  Magnetic, dielectric, and magnetoelectric properties in a spin-state
transition system are examined, motivated by the recent discovery of a
multiferroic behavior in a cobalt oxide. We construct an effective model
Hamiltonian based on the two-orbital Hubbard model, in which the spin-state
degrees of freedom in magnetic ions couple with ferroelectric-type lattice
distortions. A phase transition occurs from the high-temperature low-spin phase
to the low-temperature high-spin ferroelectric phase with accompanying an
increase of the spin entropy. The calculated results are consistent with the
experimental pressure-temperature phase diagram. We predict the magnetic-field
induced electric polarization in the low-spin paraelectric phase near the
ferroelectric phase boundary.
