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

Abstract

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 ...

Bulk versus surface contributions to the Rashba spin splitting of Shockley surface states

“…This was consistent with the density-functional-theory (DFT) calculation of Nicolay et al [4] that reproduced the spin-split surface bands on Au(111) quite well only with the aforementioned conventional SOI term. Subsequently, a number of mechanisms were proposed in order to account for large energy splittings observed for clean surfaces [5][6][7][8] as well as for those covered with heavy atoms such as Pb and Bi [9][10][11][12]. Bihlmayer et al [13] and Nagao et al [14] demonstrated that it is not the asymmetry of the potential gradient but the asymmetry of the surfacestate wave function (or charge density) that determines the size of the spin splitting.…”

Strong Linear Dichroism in Spin-Polarized Photoemission from Spin-Orbit-Coupled Surface States

“…Both effects originate from a strong linear dichroism in the angular distribution of photoelectrons and are confirmed by ab initio one-step photoemission theory. The results are obtained for the surface alloy BiAg 2 /Ag(111), a model system for spin-orbit effects [31][32][33][34] and spin-dependent photoemission [18,26,[35][36][37] The experiments were performed at room-temperature and in ultrahigh vacuum (p < 2 · 10 −10 mbar). The surface alloy [31,35] was grown as described elsewhere [38].…”

“…At the same time, the efficiency of stateof-the-art photoelectron spin detectors has been improved tremendously [11,16,17], making it now possible to measure the photoelectron spin polarization over wide regions of momentum space with varying energy and polarization of the exciting light. Despite these encouraging developments fundamental issues remain debated, namely to which degree, under which conditions, and in which way the measured photoelectron spin polarization actually reflects the intrinsic spin properties of spin-orbit split states [11,[18][19][20][21][22][23][24][25][26].Within the one-step theory of photoemission the spindependent photocurrent is determined by the photoemission matrix element which involves the initial state of the transition -the object of interest -and the final state of the outgoing photoelectron. In the vacuum ultraviolet photonenergy regime, commonly used in spin-ARPES experiments, the properties of the final state may quickly vary with the excitation energy and deviate considerably from the naive assumption of a free-electron state [27].…”

“…At the same time, the efficiency of stateof-the-art photoelectron spin detectors has been improved tremendously [11,16,17], making it now possible to measure the photoelectron spin polarization over wide regions of momentum space with varying energy and polarization of the exciting light. Despite these encouraging developments fundamental issues remain debated, namely to which degree, under which conditions, and in which way the measured photoelectron spin polarization actually reflects the intrinsic spin properties of spin-orbit split states [11,[18][19][20][21][22][23][24][25][26].…”

A case study for the formation of stanene on a metal surface

“…Also, an analysis of the unoccupied regime of the band structure neither reveals an extension of B2 nor a hole-like parabolic band close to E F connecting the occupied branches of B1 and B2. These observations are clear indications than B1 and B2 are not conventional (partially occupied) hole-like Rashba-split bands of the Sn/Au interface as for instance observed for the prototypical Rashba systems BiAg 2 and BiCu 2 [32][33][34] . Instead, we conclude that B2 has a different, most likely bulk origin (see Supplementary Note 1 and Supplementary Figure 4).…”