Inelastic neutron scattering study of magnetic interactions in ${\mathrm{CsMn}}_{\mathrm{x}}$${\mathrm{Mg}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Br}}_3$. II. Magnetic excitations in clusters of ${\mathrm{Mn}}^{2+}$ ions

Crystals of ${\mathrm{CsMn}}_{\mathrm{x}}$ ${\mathrm{Mg}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Br}}_3$ with x=0.14, 0.28, 0.50, and 0.75 were synthesized and studied by inelastic neutron scattering (INS). Excitations of isolated ${\mathrm{Mn}}^{2+}$ dimers, trimers, and tetramers could be identified on the basis of their characteristic dependences on temperature and momentum transfer. They show no energy dispersion and can be observed in all the crystals studied. From the observed energy splittings the following exchange parameters were deduced: $J_{\mathrm{dimer}=\mathrm{-}838}$ μeV (bilinear exchange), $K_{\mathrm{dimer}=8.8\mathrm{}}$ μeV (biquadratic exchange); $J_{\mathrm{trimer}=\mathrm{-}777}$ μeV, $J_{\mathrm{trimer}{}^{\mathcal{’}}=\mathrm{-}11}$ μeV (second-nearest-neighbor bilinear exchange), $K_{\mathrm{trimer}=8.4\mathrm{}}$ μeV, L=6.1 μeV (three-center interaction). Second-nearest-neighbor exchange as well as two- and three-center biquadratic terms significantly contribute to the exchange coupling. The bulk properties of pure ${\mathrm{CsMnBr}}_3$ can be reproduced with the parameters derived for the small clusters. INS spectra of the x=0.50 and x=0.75 crystals show two distinctly different types of excitations: relatively sharp bands with no energy dispersion which are predominantly due to dimer and trimer transitions; superimposed is a broad band, more intense in the x=0.75 spectrum, with spin-wave-like energy dispersion. The applicability and limits of cluster and spin-wave models to account for the observed INS features are discussed.