  We consider a spinor domain wall embedded in a five-dimensional spacetime
with a nondiagonal metric. The corresponding plane symmetric solutions for
linear and nonlinear spinor fields with different parameters are obtained. It
is shown that in the general case the metric functions and spinor fields do not
possess $Z_2$ symmetry with respect to the domain wall. We study the angular
momentum density of the domain wall arising because of the presence of the
spinor field creating the wall. The properties of test fermions located on an
arbitrary domain wall are considered. The concepts of the ``second spin''
(arising due to the properties of the Lorentz group generators in a
five-dimensional spacetime) and of the ``second magnetic field'' (representing
the components $F_{i 5}$ of the electromagnetic field five-tensor) are
introduced. We find eigenspinors of the ``second spin'' and show that some of
them represent the Bell states. In the nonrelativistic limit we derive the
Pauli equation for the test fermions on the domain wall which contains an extra
term describing the interaction of a spin-$1/2$ particle with the ``second
magnetic field''; this allows the possibility of an experimental verification
of the existence of extra dimensions.
