Antiferromagnetism in the high-pressure phases of solid oxygen: Low-energy electronic transitions Mario Santoro, 1, * Federico A. Gorelli, 1,2,² Lorenzo Ulivi, 1,3,‡ Roberto Bini, 1,4,§ and Hans J. Jodl 1,5 1 LENS, European Laboratory for Non-linear Spectroscopy and INFM, Largo E. Fermi 2, I-50125 Firenze, Italy 2 Dipartimento di Fisica dell’Universita ` di Firenze, Largo E. Fermi 2, I-50125 Firenze, Italy 3 Istituto di Elettronica Quantistica, Consiglio Nazionale delle Ricerche, Via Panciatichi 56/30, I-50127 Firenze, Italy 4 Dipartimento di Chimica dell’Universita ` di Firenze, Via G. Capponi 9, I-50121 Firenze, Italy 5 Fachbereich Physik, Universita ¨t Kaiserslautern, E. Schro ¨dinger Str., 67663 Kaiserslautern, Germany ~Received 20 March 2001; published 24 July 2001! In this work we report a study in the near infrared spectral region, at low temperature and high pressure, of solid d 2O 2 and b 2O 2 , concerning electronic excitations between the ground state 3 S g 2 and the lowest excited states 1 D g and 1 S g 1 . These transitions are essentially due to the simultaneous creation of an exciton, a magnon, and a vibron, and confirm the antiferromagnetic order of the d phase and the short-range antifer- romagnetic order of b 2O 2 . Strong phonon sidebands are also observed. A simple model let us obtain, from the frequency position of the observed bands, the exchange integral between nearest-neighbor molecules as a function of pressure, i.e., of the intermolecular distance. This result is compared with the available theoretical calculations at high pressure and other experimental data at ambient pressure. The comparison makes it possible to estimate the spin-correlation function in the b p hase. Finally, we measure a dramatic change of the spectrum at the d 2e phase transition, which is consistently interpreted on the basis of the formation of the O 4 molecule, confirming previous vibrational data. The antiferromagnetic coupling in solid oxygen appears to be the driving force leading to the formation of the diamagnetic O 4 molecule. DOI: 10.1103/PhysRevB.64.064428 PACS number~s!: 75.25.1z, 62.50.1p I. INTRODUCTION Solid oxygen is an intriguing molecular crystal, whose stability in the different phases is strongly affected by the molecular spin-spin interaction. It is the only elemental mo- lecular solid that is both insulating and, in some modifica- tions, antiferromagnetically ordered. 1–3 From an experimen- tal point of view, it is difficult to obtain a high-quality single crystal at low temperature and high pressure, thus, making it extremely hard to obtain a direct spectroscopic evidence of the weak features due to spin waves ~magnons!. Neverthe- less, the magnetic interaction can also induce the activity of new absorption bands both in the vibrational 3 and in the electronic spectrum, whose behavior can be studied as a function of temperature or external applied magnetic field. The lowest-temperature phase of solid oxygen at ambient pressure, the monoclinic a 2O 2 , is known since a long time to be antiferromagnetically ordered, with a quasi-two- dimensional character. The structural space group is C2/m with one molecule in the primitive cell, but the magnetic primitive cell contains two molecules. 1,2 In this phase, all the spins are aligned along the monoclinic axis b with an oppo- site orientation in nearest-neighbor molecules. Above 24 K, at atmospheric pressure, the a phase transforms into the rhombhoedral (R3 ¯ m) b phase. 4 In b 2O 2 the interpretation of neutron scattering data 2 is consistent with a quasihelical spin arrangement, in which the spins of all six neighbors on the hexagonal basal plane are oriented at 2 p /3 with respect to one another and lie in the ( a , b ) plane. The a 2b phase transition takes place with negligible volume change and heat of transformation, and the relative slight structural dis- tortions are interpreted as essentially due to magnetic effects. 5,6 Information about the spin ordering in the ambient pressure phases was also derived by the study of the lowest electronic transitions between the ground state 3 S g 2 and the first excited states 1 D g ~1 eV! and 1 S g 1 ~1.6 eV!. 7–9 All these states derive from the same p 4 2p * 2 configuration but differ with respect to spin orientation between the two p * elec- trons. These one-photon transitions are strictly forbidden in the isolated molecule by both spin and electric dipole selec- tion rules. Nevertheless, in the gas phase at pressures around 100 atm, the absorption bands relative to these transitions start to be detectable. 10 Their intensities increase as the square of the density, thus suggesting a pair-induced process. In solid oxygen, at room pressure and low temperature, the absorption intensity of the lowest-electronic transitions is significant, with features characteristic of molecular solids such as sidebands in the absorption spectrum. In the a phase, the 3 S g 2 → 1 D g , 1 S g 1 transitions have been interpreted mainly as exciton-magnon transitions, allowed even in the electric-dipole approximation. 8 This interpretation can ex- plain the rapid intensity decrease and the band redshift when temperature is increased up to the a 2b phase transition. Therefore, these electronic transitions represent a powerful tool to investigate the magnetic behavior of the low tempera- ture phases of solid oxygen. This investigation has never been performed up to now, at low temperature, in the high- pressure region extending between the a , b , and e phases. At room temperature and 9.6 GPa, the structure of solid oxygen has been determined to be orthorhombic ~Fmmm, D 2 h 23 ), with one molecule per primitive cell ( d phase!. Mol- ecules are parallel and form molecular planes as in the a and b phases. 14 At low temperature, two phases, a 8 and d in order of increasing pressure, were proposed on the basis of Raman studies, 11 but the existence of the a 8 phase can be ruled out on the basis of other Raman 12 and infrared. 13 In a PHYSICAL REVIEW B, VOLUME 64, 064428 0163-1829/2001/64~6!/064428~7!/$20.00 ©2001 The American Physical Society 64 064428-1