List of Figures

1. A Figure Reproduced from ``Elastic Spin-Polarized Low Energy Electron Diffraction from Non-Magnetic Surfaces'' [1], Showing the Comparison between a Band-Structure Calculation (Lines) and Experimental Measurements (Vertical Bars,) on Graphs of Reflected Electron Beam Polarization, from $Ni(001)$, against Electron Energy, for a Variety of Angles of Incidence $\theta$. For High Energies (above $\sim{}60\,\mathrm{eV}$,) the Simpler New Theory of This Chapter Predicts an Energy-Independent Polarization. The Figure Mentions that $\phi {} = 0$. The Source Describes $\phi {}$ as the `Azimuthal Angle,' and Explains That This Is the Angle Between Some Fixed Crystallographic Axis and the Normal to the Scattering Plane; Returning to the Source's Source [2] Reveals That the Fixed Crystallographic Axis is $[110]$.
2. Surface of a Bulk Magnetic Sample
3. Reflection of an Electron Wave by a Single Step in Electric Potential and Magnetic Flux Density
4. Predicted Reflected Beam Polarization against the Ratio of Weiss Field to Electric Potential, in the Sample
5. Reflection Paths for an Electron Wave in a Single Magnetic Layer
6. Current Arriving at Channeltron 1, against Rotation Angle of Sample; Points with Error Bars Show Experimental Results, and Lines Show the Predictions of Best-Fit Versions of Two Models, One with a Reflection Coefficient Independent of Angle of Incidence $I$, and One with a Reflection Coefficient Proportional to $\frac{1}{\cos^4I}$.
7. Current Arriving at Channeltron 2, against Rotation Angle of Sample; Points with Error Bars Show Experimental Results, and Lines Show the Predictions of Best-Fit Versions of Two Models, One with a Reflection Coefficient Independent of Angle of Incidence $I$, and One with a Reflection Coefficient Proportional to $\frac{1}{\cos^4I}$.
8. A Graph of the $[100]$ Component of the Magnetic Flux Density $B$, Inside the Surface Layers of $Co/Cu(001)$ Samples, as Measured Using MOKE, against the $[100]$-Direction Applied Magnetic Field Strength $H$; the Thickness of the Cobalt Layer in Any Individual Sample Is Denoted by $t$, and the Thicknesses Overlap with the Domain of Thicknesses Used for the Main Polarized Electron Reflection Experiments, Presented in this Thesis. These data have previously appeared in Electron Spin Polarimetry Studies of Ultra-Thin Magnetic Films [3].
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.
10. The Compact Retarding Potential Mott Polarimeter. $G$ Represents the Rate at which Electrons Arrive at the Front of the Polarimeter, $a$ the Fraction of Those Electrons that Are Accepted into the Polarimeter, and $H_i$ the Rate at which Electrons Are Scattered towards Channeltron $i$.
11. A Channeltron
12. A Misaligned Incident Electron Beam. Based on a diagram by Gay & Dunning [5]
13. A Schematic Diagram of the Pumps and Pressure Measurement Apparatus Connected to the Ultra-High Vacuum (UHV) Chamber, inside Which the Experiments Were Conducted; Arrows Represent Flows of Gas, and Broken Lines Represent Pressure Measurements; Pirani Gauges Measure Total Pressure in a High-Pressure Range between $4\times{}10^{-2}\,\mathrm{mbar}$ and $5\,\mathrm{mbar}$, the Penning Gauge Measures Total Pressure in an Intermediate Range, and the Ion Gauge Measures Total Pressure in a Low-Pressure Range between $8\times{}10^{-11}\,\mathrm{mbar}$ and $10^{-5}\,\mathrm{mbar}$; the Mass Spec Measures Total Pressure, and the Partial Pressures of Individual Gas Species.
14. A Schematic Diagram of the Equipment for Preparing the Sample, Contained in the UHV Chamber; Each Arrow Represents a Flow of Matter or Energy, Described alongside the Arrow, from an Item of Equipment to the Sample, Designed to Alter the Sample in a Manner Described Later in This Chapter.
15. A Schematic Diagram of the Equipment for Measuring or Observing Characteristics of the Sample; Arrows with Hollow Heads Represent Flows of Matter or Energy into the Sample, Used To Illuminate or Excite the Sample, To Render a Measurement Possible; Arrows with Filled Heads Represent Information-Carrying Flows of Matter out of The Sample; where the Arrow Is Solid, the Experiment It Represents Has Been Successfully Undertaken in This UHV Chamber; where the Arrow Is Broken, the Experiment Is a Future Possibility; Arrows of the Same Colour All Relate to the Same Illumination or Excitation of the Sample.
16. A Photograph of the UHV Chamber, inside Which the Experiments Were Conducted
17. The Sample Holder
18. Schematic Diagram of the Argon Ion Sputtering Gun
19. Schematic Diagram of the Manganese Evaporator
20. Measured Electron Arrival Rate (Points with Error-Bars) at Detectors against Incident Beam Energy for an Incident Beam Current of $(6\pm{}0.1)\,\mathrm{\mu{}A}$, Both Sample Magnetization Directions, and substrate 9 with No Film, and Corresponding Predictions from the New, Classical-Field Theory of Chapter 2 (Lines.)
21. Measured Electron Arrival Rate (Points with Error-Bars) at Detectors against Incident Beam Energy for an Incident Beam Current of $(6\pm{}0.1)\,\mathrm{\mu{}A}$, Both Sample Magnetization Directions, and Thickness 5 ( $(12.4\pm{}1.7)\,\mathrm{nm}$) on substrate 9, and Corresponding Predictions from the New, Classical-Field Theory of Chapter 2 (Lines.)
22. Deflection of an Electron Beam by a Stray Magnetic Field
23. The Distance along the Polarimeter Front that the Reflected Electron Beam Is Displaced, on Reversing the Stray Magnetic Field, against Stray Magnetic Flux Density
24. Traditional Estimator of Mott Asymmetry against Film Thickness and Incident Beam Energy, for Films on Substrate 9. The Thickness Axis Has a Fractional Calibration Error of $\pm {}14\%$. The Lines Are a Guide to The Eye. No Error Bars Are Shown; the Dominant Random Errors Are Those in Mott Asymmetry, Which Are of the Order of $0.005$.
25. Graph of spin-averaged scattering probability $\Gamma$ against energy loss window $W$, from the calibration data for the compact retarding-potential Mott polarimeter, provided in ``High-efficiency retarding-potential Mott polarization analyzer'' [6]. The error bars represent the standard deviations associated with the quantization of the author's readings from the published graph.
26. Graph of Sherman function $S$ against energy loss window $W$, from the calibration data for the compact retarding-potential Mott polarimeter, provided in ``High-efficiency retarding-potential Mott polarization analyzer'' [6]. The error bars represent the sums in quadrature of the standard deviation associated with the quantization of the author's readings from the published graph, and the error quoted on the published graph.
27. A Graph of the Inferred Electrostatic Potential in the Sample, in the Null Model, against $Co$ Thickness. The Conversion factor between the Units of Thickness on the Horizontal Axis, and More Conventional Thickness Units, Is (appendix B) $(78\pm{}11)\,\mathrm{\mu{}m}\,\mathrm{A}^{-1}\,\mathrm{s}^{-1}$.
28. A Graph of the Inferred Electrostatic Potential in the Sample, in the Main Model, against $Co$ Thickness. The Conversion factor between the Units of Thickness on the Horizontal Axis, and More Conventional Thickness Units, Is (appendix B) $(78\pm{}11)\,\mathrm{\mu{}m}\,\mathrm{A}^{-1}\,\mathrm{s}^{-1}$.
29. A Graph of the Inferred Magnetic Flux Density in the Sample, in the Main Model, against $Co$ Thickness. The Conversion factor between the Units of Thickness on the Horizontal Axis, and More Conventional Thickness Units, Is (appendix B) $(78\pm{}11)\,\mathrm{\mu{}m}\,\mathrm{A}^{-1}\,\mathrm{s}^{-1}$.
30. The Convergence of the Electrostatic Potential with No Film, Displayed as a Graph of the Iteration Mean and Root Mean Square of the Potential, for Each Model, Against Iteration Number
31. The Convergence of the Electrostatic Potential with Film Thickness 5, Displayed as a Graph of the Iteration Mean and Root Mean Square of the Potential, for Each Model, Against Iteration Number
32. The Convergence of the Magnetic Flux Density with Film Thickness 5, Displayed as a Graph of the Iteration Mean and Root Mean Square of the Flux Density, for the Main Model, Against Iteration Number
33. Measured Current at Detectors against Incident Beam Energy for an Incident Beam Current of $(108.8\pm{}0.2)\,\mathrm{\mu{}A}$, Both Sample Magnetization Directions, and Thickness 3 ( $(1800\pm{}260)\,\mathrm{pm}$) on Substrate 2.
34. Histogram Showing the Sum of the Likelihood Density Functions, for Multiple Detector Current Measurements, against Current at the Detectors, for an Incident Beam Energy of $(1000\pm{}0.29)\,\mathrm{eV}$, an Incident Beam Current of $(108.65\pm{}0.4)\,\mathrm{\mu{}A}$, Both Sample Magnetization Directions, and Thickness 4 ( $(2540\pm{}360)\,\mathrm{pm}$) on Substrate 2.
35. Histogram Showing the Sum of the Likelihood Density Functions, for Multiple Detector Current Measurements, against Current at the Detectors, for an Incident Beam Energy of $(1000\pm{}0.29)\,\mathrm{eV}$, an Incident Beam Current of $(108.25\pm{}0.04)\,\mathrm{\mu{}A}$, Both Sample Magnetization Directions, and Thickness 5 ( $(3250\pm{}510)\,\mathrm{pm}$) on Substrate 2.
36. Measured Electron Arrival Rate at Detectors against Incident Beam Energy for an Incident Beam Current of $(6\pm{}0.029)\,\mathrm{\mu{}A}$, Both Sample Magnetization Directions, and Substrate 4 with No Film. These data have previously appeared in Electron Spin Polarimetry Studies of Ultra-Thin Magnetic Films [3].
37. Measured Electron Arrival Rate at Detectors against Incident Beam Energy for an Incident Beam Current of $(6\pm{}0.029)\,\mathrm{\mu{}A}$, Both Sample Magnetization Directions, and the Film ( $(8.4\pm{}1.6)\,\mathrm{nm}$) on Substrate 7. These data have previously appeared in Electron Spin Polarimetry Studies of Ultra-Thin Magnetic Films [3].