Energy levels and exchange interactions of spin clusters

We first describe a simple method for diagonalizing the isotropic exchange Hamiltonian of a cluster of N spins in the most general case where all the exchange constants are different. The technique, based on the rotation invariance of the system, leads to a considerable reduction of the total matrix. Simple expressions of the magnetization and susceptibility are provided and an example of the determination of the exchange constants of a complex with five Cu 2+ ions is given. It is also shown that for a large variety of spin configurations occuring in metal complexes, it is possible to diagonalize the dominant isotropic exchange spin hamiltonian in a straightforward way by using recoupling techniques. This allows to solve problems up to a nine spin cluster with spins having different g values. This survey is pursued by the theoretical approach of the magnetic properties of interacting spins on a finite ring with a detailed study of an oligonuclear metal nitroxide complex formed by six Mn 2+ (S=5/2) and six free radicals (s=1/2). The temperature behaviour of the susceptibility is interpreted with a semi-classical model of a cyclic alternate finite chain. Finally we give a procedure for determining the three exchange constants of three spin 1/2 coupled by isotropic exchange constants in the unsolved case where these constants are all different