Spin-torque efficiency enhanced by Rashba spin splitting in three dimensions

Tsutsui, Kazuhiro; Murakami, Shuichi

doi:10.1103/physrevb.86.115201

Cited by 26 publications

(26 citation statements)

References 24 publications

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“…Furthermore, the Dirac point is located ∼ 94 meV above the conduction band minimum, making E F < 0 accessible at an appreciable doping level without entering the localization regime [23]. We note that this E F < 0 regime in Rashba systems is of intense theoretical interest from the standpoint of enhanced superconducting instabilities [24], spin torque efficiency [25], and superconductivity with peculiar symmetry [26]. Our present transport identification of the E F < 0 FS topology with high electronic mobility thus paves the way for realizing the material host for these exciting proposals.…”

Section: (A)mentioning

confidence: 99%

Transport signatures of Fermi surface topology change in BiTeI

Checkelsky

Kagawa

et al. 2015

Phys. Rev. B

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We report a quantum magnetotransport signature of a change in the Fermi surface topology in the Rashba semiconductor BiTeI with a systematic tuning of the Fermi level E F . Beyond the quantum limit, we observe a marked increase (decrease) in electrical resistivity when E F is above (below) the Dirac node that we show originates from the Fermi surface topology. This effect represents a measurement of the electron distribution on low-index (n = 0,−1) Landau levels and is uniquely enabled by the finite bulk k z dispersion along the c axis and strong Rashba spin-orbit coupling strength of the system. The Dirac node is independently identified by Shubnikov-de Haas oscillations as a vanishing Fermi surface cross section at k z = 0. Additionally, we find that the violation of Kohler's rule allows a distinct insight into the temperature evolution of the observed quantum magnetoresistance effects. Recently, Dirac's matrix equation of relativistic electrons [1] has been found to be profoundly linked to the dynamics of electrons in solids. Application of this formalism has been proven key in describing the intertwined (pseudo)spin degrees of freedom [2][3][4]. One striking experimental implication of the linear dispersion is that in laboratory magnetic fields, it significantly enlarges low-index Landau level energy separations compared to parabolic bands generated by a comparable tight-binding transfer integral, making emergent Dirac fermion systems an ideal platform to study quantum Landau level effects. Observations of this range from the discovery of Shubnikov-de Haas (SdH) oscillations in elemental bismuth [5] to the first report of the quantum Hall effect at room temperature in graphene [6]. In this Rapid Communication we extend the quantum transport study of such Dirac structures to the critical point of a change in the bulk Fermi surface topology. From a semiclassical point of view, it is understood that magnetoresistance (MR) is sensitive to the topology of given Fermi surfaces [7]: The magnetic field B drives the electrons in orbits around the Fermi surface (FS), sensing its geometry and topology. Here we describe the effect of the Dirac structure in this context of Fermi surface topology, which we observe as a magnetoresistance effect of pure quantum origin across the bulk Dirac node.We study the system BiTeI that possesses a Dirac node generated by Rashba-type spin-orbit coupling α · (σ × k) [8,9], where α is the structure-specific Rashba parameter, and σ and k are the spin and momentum operators, respectively. This layered semiconductor breaks inversion symmetry by crystallizing in the polar space group P 3m1 so that the spin-orbit interaction takes the form of a Rashba term in the bulk three-dimensional (3D) band structure. This has been confirmed by angle-resolved photoemission spectroscopy [10] and relativistic ab initio calculations [11]. In this system, both the conduction band minimum and the valence band maximum are located near the A point in the hexagonal * Present address: Department of Physics, Massa...

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Section: (A)mentioning

confidence: 99%

Transport signatures of Fermi surface topology change in BiTeI

Checkelsky

Kagawa

et al. 2015

Phys. Rev. B

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“…In particular, it is highly desirable to tune the Fermi level into the vicinity of the Dirac point at zero momentum in the Rashba system, since schemes to realize Majorana fermions [18] involve opening a small energy gap at the Dirac point to realize a single spin nondegenerate band. Furthermore, the spin polarization of current is largest in the vicinity of the Dirac point [20,21] and hence, such materials could be used as spin injectors, as has been proposed with topological insulators [22,23], but the surface-dominated transport is not required in this case.…”

Section: Introductionmentioning

confidence: 99%

“…1(a)]. Therefore such a transition would be an important step toward exploring spin-dependent transport and other exotic physical phenomena in the low-carrier-density regime [9,19,20]. In particular, it is highly desirable to tune the Fermi level into the vicinity of the Dirac point at zero momentum in the Rashba system, since schemes to realize Majorana fermions [18] involve opening a small energy gap at the Dirac point to realize a single spin nondegenerate band.…”

Section: Introductionmentioning

confidence: 99%

“…The high energy scale of the Rashba effect in BiTeX provides opportunities for achieving practical spintronic applications [12,13] and realizing nontrivial phenomena such as the intrinsic spin Hall effect [14], noncentrosymmetric exotic superconductivity [15,16], Majorana fermions [17,18], and topological transitions of the Fermi surface (FS) [9,19,20]. Among them, the topological transition of the FS takes place when the Fermi level is tuned down through the band-crossing point (Dirac point), as shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

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Observation of topological transition of Fermi surface from a spindle torus to a torus in bulk Rashba spin-split BiTeCl

et al. 2015

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The recently observed large Rashba-type spin splitting in the BiTeX(X=I,Br,Cl) bulk states enables observation of the transition in Fermi surface topology from spindle torus to torus with varying the carrier density and offers an ideal platform for achieving practical spintronic applications and realizing nontrivial phenomena such as topological superconductivity and Majorana fermions. Here we use Shubnikov-de Haas oscillations to investigate the electronic structure of the bulk conduction band of BiTeCl single crystals with different carrier densities. We observe the topological transition of the Fermi surface (FS) from a spindle torus to a torus. The Landau-level fan diagram reveals the expected nontrivial π Berry phase for both the inner and outer FSs. Angle-dependent oscillation measurements reveal three-dimensional FS topology when the Fermi level lies in the vicinity of the Dirac point. All the observations are consistent with large Rashba spin-orbit splitting in the bulk conduction band. The recently observed large Rashba-type spin splitting in the BiTeX(X = I, Br, Cl) bulk states enables observation of the transition in Fermi surface topology from spindle torus to torus with varying the carrier density and offers an ideal platform for achieving practical spintronic applications and realizing nontrivial phenomena such as topological superconductivity and Majorana fermions. Here we use Shubnikov-de Haas oscillations to investigate the electronic structure of the bulk conduction band of BiTeCl single crystals with different carrier densities. We observe the topological transition of the Fermi surface (FS) from a spindle torus to a torus. The Landau-level fan diagram reveals the expected nontrivial π Berry phase for both the inner and outer FSs. Angle-dependent oscillation measurements reveal three-dimensional FS topology when the Fermi level lies in the vicinity of the Dirac point. All the observations are consistent with large Rashba spin-orbit splitting in the bulk conduction band.

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“…The former and latter break the space inversion and time reversal symmetries, respectively. We assume that the system has uniaxial anisotropy, with the anisotropy axis set by the Rashba field such that α = α/|α| [87][88][89] . Then, the Hamiltonian for the conduction electrons is given by…”

Section: A Hamiltonian and Green's Functionmentioning

confidence: 99%

Theory of electromagnetic wave propagation in ferromagnetic Rashba conductor

Shibata

Takeuchi

Kohno

et al. 2018

Journal of Applied Physics

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We present a comprehensive study of various electromagnetic wave propagation phenomena in a ferromagnetic bulk Rashba conductor from the perspective of quantum mechanical transport. In this system, both the space inversion and time reversal symmetries are broken, as characterized by the Rashba field α and magnetization M , respectively. First, we present a general phenomenological analysis of electromagnetic wave propagation in media with broken space inversion and time reversal symmetries based on the dielectric tensor. The dependence of the dielectric tensor on the wave vector q and M are retained to first order. Then, we calculate the microscopic electromagnetic response of the current and spin of conduction electrons subjected to α and M , based on linear response theory and the Green's function method; the results are used to study the system optical properties. Firstly, it is found that a large α enhances the anisotropic properties of the system and enlarges the frequency range in which the electromagnetic waves have hyperbolic dispersion surfaces and exhibit unusual propagations known as negative refraction and backward waves. Secondly, we consider the electromagnetic cross-correlation effects (direct and inverse Edelstein effects) on the wave propagation. These effects stem from the lack of space inversion symmetry and yield q-linear off-diagonal components in the dielectric tensor. This induces a Rashba-induced birefringence, in which the polarization vector rotates around the vector (α × q). In the presence of M , which breaks time reversal symmetry, there arises an anomalous Hall effect and the dielectric tensor acquires off-diagonal components linear in M . For α M , these components yield the Faraday effect for the Faraday configuration q M , and the Cotton-Mouton effect for the Voigt configuration (q ⊥ M ). When α and M are noncollinear, M -and q-induced optical phenomena are possible, which include nonreciprocal directional dichroism in the Voigt configuration. In these nonreciprocal optical phenomena, a "toroidal moment," α × M , and a "quadrupole moment," αiMj + αjMi, play central roles. These phenomena are strongly enhanced at the spin-split transition edge in the electron band.

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Spin-torque efficiency enhanced by Rashba spin splitting in three dimensions

Cited by 26 publications

References 24 publications

Transport signatures of Fermi surface topology change in BiTeI

Transport signatures of Fermi surface topology change in BiTeI

Observation of topological transition of Fermi surface from a spindle torus to a torus in bulk Rashba spin-split BiTeCl

Theory of electromagnetic wave propagation in ferromagnetic Rashba conductor

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