Rhombohedral Heisenberg antiferromagnet: Infinite degeneracy of the ground state induced by the lattice structure. Application to β-oxygen

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Abstract
Exchange coupling competition between different shells of neighbors is the well-known source of helimagnetism. Unexpected interesting new features were found for suitable competition: infinite degeneracy of the ground state, soft lines in the magnon energy spectrum, absence of long-range order in 3D for any T≠0, and possible algebraic decay of the correlation function. We find a similar scenario in the rhombohedral Heisenberg antiferromagnet (RAF) even if the exchange coupling range is limited to nearest neighbors. The general expectation of a 120° three-sublattice configuration in the c planes is confirmed only if the interplane coupling J′ is rigorously zero, whereas for any ‖J′‖<3‖J‖, J being the NN in-plane coupling, the ground state is a degenerate helix (DH). The RAF model is suitable to describe solid oxygen in the β phase, where O2 molecules are arranged on a rhombohedral lattice and interact via direct exchange. The evaluation of the elastic neutron scattering cross section by a polycrystalline sample of β-O provides a non-Lorentzian peak whose width is determined by the presence of infinite isoenergetic helices in the ground state. This points out that LRO could persist in β phase in spite of the current interpretation of the large peak at zero energy transfer as an evidence of absence of LRO.