Microscopic origin of isotropic non-Heisenberg behavior in S=1 magnetic systems

We have reanalyzed the microscopic origin of the isotropic deviations that are observed from the energy spacings predicted by the Heisenberg-Dirac-van Vleck (HDVV) Hamiltonian. Usually, a biquadratic spin operator is added to the HDVV Hamiltonian to account for such deviations. It is shown here that this operator cannot describe the effect of the excited atomic non-Hund states which brought the most important contribution to the deviations. For systems containing more than two magnetic centers, non-Hund states cause additional interactions that are of the same order of magnitude as the biquadratic exchange and should have significant effects on the macroscopic properties of extended systems.