Other Workers' Published Experimental Data on the Spin Polarization of Reflected Electron Beams

Although the author is familiar with several examples [1,4,62,63,64,25,65,26,55,51] of published data, obtained using Mott polarimeters, on the spin polarization of reflected, diffracted, transmitted, inelastic, and secondary electron beams, from magnetic and non-magnetic materials, rather few of them [1,4,62,55] concern specular reflection. Unfortunately, these include only one [55] of the publications, in which copper [25,65,26,55] or cobalt [55,51] samples are used. Nevertheless, other workers' specular reflection experiments on metallic surfaces can be compared, at least qualitatively, with the new theory of this chapter, and with the published theories reviewed in this chapter.

Measurements of reflected beam polarization from a tungsten $(001)$ surface, as a function of incident electron energy and angle of incidence, have been reviewed [1]. No error estimates are given^2.4, rendering it impossible to judge the relative merits of theories quantitatively, by these measurements. However, it is easy to imagine that the random errors are large enough that, except in some narrow ( $\sim{}20\,\mathrm{eV}$,) resonance-like energy bands, the measurements are consistent with the energy-independent, angle-independent, zero polarization predicted in the new theory of this chapter. One of the narrow energy bands includes $82\,\mathrm{eV}$, allowing the measurements to be simultaneously consistent with the band-structure calculation for tungsten, mentioned earlier in this chapter. It could be conjectured that the narrow energy bands correspond to changes in wave-vector on reflection, which, in some sense, match the repeat distance of those parts of the atomic cores, which are of sufficiently deep potential to render the electrons' kinetic energy comparable with their rest mass energy, allowing spin-orbit polarizing effects to become significant, and removing these narrow energy bands from the domain of validity of the new theory in this chapter. Some of the published band-structure calculations, reviewed earlier in this chapter, appear to have captured phenomena of this type.

Also reviewed [1] are measurements of reflected beam polarization from a $Cu_3Au$ $(001)$ surface, as a function of incident beam energy, at an angle of incidence of $13\,\mathrm{^{\circ}}$. In the energy region above $\sim{}60\,\mathrm{eV}$, where the Taylor expansion allows the new theory of this chapter to make quantitative predictions, the measurements appear to tend rapidly with increasing incident energy, to the constant, zero polarization of this theory.

The same paper [1] goes on to review measurements of reflected beam polarization from a nickel $(001)$ surface, as a function of incident beam energy and angle of incidence, as does another paper [4] in the same collection. For the former data set, in the energy region above $\sim{}60\,\mathrm{eV}$, where the Taylor expansion allows the new theory of chapter 2 to make quantitative predictions, the measurements provide a very good match to the constant polarization this theory. However, they provide an approximately equally good match to the relevant, published band-structure calculation, reviewed earlier in this chapter. For philosophical reasons explained elsewhere [10], the author is inclined to assign a higher prior probability to the new theory of this chapter than to the band-structure theory, leading to the former being preferred in this case of roughly equal goodness of fit. However, prior probabilities are [10] subjective, and readers are, therefore, fully entitled to disagree. The latter data set, which uses an estimator of the polarization designed to reveal only exchange effects, not spin-orbit effects, is a rather better match to the constant polarization, predicted by the new theory of this chapter, than to any of several band-structure theories, reviewed in that chapter.

Measurements of reflected beam polarization from an iron $(110)$ surface, as a function of incident electron energy and angle of incidence, have been reviewed [4]. No error estimates are given^2.5, rendering it impossible to judge the relative merits of theories quantitatively, by these measurements. However, it is easy to imagine that the random errors are large enough that the measurements are consistent with the energy-independent, angle-independent, possibly non-zero polarization predicted in the new theory of this chapter. However, the relevant band-structure theories, reviewed earlier in this chapter, provide approximately an equally good fit.

Figure 2.9: A Figure Reproduced from ``Elastic Spin-Polarized Low-Energy Electron Scattering from Magnetic Surfaces'' [4], Showing Experimental Measurements on a Graph of Reflected Electron Beam Polarization, Due to Exchange Effects, from $Fe(110)$, as a Percentage, against Electron Energy. For High Energies (above $\sim{}60\,\mathrm{eV}$,) the Simple, New Theory of This Chapter Predicts an Energy-Independent Polarization.

Also reviewed [1] are measurements of reflected beam polarization from a platinum $(111)$ surface, as a function of the orientation of the scattering plane, relative to the crystal axes, at an incident electron energy of $60\,\mathrm{eV}$, and an angle of incidence of $43.5\,\mathrm{^{\circ}}$. Again, no error estimates are given, rendering it impossible to judge the relative merits of theories quantitatively, by these measurements. However, visually, the results appear to provide a superb match to the predictions of a band-structure calculation for this material, reviewed earlier in this chapter [1], and a very dubious match to the zero polarization predicted by the new theory of this chapter. Because the measurements were all taken at the same beam energy, the conjecture above, regarding narrow energy bands that are outside the domain of validity of the new theory in this chapter, might apply.

Also reviewed [1] are measurements of reflected beam polarization from a gold $(110)$ surface, as a function of angle of incidence and temperature, at an incident electron energy of $50\,\mathrm{eV}$. Once again, no error estimates are given, rendering it impossible to judge the relative merits of theories quantitatively, by these measurements. However, it does appear that there are substantial polarizations (up to $0.6$,) which vary with angle of incidence. At energies as low as $50\,\mathrm{eV}$, the lowest-order Taylor expansion in the inverse energy, which is used in the new theory of this chapter, is becoming dubious, and it is therefore not clear what this theory predicts, but if the Taylor expansion were valid, it would predict zero polarizations for all angles of incidence. Because the measurements were all taken at the same beam energy, the conjecture above, regarding narrow energy bands that are outside the domain of validity of the new theory in this chapter, might apply.

Since the bulk of this thesis was completed, the author has also become aware of published experimental data [55] on the spin polarization of a reflected electron beam from a $Co/Cu(001)$ film; the experiment was undertaken at a incident electron energy of $17\,\mathrm{eV}$, and for a range of thicknesses up to $\sim{}2.5\,\mathrm{ML}$; the intention was to detect the onset of ferro-magnetism with increasing thickness. Both the thicknesses and the beam energy are considerably lower than those studied in the new experiments presented in this thesis; therefore, the results are not directly comparable. At the onset of ferro-magnetism, a jump was observed from a spin polarization of zero to an ``asymmetry'' of $\sim{}0.19$. It is not clear whether this ``asymmetry'' represents an absolute polarization, or whether it requires calibration with something akin to a detector Sherman function.