Quantitative vectorial spin analysis in angle-resolved photoemission: Bi/Ag(111) and Pb/Ag(111)

The concept of vectorial spin analysis in spin and angle-resolved photoemission is illustrated in this paper. Two prototypical systems, Bi/Ag(111)(sqrt(3)×sqrt(3))R30° and Pb/Ag(111)(sqrt(3)×sqrt(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 were determined by a two-step 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 the polarization direction and its magnitude for each band. We confirm that the surface states experience a large spin splitting. Moreover, we find that all surface state bands are 100% spin polarized, and that for some states, spin polarization vectors rotate out of the surface plane. Quantitative vectorial spin analysis in ARPES: Bi/Ag(111) and Pb/Ag(111) Fabian Meier, Hugo Dil, Jorge Lobo-Checa, Luc Patthey, and Jürg Osterwalder Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland 2 Swiss Light Source, Paul Scherrer Institut, CH-5232 Villigen, Switzerland Departement Physik, Universität Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland (Dated: April 7, 2008) 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, 79.60.-i 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)( √ 3× √ 3)R30◦ [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 ( √ 3× √ 3)R30◦ 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.