Abstract

A theory of polarized electron reflection, at the surface of a magnetic material, is devised, predicting that the rate of electrons leaving the surface will be

$$G = \left(\frac{e^2V^2}{16E_b^2\cos^4I}+\frac{e^2\hbar^2B^2}{192m_e^2E_b^2\cos^4I}\right)\frac{F}{e}\textrm{,}$$ (1)

and that the reflected beam's polarization will be

$$P = -\frac{4e^2\hbar{}m_eVB}{12e^2m_e^2V^2+e^2\hbar^2B^2}\textrm{.}$$ (2)

$V$ represents the electrostatic potential inside the material, $B$ the Weiss field inside the material, $I$ the angle of incidence of the electron beam, $E_b$ each incident electron's kinetic energy, and $F/e$ the rate of electron incidence. The equations represent a lowest order Taylor expansion in $\frac{1}{E_b}$, which, for cobalt samples, renders them applicable as long as $E_b \gg{} \sim{}700\,\mathrm{meV}$. They also involve an assumption that that the topmost layer of the sample has a thickness $\gg{} 1\,\mathrm{nm}$.

Measurements are presented of spin-correlated electron arrival rates at a Mott-polarimeter's two detectors, from the reflected electron beam from $Co/Cu(001)$, as a function of cobalt thickness, incident energy, and incident intensity. Example results are displayed graphically in chapter 5. They are analysed using three distinct methodologies.

1. Visual inspection of the data is used to make qualitative suggestions about future directions for modelling of electron reflection processes at magnetic surfaces. A magnetization-dependent systematic error is discovered in electron arrival rates at the polarimeter's detectors, and is tentatively attributed to the deflection of the electron beam by a stray magnetic field, from the sample, or from some part of the sample holder. This raises the possibility, for the future, of using a reflected electron beam's spatial deflection, rather than its spin polarization, to characterize magnetic samples.
2. A traditional estimator of the Mott asymmetry, associated with the reflected polarization, is calculated for each combination of film thickness, incident energy, and incident intensity. Results are displayed graphically in section 5.2. The polarizations of most reflected beams from cobalt films are clearly non-zero, indicating that the experiment has successfully detected the cobalt's Weiss field. Quantitative determination of this polarization is, however, rather imprecise, and there is a puzzling non-zero asymmetry from the bare copper surface.
3. It is argued that the accuracy of the traditional estimator may be compromised by its non-linearity in the electron arrival rates; therefore, Bayesian inference is used to estimate the parameters in two adaptive models, based on the above theory, and to estimate relative probabilities for these models, equipped with the data. One model has a non-zero Weiss field in the films, the other does not. Results of the parameter estimation are displayed graphically in sections 5.3.2 and 5.3.3; quantitative estimation of the sample properties is, as for the traditional estimator, rather imprecise. The data are found to rule out a null hypothesis, in which the cobalt's Weiss field is zero, very strongly, leaving it with a posterior probability of $0.34\times{}10^{-2014444631}$ , indicating firmly that the experiment has successfully detected the cobalt's Weiss field.

These measurements were preceded by a process (sections 5.4, 5.5) of trial and error, in which attempted measurements of the spin polarization of reflected electron beams revealed sources of systematic error, which were addressed by adaptations to the polarimeter, and to the experimental technique.