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\large\bf {Spin-dependent cross section and spin precession of electrons in
ferromagnets}
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\underline {W. Weber}, D. Oberli, S. Riesen, and H.C. Siegmann
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{\it Laboratorium f\"{u}r Festk\"{o}rperphysik, ETH Z\"{u}rich,
CH-8093 Z\"{u}rich, Switzerland}
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weber@solid.phys.ethz.ch
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\noindent
Low energy electrons travelling across a metal are subject to
electron-electron scattering. Because of the exchange splitting in a
ferromagnetic metal this scattering becomes spin-dependent.
The origin of the scattering asymmetry is the imbalance between majority- and
minority-spin electrons in a ferromagnet. Minority holes are more abundant
than majority holes, and therefore majority-spin electrons are less
scattered than minority-spin electrons. This results in a longer mean free
path for majority-spin electrons as compared to minority-spin electrons.

To study this important phenomenon more thoroughly, the transmission of
spin-polarized electrons through free standing Au/FM/Au layers
with FM=Co, Fe is investigated. By
measuring the transmitted current for both spin polarization
$\vec{P_{0}}$ parallel and antiparallel to the sample magnetization
$\vec{M}$, the transmission asymmetry of the elastic electrons
and thus the spin-dependent cross section is determined [1].
Nonvanishing values of the asymmetry are found
within the energy range of 5 - 16 eV above the Fermi level, where an
elastic signal is still detectable. For the largest ferromagnetic film
thicknesses investigated asymmetries of up to 80 $\%$ are observed
at electron energies close to the vacuum level.

In order to fully describe the transmission of spin-polarized
electrons through ferromagnets, it turns out that it is
also important to consider the motion of the spin polarization vector.
For this purpose electrons with $\vec{P_{0}}$
perpendicular to $\vec{M}$ are also spin-analyzed
after transmission through the ferromagnetic foil [1,2].

If $\vec{P_{0}}$ is chosen perpendicular to $\vec{M}$,
the incident spin wavefunction can be described by a coherent superposition
of a spin wavefunction parallel to $\vec{M}$ and one antiparallel
to it. Due to spin-dependent absorption, the
amplitudes of the two wave functions become different on passing the
ferromagnet. A phase difference develops as well. This results in a rotation
of the spin polarization vector into the direction of $\vec{M}$
and a precession around it.

The precession angle is 15 degrees per 1 nm of Co film thickness and
20 degrees per 1 nm of Fe film thickness, measured for
electron energies close to the vacuum level. This phase difference is a
consequence of the different velocities for the majority-spin and the
minority-spin wavefunction caused by the spin dependence of the inner
potential. This motion of the spin polarization vector is in
analogy to the Faraday rotation observed when a light beam passes through a
ferromagnetic material.\\
\\
\noindent
[1] D. Oberli, R. Burgermeister, S. Riesen, W. Weber, and H.C. Siegmann,
Phys. Rev. Lett. {\bf 81}, 4228 (1998).\\
\noindent
[2] W. Weber, D. Oberli, S. Riesen, and H.C. Siegmann, New. J.
Phys. {\bf 1}, 9.1 (1999).

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