  We investigate the microscopic origin of the ferromagnetic and
antiferromagnetic spin exchange couplings in the quasi one-dimensional cobalt
compound Ca3Co2O6. In particular, we establish a local model which stabilizes a
ferromagnetic alignment of the S=2 spins on the cobalt sites with trigonal
prismatic symmetry, for a sufficiently strong Hund's rule coupling on the
cobalt ions. The exchange is mediated through a S=0 cobalt ion at the
octahedral sites of the chain structure. We present a strong coupling
evaluation of the Heisenberg coupling between the S=2 Co spins on a separate
chain. The chains are coupled antiferromagnetically through super-superexchange
via short O-O bonds.
