... ¹

Physics and Chemistry of Solids Group, Department of Physics, University of Cambridge, Madingley Road, Cambridge, UK. CB3 0HE

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... ²

Girton College, University of Cambridge, Huntingdon Road, Cambridge, UK. CB3 0JG

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... ³

vi5u0-website@yahoo.co.uk

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... ⁴

This dissertation is submitted for the degree of Doctor of Philosophy.

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... currents^2.1

Strictly, being composed of electrons, these currents are negative, but they are here presented as positive, for greater ease of discussion; all the theoretical analysis has a sign convention to match this.

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... thicknesses^2.2

In this section, the common convention of giving thicknesses in mono-layers is followed, whereas elsewhere in this thesis, thicknesses are given in units related to the metre. From comments in ``Magnetic Anisotropies of Ultrathin $Co(001)$ Films on $Cu(001)$'' [39], one can calculate that, for $Co/Cu(001)$, $1\,\mathrm{ML} = (166\pm{}36)\,\mathrm{pm}$, whereas other workers [47,58,57] state that $1\,\mathrm{ML} \approx{} 180\,\mathrm{pm}$.

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... surface^2.3

It is important to distinguish between this residual roughness of an annealed substrate surface, and the much greater roughness of as-sputtered substrates, which has been cited [38] as responsible for un-reproducible magnetic properties in epitaxial films.

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... given^2.4

However, some idea can be obtained from the level of reproducibility between different laboratories.

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... given^2.5

However, some idea can be obtained from the level of reproducibility between different laboratories.

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... given^3.1

In real experiments, the values of $R_{1\uparrow}$, $R_{1\downarrow}$, $R_{2\uparrow}$, and $R_{2\downarrow}$ are not perfectly specified, but are subject to significant random errors. In this case, the polarization obtained from equation 3.7 becomes an estimator; a given measurement will provide a polarization value, via the formula, which will not always be equal to the true value of the polarization, but whose value will be drawn from some probability distribution $P(P_{\textrm{formula}}\vert P_{\textrm{true}})$ about the true value. Frequentist statisticians might wish to ask whether it is an unbiased estimator, i.e. whether the expectation of this probability distribution is equal to $P_{\textrm{true}}$. An answer could be particularly difficult to derive, given the non-linearity of $P_{\textrm{formula}}$ in the directly measured electron arrival rates. Bayesian statisticians might prefer to abandon the estimator, and think in terms of the simpler forward probability distribution $P(R_{1\uparrow},R_{1\downarrow},R_{2\uparrow},R_{2\downarrow}\vert R_0,P_{\textrm{true}})$, using Bayes' theorem to invert it to $P(R_0,P_{\textrm{true}}\vert R_{1\uparrow},R_{1\downarrow},R_{2\uparrow},R_{2\downarrow})$

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... down^5.1

This, of course, may be a move either forward or backward in time

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... stage^5.2

Visual impressions have [86] also been used in this way in atmospheric science.

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... thickness^5.3

Drift effects on the longer time-scale between measurements on different film thicknesses would not produce the effect that needs to be explained, and are modelled within appendix 5.3.2.

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... long-term^5.4

The author has made some comments elsewhere [10] on how this situation arises.

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... characterized^5.5

This is not one of the items of controversy between Bayesian and frequentist statisticians, and is a proposition that statisticians from both camps would accept.

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... conditions^5.6

These detailed data sets are available in the transparent copy of this thesis, in the files whose names contain the word ``detailed.''

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