  Recently, there has been a revival of interest in mechanisms for changing the
spin polarization of an electron beam on transmission through, or reflection
from, a magnetic surface. An understanding of these mechanisms would allow the
use of an electron beam as a polarized radiation probe for magnetic
characterization, like light in MOKE and neutrons in PNR. Here, a mechanism is
described which, unlike simultaneously occurring processes proposed elsewhere,
polarizes an unpolarized incident beam without recourse to inelastic processes.
  A magnetic field leads to a Zeeman term in an electron's Hamiltonian, which
depends on the angle theta 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 1,) the wave-number of the transmitted wave depends
on theta. When the conditions of continuity of the wave-function, and of its
first spatial derivative, at the surface, and conservation of particles, are
applied, an electron reflection coefficient is obtained which also depends on
theta. Therefore, some polarizations are preferentially reflected, while others
are preferentially transmitted. The amplitude reflection and transmission
coefficients can readily be converted to intensity coefficients, and averaged
over an incoherent superposition of electron waves of different theta, e.g. an
unpolarized incident beam. The reflected polarization is P = -(2 e mu_B V B)/(3
e^2 V^2 + mu_B^2 B^2), which can take values -1/sqrt(3) <= P <= 1/sqrt(3),
depending on the balance between V and B.
  The analysis can be extended to multi-layers using the theory of Fabry-Perot
etalons.
