Intrinsic spin-orbit torque in a single-domain nanomagnet

Kalitsov, Alan; Nikolaev, S. A.; Velev, Julian P.; Chshiev, M.; Mryasov, O. N.

doi:10.1103/physrevb.96.214430

Cited by 22 publications

(31 citation statements)

References 41 publications

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“…1 does not generate vertical spin Hall current along the zaxis as one of the mechanisms for T e . Other interfacially based mechanisms [26] for T e = 0 require backscattering of electrons [24,[53][54][55], which is absent in the ballistic transport regime we assume, so we find T e → 0.…”

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confidence: 67%

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Proximity Spin–Orbit Torque on a Two-Dimensional Magnet within van der Waals Heterostructure: Current-Driven Antiferromagnet-to-Ferromagnet Reversible Nonequilibrium Phase Transition in Bilayer CrI₃

et al. 2020

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The recently discovered two-dimensional (2D) magnetic insulator CrI3 is an intriguing case for basic research and spintronic applications since it is a ferromagnet in the bulk, but an antiferromagnet in bilayer form, with its magnetic ordering amenable to external manipulations. Using first-principles quantum transport approach, we predict that injecting unpolarized charge current parallel to the interface of bilayer-CrI3/monolayer-TaSe2 van der Waals heterostructure will induce spin-orbit torque (SOT) and thereby driven dynamics of magnetization on the first monolayer of CrI3 in direct contact with TaSe2. By combining calculated complex angular dependence of SOT with the Landau-Lifshitz-Gilbert equation for classical dynamics of magnetization, we demonstrate that current pulses can switch the direction of magnetization on the first monolayer to become parallel to that of the second monolayer, thereby converting CrI3 from antiferromagnet to ferromagnet while not requiring any external magnetic field. We explain the mechanism of this reversible current-driven nonequilibrium phase transition by showing that first monolayer of CrI3 carries current due to evanescent wavefunctions injected by metallic transition metal dichalcogenide TaSe2, while concurrently acquiring strong spin-orbit coupling (SOC) via such proximity effect, whereas the second monolayer of CrI3 remains insulating. The transition can be detected by passing vertical read current through the vdW heterostructure, encapsulated by bilayer of hexagonal boron nitride and sandwiched between graphite electrodes, where we find tunneling magnetoresistance of 240%. arXiv:1909.13876v2 [cond-mat.mes-hall]

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confidence: 67%

“…1. Also, in the presence of disorder and thereby induced voltage drop across the central region [25,26,54] we expect that T e would become nonzero and contribute to switching.…”

Section: Sot-driven Classical Dynamics Of Magnetization-mentioning

confidence: 99%

Proximity Spin–Orbit Torque on a Two-Dimensional Magnet within van der Waals Heterostructure: Current-Driven Antiferromagnet-to-Ferromagnet Reversible Nonequilibrium Phase Transition in Bilayer CrI₃

et al. 2020

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“…However, to describe details of experiments, such as bias voltage dependence of STT in MTJs [8,9] or complex angular dependence of SOT in FM/HM bilayers [45], more involved calculations are needed employing tight-binding or first-principles Hamiltonian as an input. For example, simplistic tight-binding Hamiltonians (TBHs) with single orbital per site have been coupled [46] to nonequilibrium Green's function (NEGF) formalism [47] to compute SOT in FM/HM bilayers [48], or bias voltage dependence of DL and FL components of STT in MTJs which can describe some features of the experiments by adjusting the tight-binding parameters [9]. However, not all features of STT experiments on MTJs [10] can be captured by such NEGF+TBH approach.…”

Section: How To Model Spin Torque Using Nonequilibrium Density Mamentioning

confidence: 99%

“…However, not all features of STT experiments on MTJs [10] can be captured by such NEGF+TBH approach. Furthermore, due to spin-orbit proximity effect, driven by hybridization of wave functions from FM and HM layers [49] or FM and metallic surfaces of three-dimensional (3D) TIs [50], simplistic Hamiltonians like the Rashba ferromagnetic model [48,[51][52][53][54][55][56] or the gapped Dirac model [57] are highly inadequate to describe realistic bilayers employed in SOT experiments. This is emphasized by Fig.…”

Section: How To Model Spin Torque Using Nonequilibrium Density Mamentioning

confidence: 99%

First-Principles Quantum Transport Modeling of Spin-Transfer and Spin-Orbit Torques in Magnetic Multilayers

Nikolić¹,

Dolui²,

Petrović³

et al. 2018

Handbook of Materials Modeling

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We review a unified approach for computing: (i) spin-transfer torque in magnetic trilayers like spin-valves and magnetic tunnel junction, where injected charge current flows perpendicularly to interfaces; and (ii) spin-orbit torque in magnetic bilayers of the type ferromagnet/spin-orbit-coupledmaterial, where injected charge current flows parallel to the interface. The experimentally explored and technologically relevant spin-orbit-coupled-materials include 5d heavy metals, topological insulators, Weyl semimetals and transition metal dichalcogenides. Our approach requires to construct the torque operator for a given Hamiltonian of the device and the steady-state nonequilibrium density matrix, where the latter is expressed in terms of the nonequilibrium Green's functions and split into three contributions. Tracing these contributions with the torque operator automatically yields field-like and damping-like components of spin-transfer torque or spin-orbit torque vector, which is particularly advantageous for spin-orbit torque where the direction of these components depends on the unknown-in-advance orientation of the current-driven nonequilibrium spin density in the presence of spin-orbit coupling. We provide illustrative examples by computing spin-transfer torque in a one-dimensional toy model of a magnetic tunnel junction and realistic Co/Cu/Co spin-valve, both of which are described by first-principles Hamiltonians obtained from noncollinear density functional theory calculations; as well as spin-orbit torque in a ferromagnetic layer described by a tight-binding Hamiltonian which includes spin-orbit proximity effect within ferromagnetic monolayers assumed to be generated by the adjacent monolayer transition metal dichalcogenide. In addition, we show how spin-orbit proximity effect, quantified by computing (via first-principles retarded Green's function) spectral functions and spin textures on monolayers of realistic ferromagnetic material like Co in contact with heavy metal or monolayer transition metal dichalcogenide, can be tailored to enhance the magnitude of spin-orbit torque. We also quantify errors made in the calculation of spin-transfer torque when using Hamiltonian from collinear density functional theory, with rigidly rotated magnetic moments to create noncollinear magnetization configurations, instead of proper (but computationally more expensive) self-consistent Hamiltonian obtained from noncollinear density functional theory. * bnikolic@udel.edu 1 For easy navigation, we provide a list of abbreviations used throughout the Chapter: 1D-Particle Current z y x Co Lead Co Lead Cu(a) (b) M free fixed M Co Pt θ θ M free MoS 2 Co M free θ (c) FIG. 2. Schematic view of: (a) FM/NM/FM trilayer for calculations of STT in spin-valves; (b) FM/HM bilayer for calculations of SOT in the presence of the spin Hall current along the z-axis generated by the HM layer; and (c) FM/monolayer-TMD for calculations of SOT in the absence of any spin Hall current. The semi-infinite FM layers in (a) are chosen as Co (0001), and t...

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“…This model yields an effective current-induced magnetic field, B ef f SOT = 2m e α R I S × e z /M s , where I S is the in-plane spin cur-rent polarized along the magnetization direction and M s is the magnetic moment of the FM. [18][19][20][21] For the actual NM/FM bilayer, the same model is usually employed by introducing the Rashba SOC localized at the interfacial region. In addition to the FL-SOT, the RE effect can also give rise to DL-SOT.…”

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Microscopic origin of spin-orbit torque in ferromagnetic heterostructures: A first-principles approach

et al. 2020

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We present an ab initio-based theoretical framework which elucidates the origin of the spin-orbit torque (SOT) in Normal-Metal(NM)/Ferromagnet(FM) heterostructures. The SOT is decomposed into two contributions, namely, spin-Hall and the spin-orbital components. We find that (i) the Field-Like (FL) SOT is dominated by the spin-orbital component and (ii) both components contribute to the damping-like torque with comparable magnitude in the limit of thick Pt film. The contribution of the spin-orbital component to the DL-SOT is present only for NMs with strong SOC coupling strength. We demonstrate that the FL-SOT can be expressed in terms of the nonequilibrium spin-resolved orbital moment accumulation. The calculations reveal that the experimentally reported oxygen-induced sign-reversal of the FL-SOT in Pt/Co bilayers is due to the significant reduction of the majority-spin orbital moment accumulation on the interfacial NM atoms.

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Intrinsic spin-orbit torque in a single-domain nanomagnet

Abstract: International audienc

Cited by 22 publications

References 41 publications

Proximity Spin–Orbit Torque on a Two-Dimensional Magnet within van der Waals Heterostructure: Current-Driven Antiferromagnet-to-Ferromagnet Reversible Nonequilibrium Phase Transition in Bilayer CrI₃

Proximity Spin–Orbit Torque on a Two-Dimensional Magnet within van der Waals Heterostructure: Current-Driven Antiferromagnet-to-Ferromagnet Reversible Nonequilibrium Phase Transition in Bilayer CrI₃

First-Principles Quantum Transport Modeling of Spin-Transfer and Spin-Orbit Torques in Magnetic Multilayers

Microscopic origin of spin-orbit torque in ferromagnetic heterostructures: A first-principles approach

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Intrinsic spin-orbit torque in a single-domain nanomagnet

Abstract: International audienc

Cited by 22 publications

References 41 publications

Proximity Spin–Orbit Torque on a Two-Dimensional Magnet within van der Waals Heterostructure: Current-Driven Antiferromagnet-to-Ferromagnet Reversible Nonequilibrium Phase Transition in Bilayer CrI3

Proximity Spin–Orbit Torque on a Two-Dimensional Magnet within van der Waals Heterostructure: Current-Driven Antiferromagnet-to-Ferromagnet Reversible Nonequilibrium Phase Transition in Bilayer CrI3

First-Principles Quantum Transport Modeling of Spin-Transfer and Spin-Orbit Torques in Magnetic Multilayers

Microscopic origin of spin-orbit torque in ferromagnetic heterostructures: A first-principles approach

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Proximity Spin–Orbit Torque on a Two-Dimensional Magnet within van der Waals Heterostructure: Current-Driven Antiferromagnet-to-Ferromagnet Reversible Nonequilibrium Phase Transition in Bilayer CrI₃

Proximity Spin–Orbit Torque on a Two-Dimensional Magnet within van der Waals Heterostructure: Current-Driven Antiferromagnet-to-Ferromagnet Reversible Nonequilibrium Phase Transition in Bilayer CrI₃