  We study here, both experimentally and theoretically, the anisotropy of
magnetoresistance in atomic contacts. Our measurements on iron break junctions
reveal an abrupt and hysteretic switch between two conductance levels when a
large applied field is continuously rotated. We show that this behaviour stems
from the coexistence of two metastable electronic states which result from the
anisotropy of electronic interactions responsible for the enhancement of
orbital magnetization. In both states giant orbital moments appear on the low
coordinated central atom in a realistic contact geometry. However they differ
by their orientation, parallel or perpendicular, with respect to the axis of
the contact. Our explanation is totally at variance with the usual model based
on the band structure of a monatomic linear chain, which we argue cannot be
applied to 3d ferromagnetic metals.
