The magnetic-field-temperature phase diagram of solid oxygen is investigated by the adiabatic magnetocaloric effect (MCE) measurement with pulsed magnetic fields. Relatively large temperature decrease with hysteresis is observed at just below the $beta$-$gamma$ and $alpha$-$beta$ phase transition temperatures owing to the field-induced transitions. The magnetic field dependences of these phase boundaries are obtained as $T_mathrm{betagamma}(H)=43.8-1.55times10^{-3}H^2$ K and $T_mathrm{alphabeta}(H)=23.9-0.73times10^{-3}H^2$ K. The magnetic Clausius-Clapeyron equation quantitatively explains the $H$ dependence of $T_mathrm{betagamma}$, meanwhile, does not $T_mathrm{alphabeta}$. The MCE curve at $T_mathrm{betagamma}$ is of typical first-order, while the curve at $T_mathrm{alphabeta}$ seems to have both characteristics of first- and second-order transitions. We discuss the order of the $alpha$-$beta$ phase transition and propose possible reasons for the unusual behavior.
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