Tunneling and magnetic relaxation in mesoscopic molecules

The relaxation of the magnetization in big molecular groups embedded in crystals is studied and compared with experimental data on Mn12O12. At sufficiently high temper atures (T > 2 K in Mn12O12) the relaxation is thermally activated, and the exchange of energy with phonons produces relaxation through a cascade of elementary transitions where the component S-z of the spin along the tetragonal axis changes by delta m = +/-1 or +/-2. At lower temperatures, tunneling occurs, but energy conservation requires exchange of energy with nuclear spins in very low magnetic fields (smaller than the hyperfine field), or with phonons in higher field. The phonon assisted tunneling rate 1/tau is proportional to H-3 for weak fields H(H < 2 Tesla). A minimum of tau is expected when the field is of the order of magnitude of the maximum hyperfine field. The theoretically predicted minimum is sharper and should occur at a field value four times as small than experimentally observed.