Erratum: Quantitative vectorial spin analysis in angle-resolved photoemission:Bi∕Ag(111)andPb∕

Abstract

The concept of vectorial spin analysis in spin and angle resolved photoemission is illustrated in this report. Two prototypical systems, Bi/Ag(111)( √ 3 × √ 3)R30• and Pb/Ag(111)( √ 3 × √ 3)R30• , which show a large Rashba type spin-orbit splitting, were investigated by means of spin and angle resolved photoemission. The spin polarization vectors of individual bands are determined by a twostep fitting routine. First, the measured intensities are fitted with an appropriate number of suitable peaks to quantify the contributions of the individual bands, then the measured spin polarization curves are fitted by varying for each band the polarization direction and its magnitude. We confirm that the surface states experience a large spin splitting. Moreover, we find that all surface state bands are 100 percent spin polarized, and that for some states spin polarization vectors rotate out of the surface plane.PACS numbers: 73.20. At, 71.70.Ej, Methods that allow to control and measure the electron spin, or the average of a certain number of spins, have received growing attention in the last few years. In spintronics, the spin field-effect transistor as proposed by Datta and Das [1], which relies on the RashbaBychkov effect [2,3] (henceforth Rashba effect) to manipulate electron spins by an electric field, is one of the key elements. Spin rotation is achieved by a field and momentum dependent spin splitting of bands in a two-dimensional electron gas. While actual devices are currently realized in semiconductor heterostructures [4], fundamental issues can be more easily studied in two-dimensional metallic systems involving heavy metal atoms, where spin splittings are much larger [5,6]. Very recently, a new class of material systems was identified where this effect is even further enhanced, among them the two surface alloys Bi/Ag(111)( √ 3 × √ 3)R30• and Pb/Ag(111)(• [7,8], referred to as Bi/Ag(111) and Pb/Ag(111) henceforth. Due to an additional reduction of the surface symmetry caused by the (• surface reconstruction and due to a slight corrugation of the surface [9], the size of the Rashba type spin-orbit induced spin splitting is about one order of magnitude larger than what is observed for the Au(111) surface state [10,11]. We have performed spin and angle resolved photoemission spectroscopy (SARPES) on Bi/Ag(111) and Pb/Ag(111). Furthermore we present a novel twostep fitting routine for the determination of the threedimensional spin polarization vector of individual bands, thus revealing the complete spin structure of Rashba systems in momentum space. In order to illustrate our results and the power of SARPES in combination with an adequate model for the data analysis, this paper is arranged as follows: In the first section, the theoretical aspects of the vectorial spin analysis are outlined. In the second section some subsequently relevant physics of the studied systems is introduced, followed by an experimental section. In the last section, the experimental results are presented and discussed.

Abrupt Rotation of the Rashba Spin to the Direction Perpendicular to the Surface

“…These results indicate that theP of the surfacestate band, which lies in the surface, ''rotates abruptly'' and points along the direction perpendicular to the surface around the " K point ( e $ 34 ). Note that in contrast to the 10% spin polarization aligned perpendicular to the surface plane, which results from the slight continuous rotation of P in the direction out from the surface plane on Bi=Agð111Þ and Pb=Agð111Þ surfaces [14,15], the spin polarization is 100% along the direction perpendicular to the surface around the " K point only in the present case. In order to understand the origins of the abrupt rotation of the RB spin and the curious splitting around " K, that cannot be explained by the simple RB effect described in Eq.…”

“…This spin-splitting effect, which has been observed on clean surfaces of noble metals [5][6][7][8][9][10] and heavy group V elements [11][12][13], has recently been reported to be enhanced in systems in which heavy element atoms are adsorbed on light element substrates, such as Bi or Pb on a Ag(111) surface [14,15]. The spin-split bands observed in these studies show similar behaviors as those of the simple RB effect, i.e., they show pairs of split bands in thek space and theP almost lies in the surface plane.…”

Relativistic effects and fully spin-polarized Fermi surface at the Tl/Si(111) surface

“…13,14 On one hand, these types of surfaces have been recently found to exhibit exceptional relativistic effects, 15,16 inducing spin-orbit energy shifts two orders of magnitude bigger than those found at normal semiconductor heterojunctions. From the practical point of view, heavy elements such as Tl or Sb are widely used in electronic instruments such as infrared detectors 17 or Halleffect devices.…”

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].…”