Suggestions for Further Work

• It would be intriguing to attempt to repeat Lind's [65] method of eliminating the stray-field systematic error, by following the applied field used to set the sample magnetization direction with a smaller applied field in the opposite direction. As well as experimental reproduction of the technique, some theorizing would be in order, in the hope of understanding the physical mechanisms behind it.
• As a complement to attempts to eliminate the spatial deflection of the electron beam by a stray field from the sample or sample holder, there may be benefits in attempting to use this spatial deflection, along with spatially-resolved detection of the reflected beam, as an alternative means of determining a sample's magnetic state using an electron beam.
• The numerical method, presented in this thesis, for obtaining summary data about the Bayesian posterior probability distributions, given the experimental data presented here, has performed disappointingly: it was very slow to run, taking CPU time of the order of a month to reach the conclusions presented here, and even after this time, there remains some doubt over whether it has reached a final conclusion on the marginal likelihoods used for model comparison, given that the likelihood function may not vary smoothly in parameter space. The slowness is in large part due to the many extra adjustable parameters, which have had to be inserted into the physical models, to handle the systematic errors now attributed to stray magnetic fields, and experimental techniques that eliminate these errors may resolve the problems with the numerical method. Nevertheless, there may be benefits in exploring alternative numerical methods, particularly if it is possible to increase the simplicity of their implementation by using adaptations of widely-available fitting software, rather than having to program a Markov chain Monte Carlo method anew; since completing the analysis herein presented, the author has, in the course of a separate experimental project, made considerable progress in devising means whereby, with a little algebra, ubiquitous chi-squared fitting routines can be used for Bayesian parameter estimation and model comparison.
• It will soon be necessary to consider what kinds of samples it is most interesting to examine with the polarized electron reflection technique; the $Co/Cu(001)$ structure considered in this thesis was chosen primarily as a trial system, for development of the instrumentation. Above, the $c(2\times{}2)$ surface alloy of manganese on a cobalt $(001)$ surface, with a copper substrate, was also mentioned as a candidate system for examination by polarized electron reflection. The author would characterize the motivation for experiments on this alloy as aesthetic: the wish to peer deeper into a beautiful and unusual system. The author has discussed with colleagues a number of other combinations of copper, cobalt, and manganese, which hold similar interest. However, as has been discussed elsewhere [10], the author now takes the view that the scientific value of experimental results stems primarily not from their aesthetic appeal, but from their ability to help policy-makers reach better decisions. In the case of research in magnetic film structures, the most relevant policy-makers are managers in the magnetic data storage industry, and the most relevant decisions are those about which systems of magnetic materials to include in future hard discs, read heads, and magnetic random access memories. The author believes that the time is ripe to consult managers in this industry about how they can use information about the Weiss fields of materials in multi-layer structures, and what multi-layer structures are most important to them.