Quantum renormalizations to the spin-spin correlation functions ofCsNiF3

Abstract

The spin-spin correlation functions of ${\mathrm{CsNiF}}_{3}$, in an applied symmetry-breaking magnetic field, are calculated in the harmonic spin-wave approximation. The lowest-order quantum renormalizations are taken into account; this affects both the spin-wave dispersion relation and enhances the spin-wave amplitudes. We compare the results of our calculation to earlier calculations, which neglect the effect of the quantum renormalization, as well as to data taken from inelastic neutron scattering experiments. The present calculations reproduce a central peak ($\ensuremath{\omega}\ensuremath{\approx}0$) in the $x\ensuremath{-}x$ correlation function. This central peak observed in the neutron scattering experiments has been attributed to soliton excitations, as well as to multiple-spin-wave excitations or breather excitations. We extend the analysis to the central peak of the $y\ensuremath{-}y$ correlation function. These data have been used to argue that this represents an unambiguous observation of solitons. Our calculations for the $y\ensuremath{-}y$ correlation function do reproduce a central peak, similar to that of the neutron scattering data. It is contended that the interpretation of the experiment is not unique in that breathers should also be taken into account. The multiple-spin-wave excitations do represent a crude prototype of the multiple-spin-wave bound states that are the breathers of the quantum system. We present estimates of the relative magnitudes of the soliton and multiple-spin-wave components to the central peak.