RAF Model and Solid Oxygen: Infinite Degeneracy, Soft Lines, No LRO in Classical Approximation and Order by Quantum Disorder

Abstract

Exchange coupling competition in a Heisenberg Hamiltonian is the basic origin of non coliinear helical configurations; furthermore, on suitable phase boundaries between different helical phases in the parameter space, infinite degeneracy of the ground state appears ( for S ➔∞) corresponding to infinite unequivalent isoenergetic helices of wave vector $\vec Q$ belonging to lines ${L_{\vec Q}}$ in the reciprocal space we call “degeneration lines”. In the isotropic model the magnon dispersion curve shows “soft lines” vanishing for all wave vectors falling on ${L_{\vec Q}}$ /1/. This causes a low frequency catastrophe that destroys long-range order (LRO), even in 3D, at any finite temperature leading to an unorthodox phase with possible algebraic decay of the correlation function /2/. Planar anisotropy leaves the infinite degeneracy of the ground state but it lifts the soft lines so restoring LRO. For anisotropy small enough we expect a conventional low-temperature ordered phase followed by a “degenerate helix” (DH)-like phase at intermediate temperature before the paramagnetic high-temperature phase is reached. Further exchange interactions remove the infinite degeneracy of the ground state /2/ and lift the soft lines, but a phase reminiscent of the classical scenario is still expected at intermediate temperature.