Zero point motion and magnetic field effects on the spin configuration in a Heisenberg rhombohedral antiferromagnet. Application to solid oxygen

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Abstract
The ground state of the Heisenberg rhombohedral antiferromagnet in classical approximation exhibits infinite degeneracy corresponding to infinite unequivalent helices. We call degenerate helix (DH) such a spin configuration. In absence of anisotropy long‐range order (LRO) is lost even in 3D with a possible algebraic decay of the correlation function due to a low‐energy catastrophe related to ‘‘soft lines’’ of the magnon energy which vanishes for all wave vectors falling on the ‘‘degeneration line’’ LQ, the locus of the Q wave vectors characterizing the infinite helixes of the ground state. We have studied the effect of the zero point motion which removes the infinite degeneracy of the ground state so that quantum disorder sets up LRO. We have also studied the effect of an external magnetic field. We find that in classical approximation a magnetic field parallel to the c axis does not remove the infinite degeneracy of the ground state but it affects the spin‐wave energy spectrum what could be observed in an inelastic scattering experiment. On the contrary, dramatic changes are expected when a magnetic field is applied perpendicular to the c axis because competition arises with the zero point motion effect so that the magnetic field in this configuration should act as a device to tune the DH phase. Possible application to solid oxygen is briefly analyzed.