Non-covariant corrections to magnetic solitons in CsNiF3

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Abstract
Mikeska (1978) has shown that the excitations of a one-dimensional chain of ferromagnetically coupled spins with easy-plane anisotropy approximately satisfy the sine-Gordon equation when a weak magnetic field is applied in the easy plane. The authors rederive the equations of motion which describe the excitations, establishing the approximations involved. They find that corrections to the sine-Gordon equation arise from the discreteness of the physical spin chain and from the kinematics of the anisotropic spins. Both of these types of correction result in finite-field renormalisations of the magnetic soliton energy and form factors relevant to neutron scattering. Although these renormalisations are small in CsNiF3 for slowly-moving solitons and fields of a few kilogauss, they are markedly enhanced for fast-moving solitons. This leads to a breakdown of the Lorentz covariance present in the pure sine-Gordon approximation and the authors therefore caution against naive use of a simple, relativistic-Boltzmann-gas phenomenology for interpretation of neutron scattering experiments at temperatures so high (>or approximately=10K) that significant numbers of fast-moving solitons are present.