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Collective spin 1 singlet phase in high pressure oxygen

Oxygen, one of the most common and important elements in nature, has an exceedingly well explored phase diagram under pressure, up and beyond 100 GPa. At low temperatures, the low pressures antiferromagnetic phases below 8 GPa where O$_2$ molecules have spin S=1 are followed by the broad apparently nonmagnetic $ε$ phase from about 8 to 96 GPa. In this phase which is our focus molecules group structurally together to form quartets while switching, as believed by most, to spin S=0. Here we present theoretical results strongly connecting with existing vibrational and optical evidence, showing that this is true only above 20 GPa, whereas the S=1 molecular state survives up to at about 20 GPa. The $ε$ phase thus breaks up into two: a spinless $ε_0$ (20-96 GPa), and another $ε_1$ (8-20 GPa) where the molecules have S=1 but possess only short range antiferromagnetic correlations. A local spin liquid-like singlet ground state akin to some earlier proposals and whose optical signature we identify in existing data, is proposed for this phase. Our proposed phase diagram thus has a first order phase transition just above 20 GPa, extending at finite temperature and most likely terminating into a crossover with a critical point near 30 GPa and 200 K.