Magnon interactions in the quantum paramagnetic phase of CoNb2O6

The strongly anisotropic quasi-one-dimensional ferromagnet CoNb${}_{2}$O${}_{6}$ in a transverse field has provided a spectacular realization of the magnon decay effect in its paramagnetic phase. A self-consistent theory is proposed to regularize unphysical divergences while preserving the integrity of the singular threshold phenomena of magnon decay, demonstrating quantitative agreement with the neutron scattering results throughout the field regime inaccessible by standard spin-wave theory. Phenomenological constraints on the model, connections of CoNb${}_{2}$O${}_{6}$ to the other anisotropic-exchange materials, and the effects of longitudinal fields are explored.