  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
$T_\mathrm{\beta\gamma}(H)=43.8-1.55\times10^{-3}H^2$ K and
$T_\mathrm{\alpha\beta}(H)=23.9-0.73\times10^{-3}H^2$ K. The magnetic
Clausius-Clapeyron equation quantitatively explains the $H$ dependence of
$T_\mathrm{\beta\gamma}$, meanwhile, does not $T_\mathrm{\alpha\beta}$. The MCE
curve at $T_\mathrm{\beta\gamma}$ is of typical first-order, while the curve at
$T_\mathrm{\alpha\beta}$ 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.
