Spin-Wave Theory of Two-Magnon Raman Scattering in a Two-Dimensional Antiferromagnet

The graphical spin-wave approach to two-magnon Raman scattering which was developed in an earlier paper is applied to a study of the two-dimensional Heisenberg antiferromagnet ${\mathrm{K}}_2$Ni${\mathrm{F}}_4$. In the present treatment the one-magnon energies are taken to be renormalized in the Hartree-Fock approximation, with the two-magnon Green's function evaluated in the "ladder" approximation. It is found that the Hartree-Fock renormalization gives very good agreement with the experimental results for the temperature shift of the Raman peak up to the measured Néel temperature $T_N=97.1\mathrm{}$ °K and yields satisfactory agreement above $T_N$ up to the maximum temperatures for which Raman data are available. As in the three-dimensional case, a satisfactory explanation for the observed thermal broadening of the spectra remains to be given. Comparisons between the results for ${\mathrm{K}}_2$Ni${\mathrm{F}}_4$ and its three-dimensional analog KNi${\mathrm{F}}_3$ are made. In particular it is found that the renormalization of the zone-edge magnons for $T\simeq T_N$ is much less marked in the two-dimensional case. As has been discussed by other authors, this indicates a rather different temperature dependence of the "coherence length" for the two-dimensional system.