  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.
