Spin and orbital angular momentum structure of Cu(111) and Au(111) surface states

Kim, Beomyoung; Kim, Choong Hyun; Kim, Panjin; Jung, Wooyong; Kim, Yeongkwan; Koh, Youngwoo; Arita, Masashi; Shimada, Kenya; Namatame, H.; Takeuchi, Masaki; Yu, Jaejun; Kim, Changyoung

doi:10.1103/physrevb.85.195402

Cited by 89 publications

(125 citation statements)

References 26 publications

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“…(4). Such quasi-linear OAM patterns for the upper two bands of STO surface states is a strong, testable prediction that can be confirmed readily by the recently popular technique of circular dichroism ARPES [11,12,19].…”

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confidence: 82%

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Nature of orbital and spin Rashba coupling in the surface bands ofSrTiO3andKTaO3

Kim

Kang

et al. 2014

Phys. Rev. B

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Tight-binding models for the recently observed surface electronic bands of SrTiO3 and KTaO3 are analyzed with a view to bringing out the relevance of momentum-space chiral angular momentum structures of both orbital and spin origins. Depending on the strength of electric field associated with inversion symmetry breaking at the surface, the orbital and the accompanying spin angular momentum structures reveal complex linear and cubic dependencies in the momentum k (linear and cubic Rashba effects, respectively) in a band-specific manner. Analytical expressions for the cubic orbital and spin Rashba effects are derived by way of unitary transformation technique we developed, and compared to numerical calculations. Due to the C4v symmetry of the perovskite structure the cubic Rashba effect appears as in-plane modulations. The discovery of surface electronic states in strontium titanate (SrTiO 3 )[1, 2] has stirred great excitement at the time the material is being viewed as a critical component of the emerging field of oxide electronics [3]. The origin of surface states in SrTiO 3 and a related material KTaO 3 [4, 5] (STO and KTO for short, respectively) is currently under active investigation [5,6]. Both materials' surface states originate from t 2g -orbitals whose relevant tight-binding parameters for the electronic structure are largely determined, including the one pertaining to the degree of inversion symmetry breaking (ISB) at the surface [5,6].Several features make STO and KTO surface states an ideal ground for the study of Rashba-related phenomena. First is the way that Rashba effects would play out among the several observed bands of differing orbital characters. ARPES measurements up to now [1, 2, 4, 5] did not clearly resolve the Rashba-split bands, presumably due to the smallness of the predicted Rashba parameter [7]. Transport measurements do reveal the Rashba term, of cubic order in momentum, through analysis of the orientation-dependent magneto-resistance data on STO surface [8,9]. Existing theories treat Rashba effects of t 2g -derived bands phenomenologically [6, 10] and cannot, for instance, explain the complex band-specific spin and orbital angular momentum structures observed in the electronic structure calculation [7].It has recently been argued that multi-orbital bands, subject to the surface ISB electric field, must give rise to an entity called the chiral orbital angular momentum (OAM) in momentum space [11,12]. The argument remains valid as long as the crystal field splitting does not quench the multi-orbital degrees of freedom in a given band structure. Such conditions seem to be well met in both STO and KTO, leading to the term ∼ k × E · L where L is the OAM operator for t 2g -orbitals, k is the linear momentum, and E is the surface-normal electric field. The effect was dubbed "orbital Rashba effect" [11] in analogy to the similar chiral structure of spins on the surface [13]. It was shown that pre-existing chiral OAM structure implies the linear Rashba effect upon the inclusion of spin-orb...

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“…The chiral structure of OAM, on the other hand, should be readily observable by means of circular dichroism ARPES [12,19]. The two would-be Rashba-split bands possess the same orbital chirality in STO, and therefore give rise to the same circular dichroism response.…”

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confidence: 99%

Nature of orbital and spin Rashba coupling in the surface bands ofSrTiO3andKTaO3

Kim

Kang

et al. 2014

Phys. Rev. B

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“…After the new model was proposed, it was also found experimentally and theoretically that chiral OAM structure exists in surface states of metals [19][20][21][22] even when SOC is weak. Somewhat surprisingly, it was found that the alignment(parallel or anti-parallel) between spin and OAM are band and crystal momentum dependent.…”

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Microscopic mechanism for asymmetric charge distribution in Rashba-type surface states and the origin of the energy splitting scale

Kim

Jung

et al. 2013

Phys. Rev. B

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Microscopic mechanism for the Rashba-type band splitting is examined in detail. We show how asymmetric charge distribution is formed when local orbital angular momentum (OAM) and crystal momentum get interlocked due to surface effects. An electrostatic energy term in the Hamiltonian appears when such OAM and crystal momentum dependent asymmetric charge distribution is placed in an electric field produced from an inversion symmetry breaking (ISB). Analysis by using an effective Hamiltonian shows that, as the atomic spin-orbit coupling (SOC) strength increases from weak to strong, originally OAM-quenched states evolve into well-defined chiral OAM states and then to total angular momentum J-states. In addition, the energy scale of the band splitting changes from atomic SOC energy to electrostatic energy. To confirm the validity of the model, we study OAM and spin structures of Au(111) system by using an effective Hamiltonian for the d-orbitals case. As for strong SOC regime, we choose Bi2Te2Se as a prototype system. We performed circular dichroism angle resolved photoemission spectroscopy experiments as well as first-principles calculations. We find that the effective model can explain various aspects of spin and OAM structures of the system.

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“…However, there is no general * alberto.crepaldi@elettra.eu consensus about the physical mechanism at the origin of the dichroism in CD-ARPES experiments. Recent theoretical and experimental studies proposed to interpret the dichroism in giant spin-split states in surface alloys [17][18][19] and in TIs [20][21][22][23] as the result of local orbital angular momentum (OAM [17,18,21,(24)(25)(26)) or directly as a measure of the spin polarization [20].Recently, a large variation of the dichroism as a function of the incoming photon energy as well as the change in its sign have been reported by Scholz and co-workers for the topological insulator Bi 2 Te 3 [27]. A similar observation was reported for the TI Bi 2 Te 2 Se by Neupane et al [28].…”

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Momentum and photon energy dependence of the circular dichroic photoemission in the bulk Rashba semiconductorsBiTeX(X=I, Br, Cl)

et al. 2014

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Bulk Rashba systems BiTeX (X = I, Br, Cl) are emerging as important candidates for developing spintronics devices because of the coexistence of spin-split bulk and surface states, along with the ambipolar character of the surface charge carriers. The need to study the spin texture of strongly spin-orbit-coupled materials has recently promoted circular dichroic angular resolved photoelectron spectroscopy (CD-ARPES) as an indirect tool to measure the spin and the angular degrees of freedom. Here we report a detailed photon-energy-dependent study of the CD-ARPES spectra in BiTeX (X = I, Br, Cl). Our work reveals a large variation in the magnitude and sign of the dichroism. Interestingly, we find that the dichroic signal modulates differently for the three compounds and for the different spin-split states. These findings show a momentum and photon-energy dependence for the CD-ARPES signals in the bulk Rashba semiconductor BiTeX (X = I, Br, Cl). Finally, the outcome of our experiment indicates the important relation between the modulation of the dichroism and the phase differences between the wave functions involved in the photoemission process. This phase difference can be due to initialor final-state effects. In the former case the phase difference results in possible interference effects among the photoelectrons emitted from different atomic layers and characterized by entangled spin-orbital polarized bands. In the latter case the phase difference results from the relative phases of the expansion of the final state in different outgoing partial waves. The need for novel and advanced spintronics devices has stimulated the quest for materials hosting metallic spinpolarized bands embedded in a semiconducting bulk. Starting from the present knowledge on topological insulators (TIs) [1][2][3][4][5], the design of materials with spin-polarized bands requires the tailoring of the spin texture at the Fermi level (E F ), hence the synthesis of systems such as ternary TIs [6,7] or the bulk Rashba semiconductors BiTeX (X = I, Br, Cl) characterized by ambipolar surface states [8][9][10][11][12]. Nowadays one of the major challenges is to study the fully threedimensional spin properties of ternary TIs, and the bulk Rashba semiconductors, as is done for magnetic doped TIs [13].Spin-resolved angular resolved photoelectron spectroscopy (SR-ARPES) offers the unique possibility to directly address the spin polarization. Unfortunately, SR-ARPES, based on high-energy spin-dependent Mott scattering, is characterized by a low efficiency (1 × 10 −3 -1 × 10 −4 ) [14]. This limitation has recently renewed the interest for alternative spin detection devices based on higher-efficiency low-energy electron diffraction (IV-LEED with 1 × 10 −1 -1 × 10 −2 ) [15]. This context well explains why the possibility of indirectly studying the spin polarization via circular dichroic ARPES (CD-ARPES) was regarded as a major breakthrough [16]. CD-ARPES measures the difference between the photoemission intensities obtained with the two opposite helicities ...

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Spin and orbital angular momentum structure of Cu(111) and Au(111) surface states

Cited by 89 publications

References 26 publications

Nature of orbital and spin Rashba coupling in the surface bands ofSrTiO3andKTaO3

Nature of orbital and spin Rashba coupling in the surface bands ofSrTiO3andKTaO3

Microscopic mechanism for asymmetric charge distribution in Rashba-type surface states and the origin of the energy splitting scale

Momentum and photon energy dependence of the circular dichroic photoemission in the bulk Rashba semiconductorsBiTeX(X=I, Br, Cl)

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