Application of the discrete Wentzel-Kramers-Brillouin method to spin tunneling

A discrete version of the WKB method is developed and applied to calculate the tunnel splittings between classically degenerate states of spin Hamiltonians. The results for particular model problems are in complete accord with those previously found using instanton methods. The discrete WKB method is more elementary and also yields wavefunctions.Comment: RevTex, 2ps figures, incorporates errata (typos and omitted reference) in JMP pape

Impurity relaxation mechanism for dynamic magnetization reversal in a single domain grain

The interaction of coherent magnetization rotation with a system of two-level impurities is studied. Two different, but not contradictory mechanisms, the `slow-relaxing ion' and the `fast-relaxing ion' are utilized to derive a system of integro-differential equations for the magnetization. In the case that the impurity relaxation rate is much greater than the magnetization precession frequency, these equations can be written in the form of the Landau-Lifshitz equation with damping. Thus the damping parameter can be directly calculated from these microscopic impurity relaxation processes

Scaling analysis of a divergent prefactor in the metastable lifetime of a square-lattice Ising ferromagnet at low temperatures

We examine a square-lattice nearest-neighbor Ising quantum ferromagnet coupled to $d$-dimensional phonon baths. Using the density-matrix equation, we calculate the transition rates between configurations, which determines the specific dynamic. Applying the calculated stochastic dynamic in Monte Carlo simulations, we measure the lifetimes of the metastable state. As the magnetic field approaches $|H|/J=2$ at low temperatures, the lifetime prefactor diverges because the transition rates between certain configurations approaches zero under these conditions. Near $|H|/J=2$ and zero temperature, the divergent prefactor shows scaling behavior as a function of the field, temperature, and the dimension of the phonon baths. With proper scaling, the simulation data at different temperatures and for different dimensions of the baths collapse well onto two master curves, one for $|H|/J>2$ and one for $|H|/J<2$.Comment: published versio

Thermally Activated Resonant Magnetization Tunneling in Molecular Magnets: Mn_12Ac and others

The dynamical theory of thermally activated resonant magnetization tunneling in uniaxially anisotropic magnetic molecules such as Mn_12Ac (S=10) is developed.The observed slow dynamics of the system is described by master equations for the populations of spin levels.The latter are obtained by the adiabatic elimination of fast degrees of freedom from the density matrix equation with the help of the perturbation theory developed earlier for the tunneling level splitting [D. A. Garanin, J. Phys. A, 24, L61 (1991)]. There exists a temperature range (thermally activated tunneling) where the escape rate follows the Arrhenius law, but has a nonmonotonic dependence on the bias field due to tunneling at the top of the barrier. At lower temperatures this regime crosses over to the non-Arrhenius law (thermally assisted tunneling). The transition between the two regimes can be first or second order, depending on the transverse field, which can be tested in experiments. In both regimes the resonant maxima of the rate occur when spin levels in the two potential wells match at certain field values. In the thermally activated regime at low dissipation each resonance has a multitower self-similar structure with progressively narrowing peaks mounting on top of each other.Comment: 18 pages, 8 figure

Quantum Fluctuations in Large-Spin Molecules

A new type of mesoscopic quantum effect in large-spin molecules possessing easy-axis anisotropy, such as Mn12, is predicted. The response of such a system to an external field applied perpendicular to the easy axis is considered. It is shown that the susceptibility of this system exhibits a peculiar peak of purely quantum origin. This effect arises from very general properties of quantum fluctuations in spin systems. We demonstrate that the effect is entirely accessible for contemporary experimental techniques. Our studies show that the many-spin nature of the Mn12 clusters is important for a correct description of this quantum peak.Comment: REVTeX, 3 pages, 6 figures (postscript

A Distribution of Tunnel Splittings in Mn12_{12}-Acetate

In magnetic fields applied parallel to the anisotropy axis, the relaxation of the magnetization of Mn$_{12}$ measured for different sweep rates is shown to collapse onto a single scaled curve. The form of the scaling implies that the dominant symmetry-breaking process that gives rise to tunneling is a locally varying second-order anisotropy, forbidden by tetragonal symmetry in the perfect crystal, which gives rise to a broad distribution of tunnel splittings in a real crystal of Mn$_{12}$-acetate. Different forms applied to even and odd-numbered steps provide a distinction between even step resonances (associated with crystal anisotropy) and odd resonances (which require a transverse component of magnetic field).Comment: 4 pages, 5 figures. New title; text more clearly writte

Spin Tunneling and Phonon-assisted Relaxation in Mn12-acetate

We present a comprehensive theory of the magnetization relaxation in a Mn12-acetate crystal in the high-temperature regime (T>1 K), which is based on phonon-assisted spin tunneling induced by quartic magnetic anisotropy and weak transverse magnetic fields. The overall relaxation rate as function of the longitudinal magnetic field is calculated and shown to agree well with experimental data including all resonance peaks measured so far. The Lorentzian shape of the resonances, which we obtain via a generalized master equation that includes spin tunneling, is also in good agreement with recent data. We derive a general formula for the tunnel splitting energy of these resonances. We show that fourth-order diagonal terms in the Hamiltonian lead to satellite peaks. A derivation of the effective linewidth of a resonance peak is given and shown to agree well with experimental data. In addition, previously unknown spin-phonon coupling constants are calculated explicitly. The values obtained for these constants and for the sound velocity are also in good agreement with recent data. We show that the spin relaxation in Mn12-acetate takes place via several transition paths of comparable weight. These transition paths are expressed in terms of intermediate relaxation times, which are calculated and which can be tested experimentally.Comment: 18 pages, 22 EPS figures, REVTe

Level splittings in exchange-biased spin tunneling

The level splittings in a dimer with the antiferromagnetic coupling between two single-molecule magnets are calculated perturbatively for arbitrary spin. It is found that the exchange interaction between two single-molecule magnets plays an important role in the level splitting. The results are discussed in comparison with the recent experiment.Comment: 12 pages, to be published in Phys. Rev.

Effect of local Coulomb interactions on the electronic structure and exchange interactions in Mn12 magnetic molecules

We have studied the effect of local Coulomb interactions on the electronic structure of the molecular magnet Mn12-acetate within the LDA+U approach. The account of the on-site repulsion results in a finite energy gap and an integer value of the molecule's magnetic moment, both quantities being in a good agreement with the experimental results. The resulting magnetic moments and charge states of non-equivalent manganese ions agree very well with experiments. The calculated values of the intramolecular exchange parameters depend on the molecule's spin configuration, differing by 25-30% between the ferrimagnetic ground state and the completely ferromagnetic configurations. The values of the ground-state exchange coupling parameters are in reasonable agreement with the recent data on the magnetization jumps in megagauss magnetic fields. Simple estimates show that the obtained exchange parameters can be applied, at least qualitatively, to the description of the spin excitations in Mn12-acetate.Comment: RevTeX, LaTeX2e, 4 EPS figure

Resonant Magnetization Tunneling in Mn12 Acetate: The Absence of Inhomogeneous Hyperfine Broadening

We present the results of a detailed study of the thermally-assisted-resonant-tunneling relaxation rate of Mn12 acetate as a function of an external, longitudinal magnetic field and find that the data can be fit extremely well to a Lorentzian function. No hint of inhomogeneous broadening is found, even though some is expected from the Mn nuclear hyperfine interaction. This inconsistency implies that the tunneling mechanism cannot be described simply in terms of a random hyperfine field.Comment: Some minor revisions, title changed, updated figures, two added notes, one added reference. RevTeX, 4 pages, 3 postscript figures. Submitted to Rapid Communication