The Co-59-NMR on single crystals of LaCoO3 has been studied in order to inv
estigate the spin-stale transition through the nuclear-spin relaxation in t
his compound. Below T similar to 35 K, the spin-lattice and spin-spin relax
ation rates show a thermal-activation-type temperature dependence with an e
nergy gap of similar to 180 K. This value is close to the energy difference
between the low spin state (S=0) and the intermediate spin state (S=1) pre
dicted in the two-stage spin-state transition model with the intermediate s
pin state. The apparent spin-spin relaxation rates depend on the resonance
peaks split due to the nuclear-electric-quadrupole interaction, which is ex
plained by an indirect nuclear spin-spin interaction through the interactin
g paramagnetic electron spins. This observation is consistent with the ferr
omagnetic short-range correlation among the electron spins on Co3+ ions con
firmed by neutron-scattering experiments.