Role of dipolar interactions in three-dimensional magnetic ordering of chain compounds with very large interchain spacing

A model that takes into account the dipolar interaction between quantum spin chains is proposed to explain the occurrence of three-dimensional (3D) ordering in magnetic chain compounds, where superexchange interaction can be neglected because of large interchain spacing. The divergence of the in-chain correlation length at low temperature promotes correlated spin blocks that can interact from chain to chain through sizeable dipole-dipole coupling. Using a modified mean-field approach we show that the strength of this interaction is large enough to induce 3D magnetic ordering. The model is applied to the Mn-porphyrin-based magnets exhibiting ferrimagnetic chains well separated in space (up to 30 {} apart). Different ground-state spin alignments are analyzed. In the framework of the proposed approach, the ordering temperatures that are calculated compare well with the experimental findings. It is shown that the rate of increase of the correlation length at low temperature is the essential parameter in order to reach the observed transition temperatures. Indeed an exponential divergence of the 1D correlation length is required, which implies the existence of single-ion anisotropy, whereas the power-law divergence for 1D Heisenberg coupled spins yields transition temperatures one order of magnitude smaller than observed.