Magnetic field (H) effects on a correlated electron system with the spin-state degree of freedom are examined. The effective Hamiltonian derived from the two-orbital Hubbard model is analyzed by the mean-field approximation. Applying H to the low-spin (LS) phase induces the excitonic insulating phase, as well as the spin-state ordered phase where the LS and high-spin (HS) states are ordered alternately. In the case where H is applied to the HS phase, a reentrant transition for the HS phase appears. A rich variety of the phase diagrams are attributed to the spin-state degree of freedom and their combinations in the wave function as well as in the real-space configuration. Present results provide a possible interpretation for the recent experimental observation under the strong magnetic field in LaCoO 3 . KEYWORDS: spin state, magnetic field, excitonic insulatorSpin-state degree of freedom (SSDF) in the transitionmetal ions have been widely recognized as one of the indispensable factors which provide rich variety of physics in magnetic solids. There are multiple spin states in a single magnetic ion due to the different local electron configurations. Transitions between the multiple spin states are often seen in the iron and cobalt ions which are included not only in correlated electron materials, 1-3) but also in biomaterials, 4) and earth innercore materials. 5-7) A driving force of the spin-state transition is attributed to a competition between the crystalline-field effect and the Hund's coupling, which stabilize the low-spin (LS) and high-spin (HS) states, respectively. 8,9) Perovskite cobalt oxides and their derivatives are the prototypical examples of the correlated electron materials with SSDF. A nominal valence of the cobalt ion in LaCoO 3 is 3+ where the number of electrons occupying the 3d orbitals is six. The characteristic temperature dependences of the electrical resistivity and the magnetic susceptibility are interpreted as a crossover between the LS state of the (t 2g ) 6 configuration with S = 0 and the HS states of (t 2g ) 4 (e g ) 2 with S = 2. 2) Several exotic phenomena, such as the giant magnetoresistance, 10) magnetic clusters, 11,12) and a ferroelectricity, 14) are attributable to the spin-state change.Correlated electron materials with SSDF is recently reexamined as a plausible candidate of the excitonic insulator (EI). [15][16][17] The EI state has been studied since 1960s in the narrow gap semiconductors and semimetals, [18][19][20][21][22] and is recently reexamined from the modern viewpoints. 23,24) The EI state is expected to be realized, when the exciton binding energy exceeds the band gap energy. Since the LS and HS states in the cobalt oxides are identified as a band insulator and a Mott insulator, respectively, a narrow-gapped state is expected around a crossover between the two spin states. Actually, a phase transition around 90K observed in Pr 0.5 Ca 0.5 CoO 3 is examined from the viewpoints of the EI phase transition. 16) It is required to develop how to control the spin states ...