The extraction of exchange parameters from measured spin-wave dispersion relations has severe limitations particularly for magnetic compounds such as the transition-metal perovskites, where the nearest-neighbor exchange parameter usually dominates the couplings between the further-distant-neighbor spins. Very precise exchange parameters beyond the nearest-neighbor spins can be obtained by neutron spectroscopic investigations of the magnetic excitation spectra of isolated multimers in magnetically diluted compounds. This is exemplified for manganese trimers in the mixed three- and two-dimensional perovskite compounds KMnxZn1-xF3 and K2MnxZn1-xF4, respectively. It is shown that the small exchange couplings between the second-nearest and the third-nearest neighboring spins can be determined unambiguously and with equal precision as the dominating nearest-neighbor exchange coupling.
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