The phase diagram of solid oxygen in the magnetic-field-temperature (B-T) plane is revealed by magnetization and magnetotransmission measurements. The high-field phase of solid oxygen, which we term the θ phase, is induced at the temperature below 42 K. The transition fields at the α-θ and β-θ transitions are almost temperature independent, with the phase boundary being very steep. This phase boundary indicates that the entropy change is very small at the α-θ and β-θ transitions, in contrast to the entropy-driven β-γ transition at zero field. We argue that the θ phase differs from the high-temperature γ phase in terms of entropy
the molecular rotation is inhibited in the θ phase, whereas permitted in the γ phase. This finding consolidates the novelty of the θ phase.