Neutron scattering in the rhombohedral Heisenberg antiferromagnet: application to β-oxygen

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Abstract
The rhombohedral Heisenberg antiferromagnet has an unexpected degeneracy of the ground state in the mean-field approximation. An infinite number of isoenergetic nonequivalent helices exist and these define a degeneration line as the locus of the Q vectors of these helices. The authors study the elastic neutron scattering cross section of such a 'degenerate helix' state for single crystals and polycrystals: in a single crystal they find a line of Bragg peaks, a ridge, corresponding to scattering wave-vectors falling on the degeneration line. In the case of a polycrystal the scattering consists of a broad peak and its width is determined by the minimum and the maximum magnitude of Q. The 'degenerate helix' state is stable against spin wave excitations but these have a large number of low-energy states in the range 3-20K when they use the interaction parameters appropriate for beta -O2. They argue that the present experimental data on beta -O2 do not necessarily imply absence of long-range order, but they are compatible with a 'degenerate helix' state with long-range order. A careful investigation of the form of the elastic peak is suggested to test the asymmetry they predict.