrille; Manchon, Aurelien (Physical Review B, American Physical Society (APS), 2020-05-14) [Article]
    We compute the spin-orbit torque in a transition-metal heterostructure using Slater-Koster parametrization 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 (dampinglike) and reactive (fieldlike), 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. We find that the conventional fieldlike torque is purely interfacial. In contrast, we unambiguously demonstrate that the conventional dampinglike torque possesses both an interfacial and a bulk contribution. In addition, both fieldlike and dampinglike torques display substantial angular dependence with strikingly different thickness behaviors. While the planar contribution of the fieldlike torque decreases smoothly with the nonmagnetic metal thickness, the planar contribution of the dampinglike 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.
  • Effect of surface roughness on the anomalous Hall effect in Fe thin films

    Zhang, Qiang; Zheng, Dongxing; Wen, Yan; Zhao, Yuelei; Mi, Wenbo; Manchon, Aurelien; Boulle, Olivier; Zhang, Xixiang (Physical Review B, American Physical Society (APS), 2020-04-13) [Article]
    Surface roughness plays an important role on the magnetotransport properties of thin films, especially in ultrathin films. In this work, we prepared Fe thin films with various surface roughness by using different seed layers and studied the electrical transport and anomalous Hall effect. By tuning surface roughness scattering, the longitudinal resistivity (ρxx) measured at 5 K increases by one order of magnitude and the corresponding anomalous Hall resistivity (ρAHE) increases by three times with increasing roughness. The intrinsic, skew-scattering, and side-jump contributions to ρAHE were separated from our data. The anomalous Hall angle depends on the surface roughness, which may be of importance to the material engineering for achieving large spin Hall angle.
  • Elusive Dzyaloshinskii-Moriya interaction in Fe$_3$GeTe$_2$ monolayer

    Laref, Slimane; Kim, Kyoung-Whan; Manchon, Aurelien (arXiv, 2020-04-03) [Preprint]
    Using symmetry analysis and density functional theory calculations, we uncover the nature of Dzyaloshinskii-Moriya interaction in Fe$_3$GeTe$_2$ monolayer. We show that while such an interaction might result in small distortion of the magnetic texture on the short range, on the longrange Dzyaloshinskii-Moriya interaction 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 canted magnetic texture shall arise at the boundary of Fe$_3$GeTe$_2$ nanoflakes or nanoribbons and, most interestingly, that homochiral planar magnetic textures could be stabilized.
  • Direct imaging of an inhomogeneous electric current distribution using the trajectory of magnetic half-skyrmions

    Zhang, Senfu; Zhang, Xichao; Zhang, Junwei; Ganguly, Arnab; Xia, Jing; Wen, Yan; Zhang, Qiang; Yu, Guoqiang; Hou, Zhipeng; Wang, Wenhong; Peng, Yong; Xiao, Gang; Manchon, Aurelien; Kosel, Jürgen; Zhou, Yan; Zhang, Xixiang (Science Advances, American Association for the Advancement of Science (AAAS), 2020-02-07) [Article]
    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.
  • Controlling the deformation of antiferromagnetic skyrmions in the high-velocity regime

    Salimath, Akshaykumar; Zhuo, Fengjun; Tomasello, R.; Finocchio, G.; Manchon, Aurelien (Physical Review B, American Physical Society (APS), 2020-01-31) [Article]
    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.
  • Rashba spin-orbit coupling in two-dimensional systems

    Manchon, Aurelien (Elsevier BV, 2020-01-24) [Book Chapter]
    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.
  • Induced Spin-texture at 3$d$ Transition Metal/Topological Insulator Interfaces

    Laref, Slimane; Ghosh, Sumit; Tsymbal, Evgeny Y.; Manchon, Aurelien (arXiv, 2020-01-23) [Preprint]
    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.
  • Spin-orbit torques in a Rashba honeycomb antiferromagnet

    Sokolewicz, Robert; Ghosh, Sumit; Yudin, Dmitry; Manchon, Aurelien; Titov, Mikhail (Physical Review B, American Physical Society (APS), 2019-12-02) [Article]
    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 nonequilibrium staggered polarization that is responsible for the so-called Neél spin-orbit torque is shown to vanish identically in the symmetric model but may become finite if sublattice symmetry is broken. Similarly, antidamping spin-orbit torques vanish in the symmetric model but become finite and anisotropic in a model with broken sublattice symmetry. As expected, antidamping 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.

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