Magnetic coupling and dynamics in solid α and β-O2. I. An a b i n i t i o theoretical approach

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Abstract
This paper describes a new approach to the dynamic and magnetic properties of solid α and β oxygen which is based on two theoretical developments. First, we have constructed the lattice and spin Hamiltonian for solid O2 by including explicitly the interactions between the triplet ground state O2 molecules as obtained mainly from recent ab initio calculations. The spin coupling parameters in this Hamiltonian, especially the Heisenberg exchange parameter J, are strongly dependent on the positions and orientations of the molecules. Secondly, we have developed an integrated scheme for lattice dynamics and spin wave calculations which uses this Hamiltonian. The actual mixing between the lattice modes, phonons and librons, and the magnons appears to be small; their interaction can be largely taken into account by renormalization of the coupling terms. In the lattice dynamics part of the calculation it is essential to include the Heisenberg term, since it is the extremely strong anisotropy of the coupling parameter J that explains the anomalously large libron splitting in α-O2. The spin-wave calculation with the Hamiltonian averaged over the lattice vibrations yields reasonable values for the magnon frequencies with no empirical fit parameters.