Single-crystal X-ray diffraction provides evidence for spin collapse in solid oxygen

Oxygen is unusual among simple diatomic molecules because it has a molecular spin (S=1), which leads to a rich phase diagram. Below 8-10 GPa, intermolecular magnetic interactions align the spins antiparallel, forming the antiferromagnetic (AFM) α and δ phases – the only known examples of insulating elemental antiferromagnets. Above 10 GPa, oxygen transforms into the ε-O₂ phase, a deep-red semiconducting solid formed by molecular clustering into (O₂)₄ tetramers [1]. At the δ-ε phase transition, neutron diffraction reveals the collapse of long-range antiferromagnetic order [2], but whether O₂ molecules retain their individual spin moments has remained unclear. 

Theoretical models suggest that ε-O₂ exists in two distinct forms: a lower-pressure variant (< 20 GPa) with residual molecular spin, designated ε₁, and a higher-pressure (> 20 GPa) spinless form, ε₀, resulting from complete magnetic collapse [3]. In ε₁, the O₂ molecules maintain S=1 with short-range antiferromagnetic correlations within (O₂)₄ tetramers, producing a spin-liquid-like state in which four spin-1 molecules couple magnetoelastically into a singlet, cancelling their total magnetic moment while retaining strong local spin dynamics. In ε₀, the O₂ molecules have S=0 and exhibit no spin activity.

No ε1- ε0 transition had been detected in previous X-ray diffraction (XRD) studies [1], likely due to the subtle magnetoelastic nature of the transition or experimental limitations. To address this, high-precision single-crystal XRD measurements were conducted at the ID27 beamline. Oxygen single crystals were grown from He/O₂ fluid mixtures in diamond anvil cells (DACs) at 150°C and 11–13 GPa, then cooled gradually to room temperature (Figure 1a). Multiple annealing cycles were performed until a high-quality single crystal was obtained. The best crystal had a needle-like morphology, approximately 10 μm long and 2 μm wide. 
 

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Fig 1: a) ε-O₂ single crystals in helium within a diamond anvil cell at ≈ 12 GPa. b) Molecular structure of the ε phase, showing the (O₂)₄ tetramer unit characteristic of this phase.

Single-crystal XRD patterns were collected over 10 - 30 GPa. The structural integrity of the single-crystal domain was preserved up to about 21 GPa, enabling refinement of atomic positions. At higher pressures, the lattice parameters remained measurable, although atomic positions became less reliable. Measurements were performed with the EIGER2 X CdTe 9M area detector and monochromatic radiation (λ=0.3738 Å) focused to a 0.5 × 0.5 μm² beam spot, allowing regions smaller than individual crystal domains to be probed. This experiment was among the first high-pressure single-crystal XRD studies at ID27 after the EBS upgrade. 

Full structural refinements of the ε-O₂ phase (space group C2/m) were performed between 11 and 21 GPa, determining lattice parameters as well as all intra-O₈ distances (d₁–d₄) and angles (θ₁ and θ₂) that define the O₈ rhomboid. The analysis confirms the (O₂)₄ tetramer arrangement previously reported in [1], now resolved with higher accuracy (Figure 1b).

Figure 2 shows the pressure dependence of lattice parameters and unit-cell volume. Discontinuities at 18.1 ± 0.5 GPa were observed in two intra-cluster distances (d₂ and d₄) as well as in the lattice parameter a and monoclinic angle β. The volume compression curve also shows a change at this pressure, fitting better to two separate Birch-Murnaghan equations of state below and above the transition.
 

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Fig 2: Pressure dependence of the lattice parameters β a, b, and c (a,b) and the unit-cell volume (c) of ε-O₂, measured during compression. Lattice parameters are normalised to their values at 11.6 GPa.

These discontinuities provide strong evidence for a first-order isostructural phase transition, corresponding to the predicted ε1–ε0 transition [3]. This structural signature indicates the collapse of spin in ε-O₂, marking the transformation from a spin-liquid-like state within (O₂)₄ tetramers to a fully spinless molecular arrangement. Confirming the spin-liquid state structurally, and its subsequent collapse, opens opportunities to explore broader physical properties of these magnetically orchestrated tetramers, potentially revealing new insights into correlated quantum states in simple molecular solids.
 

Principal publication and authors
Structural Evidence for the Spin Collapse in High Pressure Solid Oxygen, F.A. Gorelli et al., Phys. Rev. Lett. 135, 076101 (2025); https://doi.org/10.1103/jvd7-v9h9

References
[1] L.F. Lundegaard et al., Nature 443, 201 (2006); H. Fujihisa et al., Phys. Rev. Lett. 97, 085503 (2006).
[2] I. N. Goncharenko, Phys. Rev. Lett. 94, 205701 (2005).
[3] Y. Crespo et al., Proc. Natl. Acad. Sci. U.S.A. 111, 10427 (2014); earlier suggestions by H.V. Gomonay, V. M. Loktev, Phys. Rev. B 76, 094423 (2007); M. Bartolomei et al, Phys. Rev. B 84, 092105 (2011).