Photoelectron spin polarization

For magnetically ordered materials, photoemitted electrons have a characteristic spin polarization that reflects the electron spin orientation occurring in the sample before the photoemission process. Recently, techniques have been developed to measure this photoelectron spin polarization (photo ESP) (21). 

The first prerequisite for measurement of photoelectron spin-polarization is the ability to separately detect the photoelectrons ejected from the different fine-structure levels (e.g., 2n3/2 and 2n1/2 for HX+ X2n). When the molecule contains a heavy atom (e.g., large spin-orbit splitting), it becomes easier to use the electron kinetic energy to distinguish the photoelectrons ejected from the different fine structure channels. For spin-polarization analysis, the accelerated electron beam (20-120 keV) can be scattered by a thin gold foil in a Mott-detector. The spin-polarization is determined from the left-right (or up-down) asymmetry in the intensities of the scattered electrons (Heinzmann, 1978). Spin polarization experiments, however, are difficult because the differential spin-up/spin-down flux of photoelectrons is typically one thousandth that obtained when recording a total photoionization spectrum. 

Figure 1.5 Components of the spin polarization vector P of ejected photoelectrons. The direction of the photoelectron is given by the polar and azimuthal angles and O (see Fig. 1.4). For an ensemble of electrons emitted in this direction, the polarization vector P then points in a certain direction in space, and one possibility for representing this vector using three orthogonal components is shown in the figure Plong in the direction of the photoelectron and P,ransX and P,ranS both perpendicular to this direction (for the definition and measurement of these components see Section 9.2.1).

The complete experiment for 2p photoionization in magnesium described previously depends on the validity of the non-relativistic LSJ-coupling scheme and on the existence of a simple subsequent Auger transition. However, such conditions are rarely met, since in heavier elements spin-orbit effects cannot be neglected, and for outer-shell photoionization no subsequent decay is possible. In order to perform a complete experiment for such cases,f measurement of the spin-polarization of the photoelectrons is necessary. As an example, 5p photoionization in xenon will be discussed. 

From the formulas listed, the components Px., Pr and Pz. of the photoelectron s spin-polarization vector P defined in the /, z detector frame can be calculated (for the definition of P see Fig. 1.5 and equ. (9.15)). If tr stands for transverse, long for longitudinal, and if the subscripts and 1 indicate the component within or perpendicular to the scattering plane, respectively, one gets1"... 

In these relations the interest lies in the spin-polarization vector of the photoelectron itself, i.e., the detector response Q is assumed to be always perfect, Qt= +1. The same procedure applies if the response of an actual detector with Q, < 1 to polarized electrons is calculated (see below where, for the case of Mott scattering, Q, has to be identified with the Sherman function Ss). 

Figure 5.20 Schematic drawing of an apparatus for measuring the spin-polarization of photoelectrons. The xyz coordinate system refers to the tilted frame introduced in Fig. 1.15. For a detailed explanation see main text. From [HSS84],...

The results of a spin-polarization measurement of xenon photoelectrons with 5p5 2P3/2 and 5p5 2P1/2 final ionic states are shown in Fig. 5.21 together with the results of theoretical predictions. Firstly, there is good agreement between the experimental data (points with error bars) and the theoretical results (solid and dashed curves, obtained in the relativistic and non-relativistic random-phase approximations, respectively). This implies that relativistic effects are small and electron-electron interactions are well accounted for. (In this context note that the fine-structure splitting in the final ionic states has also to be considered in... 

Figure 5.21 Spin-polarization parameters a, A, and tj as functions of the photon wavelength in the continuous range for photoelectrons leaving the xenon ion in the 5p5 2P1/2 and 2P3/2 states, respectively. The J value of the final state is indicated on the curves the vertical dashed line shows the J = 1/2 ionization threshold. Experimental data full circles [HSS86], Theoretical data full curves, relativistic random-phase calculation [HJC81] dashed curves non-relativistic random-phase calculation [Che79], From [HSS86] note /[HSS86] = 0.5 rj.

Fig. 4 The energy distribution for photoelectrons ejected with a left (negative spin polarization -red, solid) or right circular (positive spin polarization - blue, dashed) polarized laser. The electrons are transmitted through films of l- and D-polyalanine both bound to the surface through the carbon terminal (a and c, respectively), and through a film of D-polyalanine bound to the surface through the N-terminal (b). Angew. Chem. Int. Ed. 2002, 41, 761 Fig. 2 Copy right permission granted.

Au photoelectrons are spin polarized due to the high spin-orbit coupling of the metal. Therefore, an alternative mechanism for the transmission asymmetry obseved in [36] could be based on changes in the photoelectron spin angular momentum. We do not attribute the yield asymmetry to spin polarization because the stearoyl-lysine monolayers in [36] contain only low atomic number atoms that do not scatter spin. 

Kachel T, Carbone C, Gudat W (1993) Spin polarization of core-level photoelectrons. Phys Rev B 47 15391... 

Starke K, Kaduwela AP, Liu Y et al (1996) Spin-polarized photoelectrons excited by circularly polarized radiation from a nonmagnetic solid. Phys Rev B 53 R10544... 

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