The rhombohedral Heisenberg antiferromagnet: infinite degeneracy of the ground state and magnetic properties of solid oxygen

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Abstract
Infinite degeneracy of the ground state, a 'soft line' in the elementary excitation energy spectrum, and no long-range order in 3D at finite temperature are all found for suitable exchange competition in Heisenberg helimagnets. The authors show here that a similar scenario arises in a Heisenberg model on a rhombohedral lattice with antiferromagnetic in-plane nearest-neighbour (NN) exchange coupling J and any inter-plane NN coupling J' if mod J' mod <3 mod J mod . Moreover, for small J' the in-plane spin configuration is similar to a 120 degrees phase, but any phase relation between the planes is possible. In the absence of anisotropy there is no long-range order, with a possible algebraic decay of the correlation function. A similar unorthodox behaviour is expected at intermediate temperature if the anisotropy is small enough to leave a structure of the excitation spectrum reminiscent of the 'soft line'. The authors think that these somewhat surprising properties of a rhombohedral antiferromagnet can be useful for understanding the magnetic behaviour of the beta -oxygen.