Thermally activated escape rates of uniaxial spin systems with transverse field

Classical escape rates of uniaxial spin systems are characterized by a prefactor differing from and much smaller than that of the particle problem, since the maximum of the spin energy is attained everywhere on the line of constant latitude: theta=const, 0 =< phi =< 2*pi. If a transverse field is applied, a saddle point of the energy is formed, and high, moderate, and low damping regimes (similar to those for particles) appear. Here we present the first analytical and numerical study of crossovers between the uniaxial and other regimes for spin systems. It is shown that there is one HD-Uniaxial crossover, whereas at low damping the uniaxial and LD regimes are separated by two crossovers.Comment: 4 PR pages, 3 figures, final published versio

Field dependence of the temperature at the peak of the ZFC magnetization

The effect of an applied magnetic field on the temperature at the maximum of the ZFC magnetization, $M_{ZFC}$, is studied using the recently obtained analytic results of Coffey et al. (Phys. Rev. Lett. {\bf 80}(1998) 5655) for the prefactor of the N\'{e}el relaxation time which allow one to precisely calculate the prefactor in the N\'{e}el-Brown model and thus the blocking temperature as a function of the coefficients of the Taylor series expansion of the magnetocrystalline anisotropy. The present calculations indicate that even a precise determination of the prefactor in the N\'{e}el-Brown theory, which always predicts a monotonic decrease of the relaxation time with increasing field, is insufficient to explain the effect of an applied magnetic field on the temperature at the maximum of the ZFC magnetization. On the other hand, we find that the non linear field-dependence of the magnetization along with the magnetocrystalline anisotropy appears to be of crucial importance to the existence of this maximum.Comment: 14 LaTex209 pages, 6 EPS figures. To appear in J. Phys.: Condensed Matte

ESTIMATING RETURNS TO AGRICULTURAL RESEARCH, EXTENSION, AND TEACHING AT THE STATE LEVEL

The majority of decisions concerning investment and allocation of public funds for agricultural research, extension, and teaching (RET) are made at the state-level, while most of the quantitative RET evaluations are made on a national basis. This paper illustrates an approach for conducting a disaggregated state-level evaluation of agricultural research, extension, and teaching. Ridge regression is employed to handle multicollinearity problems.Teaching/Communication/Extension/Profession,

Quantum Thermoactivation of Nanoscale Magnets

The integral relaxation time describing the thermoactivated escape of a uniaxial quantum spin system interacting with a boson bath is calculated analytically in the whole temperature range. For temperatures T much less than the barrier height \Delta U, the level quantization near the top of the barrier and the strong frequency dependence of the one-boson transition probability can lead to the regularly spaced deep minima of the thermoactivation rate as a function of the magnetic field applied along the z axis.Comment: 4 pages, no figures, rejected from Phys. Rev. Let

Monte Carlo simulation with time step quantification in terms of Langevin dynamics

For the description of thermally activated dynamics in systems of classical magnetic moments numerical methods are desirable. We consider a simple model for isolated magnetic particles in a uniform field with an oblique angle to the easy axis of the particles. For this model, a comparison of the Monte Carlo method with Langevin dynamics yields new insight in the interpretation of the Monte Carlo process, leading to the implementation of a new algorithm where the Monte Carlo step is time-quantified. The numeric results for the characteristic time of the magnetisation reversal are in excellent agreement with asymptotic solutions which itself are in agreement with the exact numerical results obtained from the Fokker-Planck equation for the Neel-Brown model.Comment: 5 pages, Revtex, 4 Figures include

Integral Relaxation Time of Single-Domain Ferromagnetic Particles

The integral relaxation time \tau_{int} of thermoactivating noninteracting single-domain ferromagnetic particles is calculated analytically in the geometry with a magnetic field H applied parallel to the easy axis. It is shown that the drastic deviation of \tau_{int}^{-1} from the lowest eigenvalue of the Fokker-Planck equation \Lambda_1 at low temperatures, starting from some critical value of H, is the consequence of the depletion of the upper potential well. In these conditions the integral relaxation time consists of two competing contributions corresponding to the overbarrier and intrawell relaxation processes.Comment: 8 pages, 3 figure

Role of interactions in ferrofluid thermal ratchets

Orientational fluctuations of colloidal particles with magnetic moments may be rectified with the help of external magnetic fields with suitably chosen time dependence. As a result a noise-driven rotation of particles occurs giving rise to a macroscopic torque per volume of the carrier liquid. We investigate the influence of mutual interactions between the particles on this ratchet effect by studying a model system with mean-field interactions. The stochastic dynamics may be described by a nonlinear Fokker-Planck equation for the collective orientation of the particles which we solve approximately by using the effective field method. We determine an interval for the ratio between coupling strength and noise intensity for which a self-sustained rectification of fluctuations becomes possible. The ratchet effect then operates under conditions for which it were impossible in the absence of interactions.Comment: 18 pages, 10 figure

Greenberger-Horne-Zeilinger state protocols for fully connected qubit networks

We generalize the recently proposed Greenberger-Horne-Zeilinger (GHZ) tripartite protocol [A. Galiautdinov, J. M. Martinis, Phys. Rev. A 78, 010305(R) (2008)] to fully connected networks of weakly coupled qubits interacting by way of anisotropic Heisenberg exchange g(XX+YY)+g1*ZZ. Our model adopted here differs from the more familiar Ising-Heisenberg chain in that here every qubit interacts with every other qubit in the circuit. The assumption of identical couplings on all qubit pairs allows an elegant proof of the protocol for arbitrary N. In order to further make contact with experiment, we study fidelity degradation due to coupling imperfections by numerically simulating the N=3 and N=4 cases. Our simulations indicate that the best fidelity at unequal couplings is achieved when (a) the system is initially prepared in the uniform superposition state (similarly to how it is done in the ideal case), and (b) the entangling time and the final rotations on each of the qubits are appropriately adjusted.Comment: 11 pages, 1 figur

Classical and quantum magnetisation reversal studied in single nanometer-sized particles and clusters using micro-SQUIDs

Recent progress in experiment on quantum tunnelling of the magnetic moment in mesoscopic systems will be reviewed. The emphasis will be made on measurements of individual nanoparticles. These nanomagnets allow one to test the border between classical and quantum behaviour. Using the micro-SQUID magnetometer, waiting time, switching field and telegraph noise measurements show unambiguously that the magnetisation reversal of small enough single crystalline nanoparticles is described by a model of thermal activation over a single-energy barrier. Results on insulating BaFeO nanoparticles show strong deviations from this model below 0.4 K which agree with the theory of macroscopic quantum tunnelling in the low dissipation regime.Comment: 6 pages, 2 figures, conference proceedings of LT22-Helsink

Evaluation of a ln tan integral arising in quantum field theory

We analytically evaluate a dilogarithmic integral that is prototypical of volumes of ideal tetrahedra in hyperbolic geometry. We additionally obtain new representations of the Clausen function Cl_2 and the Catalan constant G=Cl_2(\pi/2), as well as new relations between sine and Clausen function values.Comment: 24 pages, no figure