Conclusions

Having presented and analysed the experimental results, it is time to summarize the conclusions that can be drawn from these results.

1. A non-zero Weiss field in the cobalt films has been detected; according to the Bayesian model comparison method, the experimental data rule out the null hypothesis, in which no such field has been detected, very strongly indeed, leaving it with a posterior probability of $0.34\times{}10^{-2014444631}$ ; this is about as firm a conclusion as it is conceivable to obtain, although properties of the Monte Carlo method used to estimate this probability suggest that some caution should be applied to the sheer size of the number.
2. The traditional estimator of the Mott asymmetry, and therefore of the reflected electron beam's spin polarization, provides well-defined, mostly non-zero values, indicating, in support of the last aforesaid Bayesian conclusion, that, despite the systematic error in the electron arrival rates, described below, the experiments have successfully detected the cobalt's Weiss field.
3. The experimental results can be used to estimate quantitatively the electrostatic potential $V$ and Weiss field $B$ in the samples; the estimates obtained, using the Bayesian parameter estimation method, are shown in figures 5.9 and 5.10. As can be seen from the figures, the estimates produced are extremely imprecise, i.e. the quoted standard deviation random errors in them are very large. The bulk of the large random error does not result from the posterior probability distribution, over the electrostatic potential or Weiss field, having a wide peak, but rather from this probability distribution having two widely-separated peaks, associated with the fact that the theoretical equation 2.8, when inverted to give the ratio $\frac{B}{V}$, as a function of the measurable reflected beam polarization, gives two solutions for $\frac{B}{V}$, for any given polarization; however, the moderately large random errors found in the traditional estimators of Mott asymmetry, related to the fact that the measured beam polarization is, in some sense, a small difference between two large numbers (the spin-up and spin-down currents,) suggest that each of the two peaks will itself be quite broad. Ironically, this lack of precision contributes positively to the ability to draw such an immensely firm conclusion that a non-zero Weiss field has been detected; underlying the Occam's razor that implements [85,52] itself automatically in Bayesian statistics is the idea that a model should not be allowed to use information from experimental data to fine-tune its adjustable parameters, then recycle the same information to support it against other models. In the problem at hand, the model with extra adjustable parameters (non-zero Weiss fields in the cobalt films) does not significantly fine-tune those parameters using the experimental data, as is evident from the large residual random errors in those parameters. Therefore, Occam's razor does not significantly penalise this model, relative to the simpler model with the Weiss fields fixed at zero.
4. The spin polarization produced by the cobalt's Weiss field, as estimated in traditional fashion, is of a similar order of magnitude ($\sim{}10\%$) to that found by other workers in various independent laboratories, using polarized electron reflection from other ferro-magnetic transition metals (section 2.10.)
5. There is some strong evidence that the stray magnetic field of the sample (or of some part of the sample holder) is significantly affecting the electron trajectories, creating a magnetization-dependent systematic error in the measured electron arrival rates at the Mott polarimeter's detectors.

The genuine effect of the cobalt's Weiss field can be detected, even in the presence of the systematic error due to stray magnetic fields, because the two have significantly different signatures in the electron arrival rates at the channeltrons. When the sample magnetization is reversed, the characteristic behaviour caused by the stray-field systematic error is for the electron arrival rates, at the two channeltrons, to change by the same factor, in the same sense, i.e. either both increase, or both decrease. The characteristic behaviour caused by a genuine spin polarization, produced by the cobalt's Weiss field, on the other hand, is for the electron arrival rates, at the two channeltrons, to change by the same factor, in opposite senses, i.e. one increases and the other decreases. It was also this dissimilarity in signatures that allowed the systematic error to be noticed in the first place (table 5.3.)

In physical terms, the various methods used to analyse the data, namely the least-squares curve fitting of chapter 5, the asymmetry estimation of section 5.2, and the Bayesian inference of section 5.3 are all seeking the same effect, notwithstanding their substantial differences of statistical approach. All of them are testing for the electron arrival rates changing, on sample magnetization reversal, by the same factor in opposite senses. All of them are, therefore, sensitive to genuine spin polarizations, rather than to the stray-field systematic error, and all of them declare decisively that they have found such polarizations.

Of course, it is possible for both a genuine polarization and a stray field to occur simultaneously, and for their effects to be superimposed on one another. This appears to be the case in the experiments discussed in the present thesis. In this case, the systematic error in the electron arrival rates, caused by the stray field, has the following two effects.

1. Quantitative estimation of the polarizations, and therefore of the electro-magnetic parameters of the sample, by any of the data processing methods, is rather imprecise, i.e. has a large random error; however, this effect does not dominate the standard deviation random errors found in the estimates of electro-magnetic parameters, the bulk of which result from the double-valued nature of equation 2.8, when inverted to give electro-magnetic parameters as a function of spin polarization.
2. Visual inspection of the electron arrival rate data cannot easily pick out the individual effects (genuine spin polarization and stray field) from the superposition of the two.

It would, therefore, be much better if a way were found to eliminate the stray field, both to make the essential physical process of spin polarization by the exchange interaction more obvious visually, and to improve quantitative estimation of the Weiss field involved. Lind [65] found such a method for his particular experimental configuration, which involved following the field applied to magnetize the sample with a smaller applied field, in the opposite direction. It is, however, unclear how Lind determined that this method was a success, what physical mechanism allows the technique to work, and whether it will be applicable to experimental apparatus other than Lind's, such as the apparatus used for the present thesis.

Having drawn conclusions from the experimental results hereinbefore presented, some suggestions will now be given as to future research directions related to the work in this thesis.