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(1) |
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(2) |
represents the electrostatic potential inside the material, 
the Weiss field inside the material, 
the angle of incidence of the
electron beam, 
each incident electron's kinetic energy, and
the rate of electron incidence. The equations represent a
lowest order Taylor expansion in 
, which, for cobalt
samples, renders them applicable as long as
. They also involve an assumption that that the
topmost layer of the sample has a thickness
.
Measurements are presented of spin-correlated electron arrival rates
at a Mott-polarimeter's two detectors, from the reflected electron beam
from 
, 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.
- 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.
- 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.
- 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
, 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.
between the electron's spin vector and the magnetic
flux. As a result, when an electron wave is incident on the surface
of a bulk magnetic material (figure 
and 
.
![\includegraphics[width=\textwidth, height=0.75\textwidth]{dhatton1}](./Natural_Sciences/Classical-Field_Theory_of_Electron_Waves_as_a_Polarized_Radiation_Probe_of_Magnetic_Surfaces/img10.png)
forms (B.-Ch. Choi, P. J. Bode, and
J. A. C. Bland. 
ferromagnetic surface alloy on 
overlayers
surface alloy
films on fcc 
. J. Magn. Magn. Mater., 1996) an issue of
controversy.
sample have been
measured.
magnetic multilayer (figure 
) Measurements Obtained Using Formula for Multiplicative
Systematic Error Elimination for Each Run of the Experiment
![$[100]$](./Natural_Sciences/Mott_Polarimetry_at_the_Cavendish_Laboratory/img59.png){kind=small}
in the remanent state after application of a strong
magnetic field in the ![$\pm [100]$](./Natural_Sciences/Mott_Polarimetry_at_the_Cavendish_Laboratory/img71.png){kind=small}
direction. This does not, of itself, demonstrate
that the manganese and cobalt layers have parallel magnetizations, nor
that the manganese layer is internally ferromagnetic. It does,
however, demonstrate the feasibility of similar experiments which will
be capable of settling these issues.
represents the degree of belief in
theory 
, from a set 
of available theories, before the
occurrence of evidence 
, the posterior probability 
represents the degree of belief in 
is the probability that 
.
, where 
is the number of postulates in 
is a normalizing constant to ensure
,
whereas in the Bayesian view, 
, is sometimes associated
with positivism, whereas Bayesian analysis can assess many such
theories. Fourthly, any positivist prohibition on the consideration
of evidence obtained with an ideology in mind is another example of
insistence on the assignment of particular values to prior
probabilities. Therefore, Bayesians, like standpoint epistemologists,
will think such a prohibition inappropriate.