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  • Semirealistic tight-binding model for spin-orbit torques

    Manchon, Guilhem; Ghosh, Sumit; Barreteau, Cyrille; Manchon, Aurelien (Physical Review B, American Physical Society (APS), 2020-05-18) [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.
  • 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.
  • Semi-realistic tight-binding model for Dzyaloshinskii-Moriya interaction

    Hajr, Ahmed; Hariri, Abdulkarim; Manchon, Guilhem; Ghosh, Sumit; Manchon, Aurelien (arXiv, 2020-02-13) [Preprint]
    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.
  • 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), 2020-02-08) [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.
  • 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.
  • Artificial gauge fields and topological insulators in Moire superlattices

    Shang, Ce; Abbout, Adel; Zang, Xiaoning; Schwingenschlögl, Udo; Manchon, Aurelien (arXiv, 2019-12-01) [Preprint]
    We propose an innovative quantum emulator based on Moire superlattices showing that, by employing periodical modulation on each lattice site, one can create tunable, artificial gauge fields with imprinting Peierls phases on the hopping parameters and realize an analog of novel Haldane-like phase. As an application, we provide a methodology to directly quantify the topological invariant in such a system from a dynamical quench process. This design shows a robustly integrated platform which opens a new door to investigate topological physics.
  • Competition between Electronic and Magnonic Spin Currents in Metallic Antiferromagnets

    Wen, Yan; Zhuo, Fengjun; Zhao, Yuelei; Li, Peng; Zhang, Qiang; Manchon, Aurelien; Zhang, Xixiang (Physical Review Applied, American Physical Society (APS), 2019-11-13) [Article]
    We investigate the spin-orbit torque in a Ta/Ir−Mn/Cu/Ni−Fe multilayer heterostructure and relate it to spin current transmission through the Ir−Mn layer. We identify several spin current transport regimes as a function of the temperature and the thickness of the Ir−Mn layer. To interpret this experiment, we develope a drift-diffusion model accounting for both electron and magnon transport in the heterostructures. This model allows us to discriminate between the contributions of electrons and magnons to the total spin current in Ir−Mn. We find that the electron-magnon spin convertance is one order of magnitude larger than the interfacial electronic spin conductance, while the magnon diffusion length is about ten times longer than the electronic spin relaxation length. This study demonstrates that magnonic spin transport dominates over electronic spin transport even in disorder metallic antiferromagnets.
  • Quantum anomalous Hall effect and Anderson-Chern insulating regime in the noncollinear antiferromagnetic 3Q state

    Ndiaye, Papa Birame; Abbout, Adel; Goli, V. M. L. D. P.; Manchon, Aurelien (Physical Review B, American Physical Society (APS), 2019-10-28) [Article]
    We investigate the emergence of both quantum anomalous Hall and disorder-induced Anderson-Chern insulating phases in two-dimensional hexagonal lattices, with an 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.
  • Interface-based tuning of Rashba spin-orbit interaction in asymmetric oxide heterostructures with 3d electrons

    Lin, Weinan; Li, Lei; Dogan, Fatih; Li, Changjian; Rotella, Hélène; Yu, Xiaojiang; Zhang, Bangmin; Li, Yangyang; Lew, Wen Siang; Wang, Shijie; Prellier, Wilfrid; Pennycook, Stephen J.; Chen, Jingsheng; Zhong, Zhicheng; Manchon, Aurelien; Wu, Tom (Nature Communications, Springer Science and Business Media LLC, 2019-07-11) [Article]
    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.
  • Nonequilibrium spin density and spin-orbit torque in a three-dimensional topological insulator/antiferromagnet heterostructure

    Ghosh, Sumit; Manchon, Aurelien (Physical Review B, American Physical Society (APS), 2019-07-10) [Article]
    We study the behavior of nonequilibrium spin density and spin-orbit torque in a topological insulator/antiferromagnet heterostructure. Unlike ferromagnetic heterostructures where the 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 dampinglike torque which is quite robust against scalar impurities when the transport energy is such that the transport is confined to the topological insulator surface. We show the contribution to the nonequilibrium spin density due to both surface and bulk topological insulator bands. Finally, we show that the torques in topological insulator/antiferromagnet heterostructures exhibit an angular dependence that is consistent with the standard spin-orbit torque obtained in Rashba system with some additional structure arising from the interfacial coupling.
  • Unidirectional Magnon-Driven Domain Wall Motion Due to the Interfacial Dzyaloshinskii-Moriya Interaction

    Kim, Kyoung-Whan; Lee, Seo-Won; Moon, Jung-Hwan; Go, Gyungchoon; Manchon, Aurelien; Lee, Hyun-Woo; Everschor-Sitte, Karin; Lee, Kyung-Jin (Physical Review Letters, American Physical Society (APS), 2019-04-09) [Article]
    We demonstrate a unidirectional motion of a quasiparticle without 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.
  • Current-driven skyrmion depinning in magnetic granular films

    Salimath, Akshaykumar; Abbout, Adel; Brataas, A.; Manchon, Aurelien (Physical Review B, American Physical Society (APS), 2019-03-12) [Article]
    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, the disorder enhances the effective skyrmion Hall effect that depends on the magnitude of the driving force (the cur- rent density and nonadiabaticity parameter). The origin is the 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 nonadiabatic Magnus force, the critical current density can be significantly reduced. Our results imply that narrow nanowires exhibit higher skyrmion mobilities.
  • Cooperative Charge Pumping and Enhanced Skyrmion Mobility

    Abbout, Adel; Weston, Joseph; Waintal, Xavier; Manchon, Aurelien (Physical Review Letters, American Physical Society (APS), 2018-12-19) [Article]
    It is well known that moving magnetic textures may pump spin and charge currents along the direction of motion, a phenomenon called electronic pumping. Here, the electronic pumping arising from the steady motion of ferromagnetic skyrmions is investigated by solving the time evolution of the Schrödinger equation implemented on a tight-binding model with the statistical physics of the many-body problem. In contrast with rigid one-dimensional magnetic textures, we show that steadily moving magnetic skyrmions are able to pump large dc currents. This ability arises from their nontrivial magnetic topology, i.e., the coexistence of the spin-motive force and the topological Hall effect. Based on an adiabatic scattering theory, we compute the pumped current and demonstrate that it scales with the reflection coefficient of the conduction electrons against the skyrmion. In other words, in the semiclassical limit, reducing the size of the skyrmion and the width of the nanowire enhances this effect, making it scalable. We propose that such a phenomenon can be exploited in the context of racetrack devices, where the electronic pumping enhances the collective motion of the train of skyrmions.
  • Spin-momentum locking and spin-orbit torques in magnetic nano-heterojunctions composed of Weyl semimetal WTe2

    Li, Peng; Wu, Weikang; Wen, Yan; Zhang, Chenhui; Zhang, Junwei; Zhang, Senfu; Yu, Zhiming; Yang, Shengyuan A.; Manchon, Aurelien; Zhang, Xixiang (Nature Communications, Springer Nature, 2018-09-28) [Article]
    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.
  • Theory of the Topological Spin Hall Effect in Antiferromagnetic Skyrmions: Impact on Current-Induced Motion

    Akosa, Collins Ashu; Tretiakov, O. A.; Tatara, G.; Manchon, Aurelien (Physical Review Letters, American Physical Society (APS), 2018-08-30) [Article]
    We demonstrate that the nontrivial magnetic texture of antiferromagnetic Skyrmions (AFM Sks) promotes a nonvanishing topological spin Hall effect (TSHE) on the flowing electrons. This effect results in a substantial enhancement of the nonadiabatic torque and, hence, improves the Skyrmion mobility. This nonadiabatic 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 the van Hove singularity. Interestingly, this effect is enhanced away from the band gap in the presence of nonmagnetic interstitial defects. Furthermore, unlike their ferromagnetic counterpart, the TSHE in AFM Sks increases with an increase in the disorder strength, thus opening promising avenues for materials engineering of this effect.
  • Correlation of the Dzyaloshinskii–Moriya interaction with Heisenberg exchange and orbital asphericity

    Kim, Sanghoon; Ueda, Kohei; Go, Gyungchoon; Jang, Peong-Hwa; Lee, Kyung-Jin; Belabbes, Abderrezak; Manchon, Aurelien; Suzuki, Motohiro; Kotani, Yoshinori; Nakamura, Tetsuya; Nakamura, Kohji; Koyama, Tomohiro; Chiba, Daichi; Yamada, Kihiro. T.; Kim, Duck-Ho; Moriyama, Takahiro; Kim, Kab-Jin; Ono, Teruo (Nature Communications, Springer Nature, 2018-04-25) [Article]
    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.
  • Current Controlled Magnetization Switching in Cylindrical Nanowires for High-Density 3D Memory Applications

    Mohammed, Hanan; Corte-León, Hector; Ivanov, Yurii P.; Lopatin, Sergei; Moreno, Julian A.; Chuvilin, Andrey; Salimath, Akshaykumar; Manchon, Aurelien; Kazakova, Olga; Kosel, Jürgen (arXiv, 2018-04-18) [Preprint]
    A next-generation memory device utilizing a three-dimensional nanowire system requires the reliable control of domain wall motion. In this letter, domain walls are studied in cylindrical nanowires consisting of alternating segments of cobalt and nickel. The material interfaces acting as domain wall pinning sites, are utilized in combination with current pulses, to control the position of the domain wall, which is monitored using magnetoresistance measurements. Magnetic force microscopy results further confirm the occurrence of current assisted domain wall depinning. Data bits are therefore shifted along the nanowire by sequentially pinning and depinning a domain wall between successive interfaces, a requirement necessary for race-track type memory devices. We demonstrate that the direction, amplitude and duration of the applied current pulses determine the propagation of the domain wall across pinning sites. These results demonstrate a multi-bit cylindrical nanowire device, utilizing current assisted data manipulation. The prospect of sequential pinning and depinning in these nanowires allows the bit density to increase by several Tbs, depending on the number of segments within these nanowires.
  • Spin-orbit torque in a three-dimensional topological insulator–ferromagnet heterostructure: Crossover between bulk and surface transport

    Ghosh, Sumit; Manchon, Aurelien (Physical Review B, American Physical Society (APS), 2018-04-02) [Article]
    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.

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