A Prerequisite for Purely Organic Molecule-Based Ferrimagnetics:  Breakdown of Simple Classical Pictures

Abstract

Spin state energies were calculated for an antiferromagnetic linear chain composed of a doublet ( S = 1 / 2 ) radical and a biradical with a triplet ( S = 1) ground state by numerical diagonalization of a finite-size Heisenberg−Dirac spin Hamiltonian. A ferrimagnetic-like ground state with a spin value of S = N /2 ( N stands for the number of repeating units) appears if the intermolecular antiferromagnetic exchange interactions are uniform between all the S = 1 / 2 sites. This finding is consistent with a simple picture of differing and neighboring spin angular moments S 's ordered in sublattices in an antiparallel manner. On the other hand, quasi-degenerate low-lying states appear as the spatial symmetry of the intermolecular antiferromagnetic interactions is lowered. The quasi-degeneracy destabilizes the ferrimagnetic-like ground state. This instability is inherent in multicentered antiferromagnetic interactions between open-shell organic molecular systems, suggesting a prerequisite for long-range magnetic order in purely organic molecule-based ferrimagnetics. Such prerequisite has never been reported until now. The results of the calculations are invoked to explain the susceptibility and the spin−spin relaxation time measured for the first model system for purely organic ferrimagnetics, a nitronyl nitroxide-based molecular crystal composed of an S = 1 / 2 and S = 1 molecules (Izuoka, A.; Fukuda, M.; Kumai, R.; Itakura, M.; Hikami, S.; Sugawara, T. J . Am . Chem . Soc . 1994, 116, 2609−2610.)