Nonexponential relaxation of magnetization at the resonant tunneling pointunder a fluctuating random noise

At resonant tunneling points of nanoscale molecular magnets, a fluctuating random field causes successive Landau-Zener-Stuckelberg transitions. We hav e studied dynamics of magnetization by a Langevin type Schrodinger equation and found that the successive transitions. result in a stretched exponenti al decay with square-root time when the fluctuation of the field is regarde d as an random walk, i.e., the, Wiener process. When the fluctuation is bou nded by a restoring force, i.e., the Ornstein-Uhlenbeck process, the relaxa tion obeys the exponential decay at the late stage, while it shows the stre tched exponential decay at the early stage. The scaling relations of the re laxation functions at both stages are also studied as functions of the para meters: the strength of the fluctuation, the restoring force, and the energ y gap of the system at the resonant point. Roles of the observed nonexponen tial decay are also discussed in various kinds of square-root time behavior found in experiments.