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J.F.Fernandez CSIC
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This is the reply to a Comment by I.S.Tupitsyn and P.C.E. Stamp (PRL v92,119701 (2004)) on a letter of ours (J.F.Fernandez and J.J.Alonso, PRL v91, 047202 (2003)).
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Comment on the paper: Magnetization Process of Single Molecule Magnets at Low Temperatures of J.F.Fernandez and J.J.Alonso (PRL 91, 047202 (2003)).
We show that correlations established before quenching to very low temperatures, later drive the magnetization process of systems of single molecule magnets, after a magnetic field is applied at t=0. We also show that in SC lattices, m propto sqrt(t), as observed in Fe_8, but only for 1+2*log_10(h_d/h_w) time decades, where h_d is a nearest neighbor dipolar magnetic field and a spin reversal can occur only if the field on it is within (-h_w,h_w). However, the sqrt(t) behavior is not universal. For BCC and FCC lattices, m propto t^p, but p simeq 0.7. The value to which m finally levels off is also given.
We model magnetization processes that take place through tunneling in crystals of single-molecule magnets, such as Mn_12 and Fe_8. These processes take place when a field H is applied after quenching to very low temperatures. Magnetic dipolar interactions and spin flipping rules are essential ingredients of the model. The results obtained follow from Monte Carlo simulations and from the stochastic model we propose for dipole field diffusion. Correlations established before quenching are shown to later drive the magnetization process. We also show that in simple cubic lattices, m propto sqrt(t) at time t after H is applied, as observed in Fe_8, but only for 1+2log_10(h_d/h_w) time decades, where h_d is some near-neighbor magnetic dipolar field and a spin reversal can occur only if the magnetic field acting on it is within some field window (-h_w,h_w). However, the sqrt(t) behavior is not universal. For BCC and FCC lattices, m propto t^p, but p simeq 0.7 . An expression for p in terms of lattice parameters is derived. At later times the magnetization levels off to a constant value. All these processes take place at approximately constant magnetic energy if the annealing energy epsilon_a is larger than the tunneling windows energy width (i.e., if epsilon_a gtrsim gmu_B h_w S). Thermal processes come in only later on to drive further magnetization growth.
Microwave radiation applied to single-molecule magnets can induce large magnetization changes when the radiation is resonant with transitions between spin levels. These changes are interpreted as due to resonant heating of the sample by the microwaves. Pulsed-radiation studies show that the magnetization continues to decrease after the radiation has been turned off with a rate that is consistent with the spins characteristic relaxation rate. The measured rate increases with pulse duration and microwave power, indicating that greater absorbed radiation energy results in a higher sample temperature. We also performed numerical simulations that qualitatively reproduce many of the experimental results. Our results indicate that experiments aimed at measuring the magnetization dynamics between two levels resonant with the radiation must be done much faster than the >20-microsecond time scales probed in these experiments.
Single-molecule magnets facilitate the study of quantum tunneling of magnetization at the mesoscopic level. The spin-parity effect is among the fundamental predictions that have yet to be clearly observed. It is predicted that quantum tunneling is suppressed at zero transverse field if the total spin of the magnetic system is half-integer (Kramers degeneracy) but is allowed in integer spin systems. The Landau-Zener method is used to measure the tunnel splitting as a function of transverse field. Spin-parity dependent tunneling is established by comparing the transverse field dependence of the tunnel splitting of integer and half-integer spin systems.
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