Collective spin 1 singlet phase in high-pressure oxygenYanier Crespoa, Michele Fabriziob, Sandro Scandoloa, and Erio Tosattia,b,1

aThe Abdus Salam International Center for Theoretical Physics, 34151 Trieste, Italy; and bInternational School for Advanced Studies and Consiglio Nazionaledelle Ricerche, Istituto Officina dei Materiali Democritos, 34136 Trieste, Italy

Edited by David Vanderbilt, Rutgers, The State University of New Jersey, Piscataway, NJ, and approved June 13, 2014 (received for review March 11, 2014)

Oxygen, one of the most common and important elements innature, has an exceedingly well-explored phase diagram underpressure, up to and beyond 100 GPa. At low temperatures, thelow-pressure antiferromagnetic phases below 8 GPa where O2

molecules have spin S = 1 are followed by the broad apparentlynonmagnetic e phase from about 8 to 96 GPa. In this phase, whichis our focus, molecules group structurally together to form quar-tets while switching, as believed by most, to spin S = 0. Here wepresent theoretical results strongly connecting with existing vibra-tional and optical evidence, showing that this is true only above20 GPa, whereas the S = 1 molecular state survives up to about 20GPa. The e phase thus breaks up into two: a spinless e0 (20−96GPa), and another e1 (8−20 GPa) where the molecules have S = 1but possess only short-range antiferromagnetic correlations. A lo-cal spin liquid-like singlet ground state akin to some earlier pro-posals, and whose optical signature we identify in existing data, isproposed for this phase. Our proposed phase diagram thus hasa first-order phase transition just above 20 GPa, extending at finitetemperature and most likely terminating into a crossover witha critical point near 30 GPa and 200 K.

molecular magnetism | IR modes | Raman modes | tetramer |density functional

Molecular systems display at high pressure a horn of plentyof intriguing phases. That is especially true of molecular

oxygen, whose diatomic molecule survives unbroken up to atleast 133 GPa (1), and where the original spin S = 1 of the gasphase plays an important role. In the phase diagram of O2 (Fig.1), we focus on the wide e-O2 phase between 8 and 96 GPa,a phase which has long intrigued the community (2). Unlike thetwo bordering phases, δ-O2, an antiferromagnetic (AF) S = 1correlated insulator at lower pressure, and ζ-O2, a regular andsuperconducting nonmagnetic (NM) metal at higher pressure,e-O2 is an insulator of more complex nature. Structurally, high-pressure X-ray diffraction (3, 4) revealed in the last decade thatat the δ−e transition at P ∼ 8 GPa, the close-packed O2 planesundergo a large distortion giving rise to molecular O8 “quartets”(Fig. 1, Inset). Spin-polarized neutron diffraction showed thatsimultaneously there is a collapse of long-range AF Néel order atthe δ−e transition (5). That observation unfortunately did notprovide conclusive information about the nature of the groundstate in e-O2 and in particular about any further role played ine-O2 by the spin of individual molecules, if any. It has beentempting to imagine that the O2 molecular magnetic state couldsimply collapse from S = 1 to S = 0 at the δ−e transition. Insupport of this idea, it can be noted that the metallic state bandstructure of a hypothetical undistorted nonmagnetic O2 (6) isprone to turn spontaneously insulating through a Peierls typedistortion, for example dimerizing (7, 8) or tetramerizing (9) themolecules. Further density functional theory (DFT) calculationsstrengthened that picture, showing that the quartet distortedgeometry (10) drives the undistorted metal to a band insulator.Moreover, DFT calculations showed that this state exhibits O2vibrations whose frequency and pressure evolution are, between20 and 96 GPa, in good agreement with infrared (IR) andRaman data (11), as will be shown in First-Principles Calculationsand Results.

An alternative, much more speculative picture insisting in-stead on a correlated state where O2 retains its S = 1 gas phasespin, and where the quartet of AF coupled sites yields a singletground state as the basic O8 block of e-O2 (12), provided no suchsuccessful predictions and had limited following so far—see,however, ref. 13.Let us provide first some background before embarking on

theoretical calculations. Several experimental authors (7, 14–17)noted that the behavior of O2 in the 8- to 20-GPa pressure rangeis in many ways anomalous compared with that above 20 GPa(18). Focusing on O2 vibrations, the good agreement found byAnh Pham et al. (11) between the band insulator calculationsand the measured IR and Raman frequencies is limited to aboveP > 20 GPa. Below this pressure, the IR mode reverts non-monotonically upward approaching the high-frequency Ramanmode at the δ-O2 phase boundary of 8 GPa, rather than droppingsteadily as predicted by the band insulator. Subtly, but not lesssignificantly, the O2 Raman data show that 20 GPa marks a deli-cate but definite breaking point with a lower rate of decrease of themode frequency with decreasing pressure. Both IR and Ramanelements hint at a possible switch of individual O2 molecules fromS = 0 to S = 1 upon decreasing pressure near 20 GPa. In particular,the frequency gap between the IR mode, where nearest neighborO2 vibrate out of phase, and the Raman mode where they vibratein phase is proportional to the IR effective charge, connectedwith electron current “pumping” between an instantaneouslyextended molecule (which attracts electrons) and a neighboringcompressed one (which expels them) in the IR mode. Thiselectron current is absent in the Raman mode, where neigh-boring molecules vibrate in phase. If the molecules have spin andcorrelations are strong, the electron hopping is reduced and thecurrent magnitude, proportional to the IR effective charge, mustdrop compared with the nonmagnetic band state. Thus, theonset of molecular spin upon decreasing pressure should be ac-companied by a collapse of the IR intensity and of the IR−Raman splitting, as is indeed observed (see First-Principles

Significance

Among the elemental diatomic molecules, O2 is the only onecarrying a spin 1 magnetic moment. In the high pressure phasesof oxygen the magnetic moment conspires with intermolecularforces to generate a rich phase diagram. Whereas, up to 80,000atmospheres the moment persists, at pressures between 80,000and 200,000 atmospheres, molecular magnetism apparently dis-appears, however with a number of unexplained vibrational andoptical anomalies. Through a fully quantum treatment of theelectronic states of the dense crystalline state we find that in thispressure range oxygen still retains a spin moment in an un-conventional and rare state of matter dominated by the quan-tum fluctuations. This state, a special case of so-called spin liquids,explains most of the observed anomalies.

Author contributions: E.T. designed research; Y.C., M.F., S.S., and E.T. performed research;Y.C., M.F., S.S., and E.T. analyzed data; and Y.C., M.F., S.S., and E.T. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1To whom correspondence should be addressed. Email: tosatti@sissa.it.

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Calculations and Results). With this background, experimentalfacts suggest dividing the vast e-O2 phase into two phases. Thefirst, e0-O2, is a higher-pressure phase between 20 and 96 GPawhere there is no molecular spin and whose physics, includinglattice vibrations, is well described as a band insulator whose gapis due to the Peierls-like quartet distortion. The second phase, e1-O2, is a lower-pressure phase between 8 and 20 GPa where thatpicture fails, and molecular spin probably resurrects signaling thatstrong correlations coexist within the quartet distortion of themolecules. The long-range Néel order typical of the lower-pres-sure undistorted phases is absent here, suggesting that it might bereplaced by some kind of correlated singlet state such as that ofref. 12. However, strong and verifiable predictions about the samemeasured vibrational and optical that are well described by theband insulator in e0-O2 have not been advanced for this typeof state.Our work has the following aims: (i) Provide first-principles

quantitative calculations of electronic and vibrational propertiesof same quality for both e0-O2 and e1-O2, including Raman andIR vibrational frequencies and intensities that could be com-pared with experiment in both regimes. The approach shouldallow, even if at the approximate mean field level, for the pres-ence of molecular spin whenever that should lower the totalenthalpy. (ii) Describe the nature, stability, and optical propertiesof the resulting model S = 1 collective singlet state description ofe1-O2, extending that in literature (12, 13), particularly includingquantum fluctuations. (iii) Predict the new phase diagram dis-playing a first-order e1–e0 low temperature phase transition near20 GPa, and a novel phase line predicting at high temperaturea new critical point roughly at 30 GPa and 200 K inside the broade-O2 phase.

First-Principles Calculations and ResultsOur starting point is a density-functional theory (DFT) elec-tronic structure calculation with full structural optimization forthe whole e-O2 pressure range. We used spin-polarized, self-interaction corrected calculations (DFT+U) (19–21) as imple-mented in Quantum-ESPRESSO (22). By allowing for staticmagnetic polarization, we permit the possible presence of mo-lecular spin to emerge—of course at the price of assuming it toexist in static and thus symmetry-breaking form. The generalizedgradient approximation (GGA) exchange-correlation functionalwas used in the version of Perdew et al. (23), and DFT+U cal-culations were carried out in the simplified version of Dudarevet al. (24) as implemented in the Quantum-ESPRESSO code(25). The inclusion of a Hubbard U for oxygen p-states is calledfor to provide cancellation of self-interactions still present insimple GGA DFT. Whereas for the uncorrected choice U = 0the calculated band gap is unrealistically small and spin po-larization does not arise (10, 11), calculations in a reasonablerange of values of the parameter U (0.8, 1.0, 1.5 and 2.0 eV) yield

antiferromagnetism below 17.6, 20.0, 25.0, and 30.0 GPa, re-spectively. We selected U = 1.0 eV as the value yielding thetransition pressure that fits more reasonably the experimentalfindings to be described below in the vibrational spectra (7, 14,16). Their frequency and intensity behavior does not change withthe value of U. We note that this method to reduce self-inter-actions is convenient but by no means unique, and other possi-bilities such as hybrid functional approximations could have beenadopted. A 4 × 4 × 4 Monkhorst−Pack k-point mesh (26) Bril-louin zone sampling was used throughout. The crystal structure(C2/m) and the initial atomic positions were taken from theexperimental data (4). Lattice and internal parameters were thenfully optimized at different pressures until forces were smallerthan 10−5 a.u. The vibrational spectra were calculated using thefropho code that calculates phonons based on the Parlinski−Li−Kawazoe method (27). Infrared intensities were calculated bydensity functional perturbation theory (28) by single-point DFTcalculations with the fully DFT+U relaxed crystal structures.The optimized structure has O2 molecules forming quartets in

each plane, quite close to the experimental ones (4). A clear AFstate prevails below 20 GPa, as shown by the enthalpy differenceof Fig. 2 between the NM and the AF state, where molecules aresimultaneously quartet distorted and antiferromagnetically spinpolarized. As anticipated, the predicted low-pressure resurgenceof molecular spin comes with an unrealistic AF static long-rangeorder, which is absent in experiment (5). How this artificial meanfield symmetry breaking can be removed by quantum fluctua-tions will be described later. Ignoring that for the moment, andassuming the mean field to yield as usual a reasonable totalenergy, we can exploit our first-principles calculations to obtaina prediction for the change of other properties brought about bythe instantaneous presence of molecular spin. We calculated,with the DFT+U approach, the vibrational spectra of both thenonmagnetic and magnetic states of e-O2. As is shown in Fig. 3B,the onset of spin breaks the monotonic drop of both Raman andIR mode frequencies with decreasing pressure, which was pre-dicted for the nonmagnetic state by previous calculations (11)but which did not agree with experiment below 20 GPa. Directcomparison of Fig. 3B with Fig. 3A shows now a better agree-ment, confirming that both the nonmonotonic rise of the IRmode and the slight stiffening of the Raman mode are spin re-lated. Many other phonon modes are also influenced by theonset of spin.In Fig. 4, our calculated evolution of the main far infrared

vibrational mode (see Fig. 4B) is shown to drop below 20 GPa inagreement with experimental data (see Fig. 4A). This evolution

Fig. 1. Currently accepted phase diagram of oxygen (adapted from ref. 2).(Inset) The unit cell of e-O2 (3, 4).

Fig. 2. Enthalpy difference calculated by DFT+U between nonmagnetic andantiferromagnetic states in e-O2. (Inset) Antiferromagnetic configurationinside the O8 “quartets.”

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of both high- and low-frequency IR modes upon lowering pres-sure below 20 GPa goes together with a corresponding change—in fact a decrease—of the mode effective charge. Fig. 5 showsthat the dramatic drop of the IR intensity observed in this regime(see Fig. 5, Inset), so far unexplained, is now well accounted forby the onset of molecular spin.We already hinted at the main physical reasons why spin

causes all these changes in the vibrational spectrum. The firstelement is that spin arises in connection with strong electroncorrelations, which characterize all lower-pressure phases in-cluding δ-O2. In the strongly correlated state, O2 molecules re-duce their mutual electron hopping, and tend to revert towardtheir gas phase state, which has spin 1, with shorter bond lengthand about 71 cm−1 higher vibrational frequency (29). Thatexplains why the highest (intramolecular) Raman mode reducesits softening rate below 20 GPa (see Fig. 3). The reduced IReffective charge, and the shrinking of the frequency gap betweenthe out-of-phase IR and the in-phase Raman modes as calcu-lated and observed, implies a reduced intermolecular electronhopping in the AF correlated state.For our subsequent understanding of the magnetic state below

20 GPa, it is also important to estimate the effective Heisenbergexchange couplings among O2 molecules. Calling J1, J2, J3, and J4the exchange values between the first, second, third, and fourthneighbors (see Fig. 6), we carried out constrained spin polarizedDFT+U calculations, based on the experimental structure at P =11.4 GPa (3) and a variety of six different AF configurations.Fitting these results, we obtained J1 = 170.0 ± 30 meV, J2 = 35.5 ±2 meV, J3 = 10.5 ± 2 meV, and J4 = 14.4 ± 4 meV. On account ofthe mean-field nature of the DFT calculations, these values areprobably somewhat larger values than real and should be con-sidered upper bounds.

Lattice Singlet Model and Quantum Fluctuations of S = 1SpinsS = 1 Lattice Model. First-Principles Calculations and Resultsshowed that the resurgence of molecular spin below 20 GPacould simultaneously explain several observed O2 vibrationalanomalies. However, the mean-field long-range AF orderobtained by DFT disagreed with the lack of long-range spin or-der found experimentally (5). A state where molecular spins arepresent without T = 0 long-range order would constitute a kind ofspin 1 liquid. In this section, we discuss extending the pictureearlier proposed by Gomonay and Loktev (12) and more recentlypursued by Bartolomei et al. (13) consisting of an overall singletstate of an isolated quartet of S = 1 molecules.The quantum mechanical competition between AF long-range

order and an overall singlet state must be pursued in the wholee1-O2 lattice. For that purpose, we simplify the system as a 2Dsquare lattice model made of plaquettes (quartets) of S = 1Heisenberg sites. Each site, representing an O2 molecule, is AFcoupled to nearest neighbors within the same plaquette by AFexchange couplings J1 > 0, and to nearest neighbors in the nextplaquettes by J2 < J1; see Fig. 7. Two different states compete:the Neél AF configuration, as obtained by DFT and whichbreaks spin SU(2) symmetry, and a singlet, NM state that is akin

Fig. 3. Vibrational frequencies of the O2 stretching modes as a function ofpressure. (A) Solid line with squares: calculated Raman and IR modes fromref. 11. Dashed line with circles: Raman mode data from ref. 16. Dashed linewith triangles: IR mode data from ref. 7. Displacement patterns for the IRand Raman modes are shown in the Lower Right Inset and Upper Left Inset,respectively. (B) Calculated Raman and IR modes for the nonmagnetic andthe antiferromagnetic configurations (this work).

Fig. 4. Frequency of the far-IR vibrational mode as a function of pressure.(A) Data from ref. 7. (B) Calculations using the nonmagnetic and the anti-ferromagnetic configurations. (Inset) Calculated displacement pattern of thefar-IR mode.

Fig. 5. Calculated Intensities for mid-IR modes (1,500−1,600 cm−1) of bothnonmagnetic and antiferromagnetic configurations (this work). (Inset) Solidsquares, measured IR intensities of the mid-IR mode (1,200−1,800 cm−1);open squares, far IR mode (200−600 cm−1) intensities from ref. 7.

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to a collection of independent plaquettes, each in its singletground state. The singlet ground state of an isolated plaquette ofenergy E0 = −6J1 is obtained by coupling second neighbor sites 1and 3 to S13 = S1 + S3 = 2, coupling sites 2 and 4 to S24 = S2 + S4 =2 (see Fig. 7), and then coupling S13 and S24 to a total singlet S =S13 + S24 = 0. The energy per site of an independent collection ofplaquettes thus is (note that the number of plaquettes N□ is one-quarter the number of sites)

E Ne�el =−32  J1: [1]

By comparison, the classical energy per site of the Neél AFconfiguration is

E Ne�el =− J1 − J2: [2]

Therefore, for J2 < J1/2, the nonmagnetic collection of indepen-dent plaquettes will be lower in energy than the Neél configura-tion. If we use J2 ’ 35 meV and J1 ’ 170 meV > 2 J2, we mayconclude that the actual ground state is a collection of indepen-dent nonmagnetic plaquettes. This state is akin to that proposedin ref. 12. We observe further that the next-nearest-neighborexchange J3 > 0 frustrates and penalizes the Neél configurationmore than the nonmagnetic one, leading to the energy balancewithin each plaquette from E□ − ENeél = −J1/2 + J2 → −J1/2 + J2 −J3/2. Moreover, the interplane exchange J4 gives no contribution tothe classical energy, since its effects cancel out as can be seen inFig. 6. Since both J3 and J4 are anyhow smaller than J2, we shall notconsider them in the following analysis.The above treatment, however, is still crude, as it does not

take into account quantum fluctuations. To evaluate their im-pact, we assess the stability of the nonmagnetic state againstquantum fluctuations. Elementary quantum fluctuations arebuilt by combining into an overall singlet two separate spinfluctuations in neighboring plaquettes. The first excited state ofthe isolated plaquette is still obtained by S13 = 2 and S24 = 2, nowcoupled into a total spin S = S13 + S24 = 1, at energy J1 above theground state. Let us denote as jSi the plaquette singlet groundstate, and as jT;Mi the excited triplet with Sz = M = −1, . . ., +1.If we consider two nearest neighboring plaquettes, identified bythe positions R and R′, application of the exchange J2 to the statein which both plaquettes are in the ground state,

HJ2��S;R

���S;R′�=−J2

X+1

M=−1ð−1ÞM ×

��T;M;R���T; −M;R′

�; [3]

excites in both plaquettes the spin-triplet configurations, with thetwo coupled to a singlet. This process has an amplitude

ffiffiffi3

p  J2.

These two excitations could move, still remaining in a full singletconfiguration,

HJ2

��S;R���T;M;R′

�=−J2

��T;M;R���S;R′

�: [4]

They are not independent, since they gain an energy −J2/4 whenthey are nearest neighbors. This attraction, however, cannotovercome the hard-core constraint, since the two triplets cannotreside on the same plaquette. The problem is thus equivalent totwo hard-core bosons, each costing an energy J1 and able to hopbetween nearest neighbor plaquettes with an amplitude −J2. De-spite the weak nearest neighbor attraction −J2/4, their lowestenergy state is unbound and has energy 2J1 − 8J2. The overallsinglet, spin liquid state will be stable so long as this excitationgap is positive, whereas antiferromagnetism will prevail if it iszero or negative. Based on this result, a better estimate for thestability of the overall singlet is the condition 2J1 J 8J2, whichleads to J2 < J1/4. The estimated values of the exchange couplingssatisfy this inequality, confirming the stability of an overall sin-glet state, even once quantum fluctuations are included. The spinliquid singlet state, a lattice of plaquettes each made of fourantiferromagnetically correlated S = 1 sites, with weaker butnonzero interplaquette correlations, represents in conclusionour best model for e1-O2 below 20 GPa.

Infrared Spectrum in the Lattice Singlet Model. One burning ques-tion is, at this point, what evidence can one identify proving theexistence of a nonzero molecular spin in low pressure e-O2, de-spite its lack of magnetic long-range order? There is, in fact, atleast one such piece of evidence, long published but not inter-preted yet, and it is optical. Near-infrared spectroscopy acrossthe δ-e transition shows the excitation of a single O2 moleculefrom its lowest-energy  3Σ−

g S = 1 configuration to the lowestS = 0 1Δg state. This process, forbidden by spin and parity in isolatedO2, is allowed in a lattice of molecules and shows up in high-pressure optical absorption (15). The peak correspondingto  3Σ−

g → 1Δg (and its first vibrational satellite, triggered bymolecular elongation in the S = 0 state) is clearly visible in the δphase, at an energy ∼ 8–9.000 cm−1, a frequency comparable tothat of the isolated molecule. When the e phase sets in above8 GPa, the  3Σ−

g → 1Δg is abruptly blue shifted to ∼12.400 cm−1

and very considerably broadened, to the extent that its vibra-tional satellites are not anymore distinguishable (15). That op-tical observation can now be explained.In the S = 1 Heisenberg model representation, the  3Σ−

g → 1Δgexcitation of a single molecule amounts to annihilating a spin 1site in a plaquette, leaving a vacancy in its place. We should

Fig. 6. Long-range antiferromagnetic order and interactions between thefirst four neighbors J1 (inside the quartet), J2 with the two or three nearestquartets, J3 third nearest neighbors in the plane, and J4 with molecules lo-cated in the planes above and below.

Fig. 7. Simplified 2D Heisenberg model.

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expect optical absorption at a frequency equal to the E  3Σ−g → 1Δg

molecular excitation energy plus the energy cost of the molecularvacancy. An experimental estimate of this cost was given asa mere 250 cm−1 in the δ phase at much lower pressure (15),where the absorption peak is close to the molecular excitationenergy, and its broadening, attributable to shake-up of spinwaves, is small. As pressure rises, the exchange coupling J1 in-creases rapidly, as signaled by the blue shift and broadening ofthis transition visible within the δ phase (15). In the O2 quartetsinglet state, a vacancy costs roughly the energy difference be-tween the ground state of the three surviving O2 molecules andthe initial four-molecule state. This difference is readily found tobe 3J1. Moreover, since the three-molecule state has S = 1, whilethe initial four-molecule state was a singlet, an itinerant spin-1excitation must be created in addition to the vacancy, costing anadditional energy ω ∈ [J1 − 4J2, J1 + 4J2] (see Fig. 8, Inset). Wetherefore predict the absorption line to undergo at the δ → etransition a sudden blue shift of K 4(J1 − J2) with a largebroadening ∼ 8J2 due to interplaquette exchange. With the cal-culated exchange values at 11.4 GPa, that means ’ 0.54 eV =4,355 cm−1 and ’ 0.28 eV = 2,258 cm−1, respectively, values thatare reasonably close to the experimental ones (15) (see Fig. 8). Inconclusion, the abrupt change of optical absorption is explained bythe onset of a correlated singlet state at the δ → e transition.

New Phase DiagramThe ground state of high-pressure e-O2, correctly described asa Peierls-distorted nonmagnetic band insulator and an overall spinsinglet above 20 GPa, turns below 20 GPa into a correlated in-sulator, where molecules recover their S = 1 spin, but where ex-change couplings and quantum fluctuations between spins conspireto yield another, different overall spin singlet ground state. Sharingvery similar quartet lattice structures, the two states appear to havethe same symmetry, and the question is whether the phase diagramshould show a phase transition between the two or not. Assumingsame symmetry, there could only be a first-order transition or

a smooth crossover. On account of the mechanical coupling whichthe onset of molecular spin must exert on the overall latticestructure, the likeliest candidate is a first-order transition.As it turns out, there is in literature, ignored so far by most,

rather clear evidence of a low-temperature, first-order phasetransition (17), signaled around 25 GPa at 20 K by a small butsharp and sudden 10 cm−1 splitting of a low-frequency vibration.We propose that this could signal precisely the first-order lineseparating the low-pressure phase, say e1-O2, and the high-pressure one, say e0-O2. This phase line will extend at finitetemperature but, on account of same symmetry, should terminatewith a critical point. Because there are underlying spins in e1-O2but not in e0-O2, the phase line must turn toward higher pressuresas temperature grows, because e1-O2 possesses a high-temperaturespin entropy S ∼ ln3 per molecule whereas e0-O2 does not. Ac-curate room temperature vibrational data (16) actually indicatea smooth crossover between unsplit and split modes above 30 GPa,a pressure definitely higher than the 20 K sharp transition near 25GPa. That confirms our suggestion, and supports the prediction ofa critical point below 300 K and near 30 GPa. Our new proposedphase diagram is therefore summarized in Fig. 9.

ConclusionsA fresh ab initio study connects with existing vibrational evi-dence to indicate that molecular spin plays an important rolein the lower-pressure part of the e-O2 oxygen phase diagram.Specifically, we propose replacing the single broad e-O2 phasefrom 8 to 96 GPa with two phases e1-O2 and e0-O2—the firsta local singlet spin 1 liquid, the second a regular, Peierls bandinsulator—separated by a first-order phase transition near20 GPa. The predicted phase line should evolve with temper-ature, terminating with a novel critical point, probably near30 GPa and 200 K. The high-temperature region below 30 GPamust be characterized by thermally fluctuating S = 1 spins, whosepresence should be directly detectable by magnetic susceptibilitymeasurements in the 8- to 30-GPa pressure range. At low tem-peratures, the wealth of low-energy spin excitations present in e1-O2 but absent in e0-O2 should in addition give rise to very newenergy dissipation channels and processes in the former phase.

ACKNOWLEDGMENTS. The authors would like to thank G. Baskaran, OttoGonzales, Sadhana Chalise, Carlos Pinilla, and Nicola Seriani for fruitfuldiscussions. This work, and in particular Y.C.’s position, was partly sponsoredby European Research Council Advanced Grant 320796 – MODPHYSFRICT.Contracts PRIN/ COFIN 2010LLKJBX 004 and 2010LLKJBX 007, EuropeanUnion-Japan Project LEMSUPER, and Sinergia CRSII2136287/1 are alsoacknowledged.

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Fig. 8. Explanation of the blue shift at the δ → e transition. Solid lines aredata of the IR absorption from ref. 15, dashed green line is a linear ex-trapolation of the peak corresponding to  3Σ−

g → 1Δg process at 11.5 GPa, andthe blue arrow represents the blue shift of 4J1 with a 8J2 broadening rep-resented by the double blue arrow. (Inset) Initial plaquette and final S = 1trimer state; an itinerant spin 1 excitation is emitted by spin conservation(red wavy arrow), which costs an additional energy of hν ’ 4(J1 ± J2).

Fig. 9. Proposed new phase diagram of oxygen.

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