Resonances in two-magnon Raman spectra and the effect of several exchange parameters

The first calculations of two-magnon Raman line shapes to fully incorporate second-neighbor exchange and all magnon-magnon interactions are reported. Using a spin-orbit coupling mechanism for the excitation of two spin deviations on a single site of a fcc Heisenberg ferromagnet at $T=0\mathrm{}°$ K, we find a resonance well inside the two-magnon band which is qualitatively similar to that seen in antiferromagnets. This resonance is located close to the Ising energy of two spin deviations on a single site, in contrast to the antiferromagnetic situation where the excitations are usually created on neighboring sites for which the resonance is close to the Ising bound-state energy. The line shape and its position are shown to be sensitive to the ratio, $\eta =\frac{J_2}{J_1}$, of exchange parameters for nearest- and next-nearest-neighbor interactions. This sensitivity is illustrated through plots of spectra for $\eta =0, \pm 0.25$ for $S=1\mathrm{}$ and $S=\frac{7}{2}$. The latter spin value affords an opportunity to assess the observational prospects for EuO. The effect of finite temperatures is discussed and a second resonance predicted in view of the existence of a resonance in the one-magnon propagator at finite temperature. For a nearest-neighbor sc ferromagnet this secondary resonance should occur at a higher frequency than the primary resonance that we have found at $T=0\mathrm{}°$ K. The relationship between Raman resonances and two-magnon bound states is discussed in the light of results for ferromagnets and antiferromagnets. It is anticipated that new progress can be made in respect of distant-neighbor interactions in antiferromagnets by using a similar computational approach to calculate the appropriate lattice Green's functions.