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

Tunneling Rate for Superparamagnetic Particles by the Instanton Method

We derive the tunneling rate for paramagnetic molecules in the context of a collective spin model. By means of path integral methods an analytical expression is derived. Given the very large spins in question (s ~ 3000 hbar), the observation of magnetization changes due to pure unitary tunnel effects is unlikely.Comment: 16 pages, 2 figure

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

Linewidth of single photon transitions in Mn12_{12}-acetate

We use time-domain terahertz spectroscopy to measure the position and linewidth of single photon transitions in Mn$_{12}$-acetate. This linewidth is compared to the linewidth measured in tunneling experiments. We conclude that local magnetic fields (due to dipole or hyperfine interactions) cannot be responsible for the observed linewidth, and suggest that the linewidth is due to variations in the anisotropy constants for different clusters. We also calculate a lower limit on the dipole field distribution that would be expected due to random orientations of clusters and find that collective effects must narrow this distribution in tunneling measurements.Comment: 5 pages, accepted to Physical Review

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

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

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.

Magnetization of Mn_12 Ac in a slowly varying magnetic field: an ab initio study

Beginning with a Heisenberg spin Hamiltonian for the manganese ions in the Mn_12 Ac molecule, we find a number of low-energy states of the system. We use these states to solve the time-dependent Schrodinger equation and find the magnetization of the molecule in the presence of a slowly varying magnetic field. We study the effects of the field sweep rate, fourth order anisotropic spin interactions and a transverse field on the weights of the different states as well as the magnetization steps which are known to occur in the hysteresis plots in this system. We find that the fourth order term and a slow field sweep rate are crucial for obtaining prominent steps in magnetization in the hysteresis plots.Comment: LaTeX, 11 pages, 12 eps figure