  By using ab initio methods on different levels we study the magnetic ground
state of (finite) atomic wires deposited on metallic surfaces. A
phenomenological model based on symmetry arguments suggests that the
magnetization of a ferromagnetic wire is aligned either normal to the wire and,
generally, tilted with respect to the surface normal or parallel to the wire.
  From a first principles point of view, this simple model can be best related
to the so--called magnetic force theorem calculations being often used to
explore magnetic anisotropy energies of bulk and surface systems. The second
theoretical approach we use to search for the canted magnetic ground state is
first principles adiabatic spin dynamics extended to the case of fully
relativistic electron scattering. First, for the case of two adjacent Fe atoms
an a Cu(111) surface we demonstrate that the reduction of the surface symmetry
can indeed lead to canted magnetism. The anisotropy constants and consequently
the ground state magnetization direction are very sensitive to the position of
the dimer with respect to the surface. We also performed calculations for a
seven--atom Co chain placed along a step edge of a Pt(111) surface. As far as
the ground state spin orientation is concerned we obtain excellent agreement
with experiment. Moreover, the magnetic ground state turns out to be slightly
noncollinear.
