  An explanation is given for the charge order, orbital order and insulating
state observed in half-doped manganese oxides, such as
Nd$_{1/2}$Sr$_{1/2}$MnO$_{3}$. The competition between the kinetic energy of
the electrons and the magnetic exchange energy drives the formation of
effectively one-dimensional ferromagnetic zig-zag chains. Due to a topological
phase factor in the hopping, the chains are intrinsically insulating and
orbital-ordered. Most surprisingly, the strong Coulomb interaction between
electrons on the same Mn-ion leads to the experimentally observed charge
ordering. For doping less than 1/2 the system is unstable towards phase
separation into a ferromagnetic metallic and charge-ordered insulating phase.
