ABSTRACT
Resonant tunneling of magnetisation (or spins) between spin states in magnetic molecules has attracted much attention since it was observed in Mn,, acetates (or Mn,,) several years ago (Friedman et a1 1996, Hernandez et a1 1996 and Thomas et a1 1996). The most interesting feature is that at low temperatures the relaxation rate shows maximums at the regularly spaced magnetic field applied along the easy axis of magnetisation which correspond to resonances between spin states (Hernandez et a1 1996, Hernandez et a1 1997 and Luis et a1 1997). The spin dynamics in Mn,, can be described quantitatively by a sample Hamiltonian: H=- D S Z ~ - ~ ~ , S . B , D is the magnetic anisotropy energy and positive, indicating the spin of molecule to lie along the Z-axis (the c-axis of the Mn,, tetraganal lattice) and B is the magnetic induction. The system can be modelled as a double well potential, as shown in Fig. 1, in which the levels represent the different eigenstates of S,. When magnetic field is zero, all the levels in the double-well match each other (or in resonant), Fig. la. The magnetic field (or B ) applied along the z-axis will tilt the potential, Fig.lb, raising and lowering the energies of the states, and bringing the levels into resonance at particular value of B (=nD/g& =nHo, n=O, f l , k2, ... (Hernandez et a1 1997 )), Fig.lb. It has been shown that the tunneling rate from the excited level near the top of the barrier is much faster than from the low-lying levels (Hernandez et a1 1997). The dynamics of Mn,, can be described as: the system is first thermally activated to some highlying levels near the top of the barrier where the tunneling rate is approximately
equal to the thermally population of the level(s); it then tunnels through the barrier and decays down into the other well (Fig. lb). Thus, the energy barrier involved in the process should be the effective barrier rather than the total barrier. This effective barrier should vary with temperature when applied magnetic field equals nD/g&. Only when applied field is far from the resonant field H= nD/g& where the levels in the double-well are fully mismatched, should the barrier be given by classical reduction of energy barrier due to applied field: U(H)=DS2(1H/H,,)' and is independent of temperature, where Ha,=2DS/gk is the anisotropy energy. This has not been experimentally demonstrated yet and the energy barrier U (=Ds~, S=10) between 56K to 86K was extracted from different experiments using different techniques (Luis et a1 1997, Sessoli 1995 and Sessoli et a1 1993). Here we report on the experimental evidence of the temperature dependent effective energy barrier when the applied field equals the resonant field (H= nD/g&) or near to it and the temperature independent classical energy barrier when applied field is far from the resonant field H= nD/g& .
