Hierarchical spin-orbital polarization of a giant Rashba system

Bawden, L.; Riley, J. M.; Kim, Choong Hyun; Sankar, Raman; Monkman, Eric; Shai, Daniel; Wei, Haofei I.; Lochocki, Edward; Wells, Justin W.; Meevasana, W.; Kim, T. K.; Hoesch, Moritz; Ohtsubo, Yoshiyuki; Fèvre, P. Le; Fennie, Craig J.; Shen, Kyle; Chou, F. C.; King, P. D. C.

doi:10.1126/sciadv.1500495

Cited by 42 publications

(43 citation statements)

References 38 publications

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“…This explains not only that the even-and odd-parity orbitals couple with opposite spins but also that the SO entanglement is a general consequence of the SO coupling. Indeed the similar SO-coupled states have been recently confirmed in surface states of topological insulators [34][35][36][37][38][39] and Rashba states in BiTeI [40,41].…”

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confidence: 53%

Direct mapping of spin and orbital entangled wave functions under interband spin-orbit coupling of giant Rashba spin-split surface states

et al. 2017

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We use spin-and angle-resolved photoemission spectroscopy (SARPES) combined with polarization-variable laser and investigate the spin-orbit coupling effect under interband hybridization of Rashba spin-split states for the surface alloys Bi/Ag(111) and Bi/Cu(111). In addition to the conventional band mapping of photoemission for Rashba spin-splitting, the different orbital and spin parts of the surface wavefucntion are directly imaged into energy-momentum space. It is unambiguously revealed that the interband spin-orbit coupling modifies the spin and orbital character of the Rashba surface states leading to the enriched spin-orbital entanglement and the pronounced momentum dependence of the spin-polarization. The hybridization thus strongly deviates the spin and orbital characters from the standard Rashba model. The complex spin texture under interband spin-orbit hybridyzation proposed by first-principles calculation is experimentally unraveled by SARPES with a combination of p-and s-polarized light. PACS numbers:A realization of functional capabilities to generate spinsplitting of electronic states without any external magnetic field is a key subject in the research of spintronics [1]. A promising strategy exploits the influence of spin-orbit (SO) interaction that can give rise to the lifting of spin degeneracy under broken space inversion symmetry, the so-called Rashba effect [2]. In the conventional Rashba model, an eigenstate of the SO-induced spin-splitting is treated with an assumption of a pure spin state fully chiral spin-polarized which protects electrons from backscattering [2][3][4][5]. However, in real materials, the assumption can be usually broken because the SO coupling mixes different states with different orbitals and orthogonal spinors in a quasiparticle eigenstate [6][7][8]. The SO entanglement can permit the spin-flip electron backscattering [9] and moreover orbital mixing in the eigenstate can play a significant role in an emergence of the large spin-splitting [10][11][12][13][14]. Therefore, it is essentially important to experimentally explore the SO coupling not only in the lifting spin degeneracy but also in the spin and orbital wavefunction as eigenstates.Beyond the conventional Rashba model, a well-ordered surface alloy BiAg 2 grown on Ag(111) provides an ideal case to study the SO entanglement in Rashba surface states. In the surface alloy, an occupied sp z -like band and a mostly unoccupied p xy -like band show significant Rashba spin splitting [15,16] and cross each other at the specific k || [17][18][19] as shown in Fig. 1 (b). In particular, density functional theory (DFT) calculations showed the strong SO entanglement [8,9] and predicted the complex spin texture that is significantly different from the conventional Rashba model; the sp z band switches spinpolarization at the crossing through SO-induced interband hybridization [19] which is in contrast to the similar system BiCu 2 /Cu(111) as shown in Fig. 1 (b) [14,20,21]. While the presence of the spin-polarized electronic bands ...

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confidence: 53%

Direct mapping of spin and orbital entangled wave functions under interband spin-orbit coupling of giant Rashba spin-split surface states

et al. 2017

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“…In addition to study of spin splitting and texture in materials with strong SOI, several works have also investigated the orbital switching in topological insulators [13,14] and in hexagonal 3D Rashba semiconductors [15,16]. Specifically, Cao et al found that below the Dirac point the wavefunctions are more radial while above the Dirac point the wavefunctions are more tangential [13].…”

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confidence: 99%

“…Spin and Orbital Texture-Lastly, we investigate the orbital texture of PbS as it has been shown that TIs and hexagonal 3D Rashba materials have orbital switching at the Dirac point [13][14][15][16]. To our best knowledge, such analysis has not been done for monolayers with square symmetry.…”

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confidence: 99%

Two-dimensional square buckled Rashba lead chalcogenides

et al. 2017

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We propose the lead sulphide (PbS) monolayer as a 2D semiconductor with a large Rashba-like spin-orbit effect controlled by the out-of-plane buckling. The buckled PbS conduction band is found to possess Rashba-like dispersion and spin texture at the M and Γ points, with large effective Rashba parameters of λ ∼ 5 eVÅ and λ ∼ 1 eVÅ, respectively. Using a tight-binding formalism, we show that the Rashba effect originates from the very large spin-orbit interaction and the hopping term that mixes the in-plane and out-of-plane p orbitals of Pb and S atoms. The latter, which depends on the buckling angle, can be controlled by applying strain to vary the spin texture as well as the Rashba parameter at Γ and M . Our density functional theory results together with tight-binding formalism provide a unifying framework for designing Rashba monolayers and for manipulating their spin properties.Introduction-Over the past two decades there has been a growing interest in materials with strong spin-orbit interaction (SOI), as they are of a profound importance for fundamental understanding of quantum phenomena at the atomic level and applications to spintronics. This relativistic interaction is linked to important effects such as Rashba, Zeeman, spin-Hall effect, and topological insulator (TI) states [1][2][3][4].

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“…This model shows the orbital texture switch seen in ARPES studies 1,2,5 . This model also predicts that this feature is not unique to these materials, and in fact should be present in all strong-spin orbit coupled materials with broken inversion symmetry.…”

Section: Discussionmentioning

confidence: 57%

“…As part of this physics, different orbital states directly couple to specific spins 7 . In the case of Bi 2 Se 3 , the different orbitals can couple to spins that do not follow the net helicity of the spin bands 1,2,5 . This has ramifications when considering the bands as being entirely spin polarized, since in reality they are a superposition of opposing spins coupled to different orbitals.…”

Section: Introductionmentioning

confidence: 99%

Minimal ingredients for orbital-texture switches at Dirac points in strong spin–orbit coupled materials

et al. 2016

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Recent angle resolved photoemission spectroscopy measurements on strong spin-orbit coupled materials have shown an in-plane orbital texture switch at their respective Dirac points, regardless of whether they are topological insulators 1 or "trivial" Rashba materials 2 . This feature has also been demonstrated in a few materials (Bi2Se3, Bi2Te3, and BiTeI) though DFT calculations 1-3 . Here we present a minimal orbital-derived tight binding model to calculate the electron wave-function in a two-dimensional crystal lattice. We show that the orbital components of the wave-function demonstrate an orbital-texture switch in addition to the usual spin switch seen in spin polarized bands. This orbital texture switch is determined by the existence of three main properties: local or global inversion symmetry breaking, strong spin-orbit coupling, and non-local physics (the electrons are on a lattice). Using our model we demonstrate that the orbital texture switch is ubiquitous and to be expected in many real systems. The orbital hybridization of the bands is the key aspect for understanding the unique wave function properties of these materials, and this minimal model helps to establish the quantum perturbations that drive these hybridizations.

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Hierarchical spin-orbital polarization of a giant Rashba system

Abstract: Angle-resolved photoemission reveals the emergence of complex orbital texture concomitant with spin splitting in the Rashba compound BiTeI.

Cited by 42 publications

References 38 publications

Direct mapping of spin and orbital entangled wave functions under interband spin-orbit coupling of giant Rashba spin-split surface states

Direct mapping of spin and orbital entangled wave functions under interband spin-orbit coupling of giant Rashba spin-split surface states

Two-dimensional square buckled Rashba lead chalcogenides

Minimal ingredients for orbital-texture switches at Dirac points in strong spin–orbit coupled materials

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