We investigate the quantum corrections to the energy of the static soliton in the $\mathrm{XY}$-like ferromagnetic spin chain in a symmetry-breaking external field. We apply a semiclassical continuum approximation which allows us to treat the leading-order deviations from idealized planar behavior. The equivalent quantum-field theory, an extension of the quantum sine-Gordon theory, is renormalized and its soliton energy is shown to depend strongly on this deviation. The quantum-field-theoretical renormalization, however, does not affect the energy of the magnetic soliton, which is calculated to leading order in $\frac{1}{S}$, where $S$ is the spin length. The sine-Gordon limit is found applicable only for very large anisotropies; for realistic anisotropies, the reduction of the soliton energy owing to quantum effects is enhanced and depends only on $S$. A quantitative calculation for the $S=1\mathrm{}$ system CsNi${\mathrm{F}}_3$ is likely to require higher-order terms in $\frac{1}{S}$.

• Received 24 February 1982

DOI:https://doi.org/10.1103/PhysRevB.26.5213