  We study domain wall solutions of a real spinor field coupling with
gravitation in five dimensions. We find that the nonlinear spinor field
supports a class of soliton configurations which could be viewed as a wall
embedded in five dimensions. We begin with an illuminating solution of the
spinor field in the absence of gravitation. In a further investigation, we
exhibit three sets of solutions of the spinor field with nonconstant curvature
bulk spacetimes and three sets of solutions corresponding to three constant
curvature bulk spacetimes. We demonstrate that some of these solutions in
specific conditions have the energy density distributions of domain walls for
the spinor field, where the scalar curvature is regular everywhere. Therefore,
the configurations of these walls can be interpreted as spinor walls which are
interesting spinor field realizations of domain walls. In order to investigate
the stability of these spinor configurations, the linear perturbations are
considered. The localization of the zero mode of tensor perturbation is also
discussed.
