  Magneto-resistance is a physical effect of great fundamental and industrial
interest since it is the basis for the magnetic field sensors used in computer
read-heads and Magnetic Random Access Memories. As device dimensions are
reduced, some important physical length scales for magnetism and electrical
transport will soon be attained. Ultimately, there is a strong need to know if
the physical phenomena responsible for magneto-resistance still hold at the
atomic scale. Here, we show that the anisotropy of magneto-resistance is
greatly enhanced in atomic size constrictions. We explain this physical effect
by a change in the electronic density of states in the junction when the
magnetization is rotated, as supported by our ab-initio calculations. This
stems from the "spin-orbit coupling" mechanism linking the shape of the
orbitals with the spin direction. This sensitively affects the conductance of
atomic contacts which is determined by the overlap of the valence orbitals.
