Magnetism of solid oxygen

Magnetic susceptibilities of single-crystal $\ensuremath{\gamma}\ensuremath{-}{\mathrm{O}}_{2}$ and preferentially oriented polycrystalline samples of $\ensuremath{\beta}\ensuremath{-}{\mathrm{O}}_{2}$ and $\ensuremath{\alpha}\ensuremath{-}{\mathrm{O}}_{2}$ have been measured, employing a mutual-inductance bridge method. The susceptibility of paramagnetic $\ensuremath{\gamma}\ensuremath{-}{\mathrm{O}}_{2}$ is isotropic and exhibits a temperature dependence which is not strictly Curie-Weiss, due to short-range correlations and partially hindered rotation. The susceptibility of $\ensuremath{\beta}\ensuremath{-}{\mathrm{O}}_{2}$ exhibits very little anisotropy, but has an unusual temperature dependence which is probably due to the novel behavior of the lattice constants, modulation of inplane and out-of-plane exchange interactions, and short-range order. The susceptibility of anti-ferromagnetic $\ensuremath{\alpha}\ensuremath{-}{\mathrm{O}}_{2}$ is anisotropic, and data from five differently oriented samples have been analyzed in terms of principal antiferromagnetic susceptibilities. The data are consistent with the assumption that the easy axis is the twofold axis, ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{b}}}_{\ensuremath{\alpha}}$, though the direction ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{a}}}_{\ensuremath{\alpha}}$ cannot be excluded. A comprehensive analysis of the present susceptibility results and other magnetic, spectroscopic, and thermal measurements is made, with special reference to $\ensuremath{\alpha}\ensuremath{-}{\mathrm{O}}_{2}$. The perpendicular susceptibility implies an unreasonably large N\'eel temperature, 211 K, and a correspondingly large intersublattice exchange interaction, $\frac{|{J}_{2}|}{k}=19.8$ K. The effects of anisotropy and zeropoint spin deviations do not reduce this estimate by more than 15%. The temperature dependence of the parallel susceptibility suggests a much smaller value for the effective exchange interaction, $\frac{|J|}{k}=5.3$ K, and appears to be well accounted for assuming a single spin-wave excitation. Antiferromagnetic resonance frequencies are analyzed and shown to yield, on assuming a dominant anisotropy equal to that of the free molecule, $\frac{|{J}_{2}|}{k}=4.3$ K. An approximate separation of lattice and magnetic heat capacities is effected, and a value $\frac{|J|}{k}=3.0$ K deduced. The data appear to require the assumption of two spin-wave modes. Except for the perpendicular susceptibility, experimental results suggest a N\'eel temperature between 30 and 40 K. Meanfield and other theories lead to similar estimates, assuming that $\frac{|J|}{k}$ is between 3 and 4 K. The effect of the anisotropy on ${T}_{N}$ is minor, and no significant spin-shortening effect is predicted. Other experimental results are considered, and a disparate set of estimates for the exchange interaction and zone-boundary spin-wave energies is discussed. Including the effects of intrasublattice exchange interactions within the context of a two-sublattice model does not seem sufficient to remove the various discrepancies. An approximate calculation of relative overlap integrals and exchange interactions between different pairs of molecules in $\ensuremath{\alpha}\ensuremath{-}{\mathrm{O}}_{2}$ is made. It is suggested that a multisublattice model for the magnetic structure, and possibly one involving noncollinear sublattices, may provide an eventual resolution of the various difficulties. A "quasi-two-dimensional" description of $\ensuremath{\alpha}\ensuremath{-}{\mathrm{O}}_{2}$ is also considered, but appears not to offer a satisfactory explanation of the unusual and imperfectly correlated properties of this phase.