Thermally activated resonant magnetization tunneling in molecular magnets: ${\mathrm{Mn}}_{12}\mathrm{Ac}$ and others

The dynamical theory of thermally activated resonant magnetization tunneling in uniaxially anisotropic magnetic molecules such as Mn${}_{12}\mathrm{Ac}$$\mathrm{}(S=10\mathrm{})\mathrm{}$ is developed. The observed slow dynamics of the system is described by master equations for the populations of spin levels. The latter are obtained by the adiabatic elimination of fast degrees of freedom from the density matrix equation with the help of the perturbation theory developed earlier for tunneling level splitting [D. A. Garanin, J. Phys. A 24, L61 (1991)]. There exists a temperature range (thermally activated tunneling) where the escape rate follows the Arrhenius law, but has a nonmonotonic dependence on the bias field due to tunneling at the top of the barrier. At lower temperatures this regime crosses over to the non-Arrhenius law (thermally assisted tunneling). The transition between the two regimes can be first or second order, depending on the transverse field, which can be tested in experiments. In both regimes the resonant maxima of the rate occur when spin levels in the two potential wells match at certain field values. In the thermally activated regime at low dissipation each resonance has a multitower self-similar structure with progressively narrowing peaks mounting on top of each other.