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.

Surfaces are at the frontier of every known solid. They provide versatile supports for functional nanostructures and mediate essential physicochemical processes. Intimately related to two-dimensional materials, interfaces and atomically thin films often feature distinct electronic states with respect to the bulk, which is key to many relevant properties, such as catalytic activity, interfacial charge-transfer, and crystal growth mechanisms. To induce novel quantum properties via lateral scattering and confinement, reducing the surface electrons' dimensionality and spread with atomic precision is of particular interest. Both atomic manipulation and supramolecular principles provide access to custom-designed molecular assemblies and superlattices, which tailor the surface electronic landscape and influence fundamental chemical and physical properties at the nanoscale. Here the confinement of surface-state electrons is reviewed, with a focus on their interaction with molecular scaffolds created by molecular manipulation and self-assembly protocols under ultrahigh vacuum conditions. Starting with the quasifree twodimensional electron gas present at the ð111Þ-oriented surface planes of noble metals, the intriguing molecule-based structural complexity and versatility is illustrated. Surveyed are low-dimensional confining structures in the form of artificial lattices, molecular nanogratings, or quantum dot arrays, which are constructed upon an appropriate choice of their building constituents. Whenever the realized (metal-)organic networks exhibit long-range order, modified surface band structures with characteristic features emerge, inducing noteworthy physical phenomena such as discretization, quantum coupling or energy, and effective mass renormalization. Such collective electronic states can be additionally modified by positioning guest species at the voids of open nanoarchitectures. The designed scattering potential landscapes can be described with semiempirical models, bringing thus the prospect of total control over surface electron confinement and novel quantum states within reach.

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