Relativistic Low Energy Electron Diffraction from W(001)

Abstract

Motivated by the importance of spin polarization and further relativistic effects in low energy electron scattering from large Z atoms (cf. review article (I)), we have developed a formalism based on Dirac' s equation for calculating intensities and spin polarizations in LEED from crystal surfaces (2,3). Applying this formalism to W(OOl), we find sizeable spin polarization values. In the fol lowing we first state the particular model assumptions underlying our computations and then present and discuss some numerical results.Following (3) we use,a model crystal consisting of our relativistic KKRZtype pseudopotential and an energy-dependent imaginary potential. The atomic phase shifts, which determine the pseudopotential coefficients, are obtained, as in (4), from Mattheiss' APW potential (5). We include five phase shifts in our computation. The effect of inelastic processes i s ideally taken into account by an imaginary self-energy part, which i s calculated by a many-body treatment of the electron gas in W. In the absence of such a calculation we content ourselves initially with an adjustable imaginary quantity, the choice of the energy dependence of which i s guided by experimental loss profiles (6). Since the threshold energy for a particular loss mode i s obtained a s the loss energy minus the work function ( 4 . 6 5 eV for W(OO1) (7)), the large loss around 10 e V (cf. Fig. 1 of (6)) suggests an increase in the imaginary potential V. in the vicinity of E = 5 . 3 5 eV (energy of the incident electron). In the present computation we choose V. = -1 . 5 eV for E 4 . 5 eV, V. = -2 e V for E P 4 . 5 eV. The real inner 'potential i s taken into account by shifting the intensity profiles calculated with zero inner potential to match the measured profiles. Thermal lattice motion is neglected at present.

Spin polarization of low-energy electrons interacting with solid surfaces

“…Значительный интерес представляет рабо-та 178 , в которой при исследовании АЭЭ из вольфрама обнаружено сильное влияние подсветки на поляризацию эмиттированных электронов. В 179 -181 найдены условия, при которых возможна поляризация оже-электронов, а в 182 она обнаружена экспериментально при исследовании намагниченного ферромагнитного стекла Fe 83 B 17 .…”

Relativistic Theory of Low Energy Electron Diffraction: Application to the (001) and (110) Surfaces of Tungsten

“…I n the computational application of our LEED formalism to tungsten we make several specific assumptions in addition to the general model assumptions (cf. [3], Section 2) underlying the formalism. Fig.…”

“…A formalism based on Dirac's equation has been developed for calculating intensities and spin polarization properties in low energy electron diffraction (LEED) from surfaces of single crystals composed of heavy atoms [ l , 21. An initial computational application of this formalism to the case of normal incidence on the (001) surface of tungsten has revealed appreciable degrees of spin polarization in the nonspecular beams [3]. In the present work, we report more comprehensive intensity and spin polarization results for several angles of incidence on W(OO1) and for normal incidence on W(lOl).l) Since the fine structure of LEED intensity profiles is sensitive to the 'surface potential barrier' r4, 51, i.e.…”