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Register a new userTime relaxation of interacting single--molecule magnets
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J.F.Fernandez CSIC
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We study the relaxation of interacting single--molecule magnets (SMMs) in both spatially ordered and disordered systems. The tunneling window is assumed to be, as in Fe8, much narrower than the dipolar field spread. We show that relaxation in disordered systems differs qualitatively from relaxation in fully occupied cubic and Fe_8 lattices. We also study how line shapes that develop in hole--digging experiments evolve with time t in these fully occupied lattices. We show (1) that the dipolar field h scales as t^p in these hole line shapes and show (2) how p varies with lattice structure. Line shapes are not, in general, Lorentzian. More specifically, in the lower portion of the hole, they behave as (h/t^p)^{(1/p)-1} if h is outside the tunnel window. This is in agreement with experiment and with our own Monte Carlo results.
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It is shown that dipolar and weak superexchange interactions between the spin systems of single-molecule magnets (SMM) play an important role in the relaxation of magnetization. These interactions can reduce or increase resonant tunneling. The one-body tunnel picture of SMMs is not always sufficient to explain the measured tunnel transitions. We propose to improve the picture by including also two-body tunnel transitions such as spin-spin cross-relaxation (SSCR). A Mn4 SMM is used as a model system to study the SSCR which plays also an important role for other SMMs like Mn12 or Fe8. At certain external fields, SSCRs can lead to quantum resonances which can show up in hysteresis loop measurements as well defined steps. A simple model allows us to explain quantitatively all observed transitions. Including three-body transitions or dealing with the many-body problem is beyond the slope of this paper.
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.
The time-dependent transport through single-molecule magnets coupled to magnetic or non-magnetic electrodes is studied in the framework of the generalized master equation method. We investigate the transient regime induced by the periodic switching of the source and drain contacts. If the electrodes have opposite magnetizations the quantum turnstile operation allows the stepwise writing of intermediate excited states. In turn, the transient currents provide a way to read these states. Within our approach we take into account both the uniaxial and transverse anisotropy. The latter may induce additional quantum tunneling processes which affect the efficiency of the proposed read-and-write scheme. An equally weighted mixture of molecular spin states can be prepared if one of the electrodes is ferromagnetic.
Four discrete MnIII/MnII tetra-nuclear complexes with double-cuboidal core were synthesized. dc magnetic measurements show that both Mn2+ - Mn3+ and Mn3+ - Mn3+ magnetic interactions are ferromagnetic in three samples leading to an S = 9 ground state for the Mn4 unit. Furthermore, these complexes are Single-Molecule Magnets (SMMs) clearly showing both thermally activated and ground state tunneling regimes. Slight changes in the [Mn4] core geometry result in an S = 1 ground state in fourth sample. A one-dimensional assembly of [Mn4] units was obtained in the same synthetic conditions with the subsequent addition of NaN3. Double chair-like N3- bridges connect identical [Mn4] units into a chain arrangement. This material behaves as an Ising assembly of S = 9 tetramers weakly antiferromagnetically coupled. Slow relaxation of the magnetization is observed at low temperature for the first time in an antiferromagnetic chain, following an activated behavior with 47 K and tau_0 = 7x10^-11 s. The observation of this original thermally activated relaxation process is induced by finite-size effects and in particular by the non-compensation of spins in segments of odd-number units. Generalizing the known theories on the dynamic properties of poly-disperse finite segments of antiferromagnetically coupled Ising spins, the theoretical expression of the characteristic energy gaps were estimated and successfully compared to the experimental values.
We present a new family of exchange biased Single Molecule Magnets in which antiferromagnetic coupling between the two components results in quantum behaviour different from that of the individual SMMs. Our experimental observations and theoretical analysis suggest a means of tuning the quantum tunnelling of magnetization in SMMs. See also: W. Wernsdorfer, N. Aliaga-Alcalde, D. Hendrickson, G. Christou, Nature 416 (2002) 406.
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