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Reply to the Comment of J.J. Alonso and J.F. Fernandez on the paper Hole-digging in ensembles of tunneling molecular magnets of I.S. Tupitsyn, P.C.E. Stamp and N.V. Prokofev (Phys. Rev. B 69, 132406, (2004)).
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Tupitsyn et al. [Phys. Rev. B v69, 132406 (2004)] have recently reported results for the relaxation of crystalline systems of single--molecule magnets, such as Fe_8. They claim that, quite generally, (1) the magnetization and hole widths of field--distributions evolve with time t as sqrt{t}, and (2) the holes line shapes are Lorentzian. We give a counter--example to these conclusions, and show that the main assumption on which they rest is invalid.
The nuclear spin-mediated quantum relaxation of ensembles of tunneling magnetic molecules causes a hole to appear in the distribution of internal fields in the system. The form of this hole, and its time evolution, are studied using Monte Carlo simulations. It is shown that the line-shape of the tunneling hole in a weakly polarised sample must have a Lorentzian lineshape- the short-time half-width $xi_o$ in all experiments done so far should be $sim E_0$, the half-width of the nuclear spin multiplet. After a time $tau_o$, the single molecule tunneling relaxation time, the hole width begins to increase rapidly. In initially polarised samples the disintegration of resonant tunneling surfaces is found to be very fast.
Below 360 mK, Fe8 magnetic molecular clusters are in the pure quantum relaxation regime. We showed recently that the predicted ``square-root time relaxation is obeyed, allowing us to develop a new method for watching the evolution of the distribution of molecular spin states in the sample. We measured the distribution P(H) of molecules which are in resonance at the applied field H. Tunnelling initially causes rapid transitions of molecules, thereby ``digging a hole in P(H). For small initial magnetisation values, the hole width shows an intrinsic broadening which may be due to nuclear spins. We present here hole digging measurements in the thermal activated regime which may allow to study the effect of spin-phonon coupling.
It is shown that a single molecular magnet placed in a rapidly oscillating magnetic field displays the phenomenon of quenching of tunneling processes. The results open a way to manipulate the quantum states of molecular magnets by means of radiation in the terahertz range. Our analysis separates the time evolution into slow and fast components thereby obtaining an effective theory for the slow dynamics. This effective theory presents quenching of the tunnel effect. In particular, stands out its difference with the so-called coherent destruction of tunneling. We support our prediction with numerical evidence based on an exact solution of the Schrodingers equation.
We reply to the comment of Chudnovsky and Garanin on the tunneling rate in Mn_{12}.
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