Spin-orbit torque in a three-dimensional topological insulator–ferromagnet heterostructure: Crossover between bulk and surface transport

Ghosh, Sumit; Manchon, Aurélien

doi:10.1103/physrevb.97.134402

Cited by 75 publications

(79 citation statements)

References 82 publications

(119 reference statements)

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“…Indeed, most experiments involve topological insulators with sizable bulk conductivity, suggesting that bulk states might participate to the spin-charge conversion mechanism. Spin transport in such systems has been recently investigated using driftdiffusion model (Fischer et al, 2016), non-equilibrium Green's function technique (Mahfouzi et al, 2016) and Kubo formula (Ghosh and Manchon, 2017b). The first two studies show that spin diffusion in the FM and spinflip scattering at the interface can enhance the DL torque.…”

Section: G Three-dimensional Topological Insulatorsmentioning

confidence: 99%

Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems

et al. 2019

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Section: G Three-dimensional Topological Insulatorsmentioning

confidence: 99%

Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems

et al. 2019

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“…The TI is modeled following the method described in Ref. 40 with the same set of parameters. To define the G-type antiferromagnet we have to double the unit cell ( Fig.…”

Section: Methodsmentioning

confidence: 99%

“…where I 4 is the identity matrix of rank 4, while M , A, B, c, d, A 1 and B 1 are the material parameters 40 . The Γ matrices are defined as…”

Section: Methodsmentioning

confidence: 99%

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Nonequilibrium spin density and spin-orbit torque in a three-dimensional topological insulator/antiferromagnet heterostructure

Ghosh

Manchon

2019

Phys. Rev. B

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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.

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“…(1) is directly related to the spin operator σ. As the result, the response of the in-plane spin density s = (s x , s y ) to electric field E = −∂A/∂t is defined by the conductivity tensor 28,33 . This also means that the non-equilibrium contribution to s from the electric current density J is given by s = (ẑ × J )/ev for any frequency and momentum irrespective of type of scattering for conduction electrons and even beyond the linear response.Thus, the response of s defines an exceptionally universal field-like spin-orbit torquethat acts in the same way as in-plane external magnetic field applied perpendicular to the charge current.…”

mentioning

confidence: 99%

Spin-torque resonance due to diffusive dynamics at the surface of a topological insulator

Sokolewicz¹,

Ado²,

Katsnelson

et al. 2019

Phys. Rev. B

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We investigate spin-orbit torques on magnetization in an insulating ferromagnetic (FM) layer that is brought into a close proximity to a topological insulator (TI). In addition to the well-known fieldlike spin-orbit torque, we identify an anisotropic anti-damping-like spin-orbit torque that originates in a diffusive motion of conduction electrons. This diffusive torque is vanishing in the limit of zero momentum (i. e. for spatially homogeneous electric field or current), but may, nevertheless, have a strong impact on spin-torque resonance at finite frequency provided external field is neither parallel nor perpendicular to the TI surface. The required electric field configuration can be created by a grated top gate.It is widely known that spin-orbit interaction provides an efficient way to couple electronic and magnetic degrees of freedom. It is, therefore, no wonder that the largest torque on magnetization, which is also referred to as the spin-orbit torque, emerges in magnetic systems with strong spin-orbit interaction 1,2 as has been long anticipated 3 .The spin-orbit coupling may be enhanced by confinement potentials in effectively two-dimensional systems consisting of conducting and magnetic layers. The inplane current may efficiently drive domain walls or switch magnetic orientation in such structures with the help of spin-orbit torque 4-7 , which is present even for uniform magnetization, or with the help of spin-transfer torque, which requires the presence of magnetization gradient (due to e. g. domain wall) [8][9][10][11] .Topological insulators (TI) 12-15 may be thought as materials with an ultimate spin-orbit coupling. Indeed, the effective Hamiltonian of conduction electrons at the TI surface contains essentially nothing but spin-orbit interaction term that provides a perfect spin-momentum locking. Thus, the magnetization dynamics in a thin ferromagnetic (FM) film in a proximity to TI surface is expected to be strongly affected by electric currents and/or electric fields 16 . There seems to be, indeed, a substantial experimental evidence that the efficiency of domain switching in TI/FM heterostructures is dramatically enhanced as compared to that in metals [17][18][19][20][21][22] .Nowadays the symmetry of spin-orbit torques is routinely inferred from the ferromagnetic resonance measurements in which an alternating microwave-frequency current (with frequencies 7 − 12 GHz) is applied within the sample plane 17,[23][24][25][26] .In this work we identify a novel anti-damping-like torque originating in a diffusive motion of conduction electrons at the TI surface. Such a torque originates in a non-local diffusive response of z component of the conduction electron spin density to the in-plane electric field. The non-locality of the response is determined by the socalled diffusion pole in analogy to the density-density re-FIG. 1. Proposed experimental setup. Non-homogeneous inplane electric field components are created by an ac top-gate voltage Vtop that induce a strong diffusive spin-orbit torque (4) of the ...

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Spin-orbit torque in a three-dimensional topological insulator–ferromagnet heterostructure: Crossover between bulk and surface transport

Cited by 75 publications

References 82 publications

Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems

Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems

Nonequilibrium spin density and spin-orbit torque in a three-dimensional topological insulator/antiferromagnet heterostructure

Spin-torque resonance due to diffusive dynamics at the surface of a topological insulator

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