  Motivated by recent observation of magnetic field induced transition in
LaCoO3 we study the effect of external field in systems close to instabilities
towards spin-state ordering and exciton condensation. We show that, while in
both cases the transition can be induced by an external field, temperature
dependencies of the critical field have opposite slopes. Based on this result
we argue that the experimental observations select the exciton condensation
scenario. We show that such condensation is possible due to high mobility of
the intermediate spin excitations. The estimated width of the corresponding
dispersion is large enough to overrule the order of atomic multiplets and to
make the intermediate spin excitation propagating with a specific wave vector
the lowest excitation of the system.
