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The nonlinear ac stationary response of antiferromagnetic nanoparticles subjected to both external ac and dc fields of arbitrary strength and orientation is investigated using Brown's continuous diffusion model. The nonlinear complex susceptibility and dynamic magnetic hysteresis (DMH) loops of an individual antiferromagnetic nanoparticle are evaluated and compared with the linear regime for extensive ranges of the anisotropy, the ac and dc magnetic fields, damping, and the specific antiferromagnetic parameter. It is shown that the shape and area of the DMH loops of antiferromagnetic particles are substantially altered by applying a dc field that permits tuning of the specific magnetic power loss in the nanoparticles. [ABSTRACT FROM AUTHOR]

The dc component of the magnetization of noninteracting fine magnetic particles possessing simple uniaxial anisotropy and subjected to strong ac and dc bias magnetic fields is calculated via the magnetic Langevin equation. In the presence of an ac driving field, the dc component of the magnetization of uniaxial particles alters drastically leading to new nonlinear effects; in particular, it becomes frequency-dependent. In axial symmetry, where the strong ac field is parallel to the easy axis of a particle, two distinct dispersion regions in the dc magnetization at low and mid-frequencies emerge, corresponding to longitudinal overbarrier and intrawell relaxation modes. Such frequency-dependent behavior allows one to estimate the magnetization reversal time via the half-width of the low-frequency dispersion band. Otherwise, by applying the strong ac field at an angle to the easy axis of a particle so breaking the axial symmetry, a third high-frequency nonlinear resonant dispersion in the dc component of the magnetization appears accompanied by parametric resonance behavior due to excitation of transverse modes with frequencies close to the precession frequency. [ABSTRACT FROM AUTHOR]

The nonlinear ac susceptibility and dynamic magnetic hysteresis (DMH) of a single domain ferromagnetic particle with biaxial anisotropy subjected to both external ac and dc fields of arbitrary strength and orientation are treated via Brown's continuous diffusions model [W. F. Brown, Jr., Phys. Rev. 130, 1677 (1963)] of magnetization orientations. The DMH loops and nonlinear ac susceptibility strongly depend on the dc and ac field strengths, the polar angle between the easy axis of the particle, the external field vectors, temperature, and damping. In contrast to uniaxial particles, the nonlinear ac stationary response and DMH strongly depend on the azimuthal direction of the ac field and the biaxiality parameter Δ. [ABSTRACT FROM AUTHOR]

The nonlinear stationary ac response of the magnetization of assemblies consisting of (i) noninteracting uniaxial superparamagnetic nanoparticles with aligned easy axes and (ii) randomly oriented nanoparticles subjected to superimposed ac and dc bias magnetic fields of arbitrary strength and orientation is calculated by averaging Gilbert's equation augmented by a random field. The magnetization dynamics of uniaxial particles driven by a strong ac field applied at an angle to the easy axis of the particle (so that the axial symmetry is broken) alters drastically leading to new nonlinear effects due to coupling of the thermally activated magnetization reversal mode with the precessional modes via the driving ac field. In particular, the high frequency response reveals significant nonlinear effects in the precessional motion with significant consequences for the dynamic hysteresis and ultra-fast switching of the magnetization following an ultrafast change in the applied field. [ABSTRACT FROM AUTHOR]

Quantum effects in the noninertial Brownian motion of a particle in a double well potential are treated via a semiclassical Smoluchowski equation for the time evolution of the reduced Wigner distribution function in configuration space allowing one to evaluate the position correlation function, its characteristic relaxation times, and dynamic susceptibility using matrix continued fractions and finite integral representations in the manner of the classical Smoluchowski equation treatment. Reliable approximate analytic solutions based on the exponential separation of the time scales of the fast intrawell and slow overbarrier relaxation processes are given. Moreover, the effective and the longest relaxation times of the position correlation function yield accurate predictions of both the low and high frequency relaxation behavior. The low frequency part of the dynamic susceptibility associated with the Kramers escape rate behaves as a single Lorentzian with characteristic frequency given by the quantum-mechanical reaction rate solution of the Kramers problem. As a particular example, quantum effects in the stochastic resonance are estimated. [ABSTRACT FROM AUTHOR]

The inertial rotational Brownian motion and dielectric relaxation of an assembly of noninteracting rodlike polar molecules in a uniaxial potential are studied. The infinite hierarchy of differential-recurrence relations for the equilibrium correlation functions is generated by averaging the governing inertial Langevin equation over its realizations in phase space. The solution of this hierarchy for the one-sided Fourier transforms of the relevant correlation functions is obtained using matrix continued fractions yielding the longitudinal dipole correlation function, the correlation time, and the complex polarizability, which are calculated for typical values of the model parameters. Pronounced inertial effects appear in these characteristics in the high-frequency region for low damping. The exact longitudinal correlation time is compared with the predictions of the Kramers theory of the escape rate of a Brownian particle from a potential well as extended by Mel’nikov and Meshkov [J. Chem. Phys. 85, 1018 (1986)]. In the low temperature limit, the universal Mel’nikov and Meshkov formula for the inverse of the escape rate provides a good estimate of the longitudinal correlation time for all values of the dissipation including the very low damping, very high damping, and Kramers turnover regimes. Moreover, the low-frequency part of the spectra of the longitudinal correlation function may be approximated by a single Lorentzian with a halfwidth determined by this universal escape rate formula. [ABSTRACT FROM AUTHOR]

A method of calculation of nonlinear transient responses of an assembly of noninteracting polar linear molecules due to sudden changes in a strong external dc electric field is presented. The infinite hierarchy of differential-recurrence relations for the decay functions describing the relaxation of the system is derived by averaging the underlying inertial Langevin equation. The solution of this hierarchy is obtained in terms of matrix continued fractions. The integral relaxation time and the spectrum of the electric polarization for various nonlinear transient responses (step-on, step-off, and rapidly rotating field) are calculated for typical values of the model parameters. The nonlinear transient responses exhibit pronounced nonlinear effects due to the strong dc field. Analytical equations for the quantities of interest are presented in the overdamped limit. Furthermore, the linear response relaxation function and linear dynamic susceptibility are obtained as a particular case of a general nonlinear theory. [ABSTRACT FROM AUTHOR]

Quantum effects in the Brownian motion of a particle in the symmetric double well potential V(x)=ax2/2+bx4/4 are treated using the semiclassical master equation for the time evolution of the Wigner distribution function W(x,p,t) in phase space (x,p). The equilibrium position autocorrelation function, dynamic susceptibility, and escape rate are evaluated via matrix continued fractions in the manner customarily used for the classical Fokker-Planck equation. The escape rate so yielded has a quantum correction depending strongly on the barrier height and is compared with that given analytically by the quantum mechanical reaction rate solution of the Kramers turnover problem. The matrix continued fraction solution substantially agrees with the analytic solution. Moreover, the low-frequency part of the spectrum associated with noise assisted Kramers transitions across the potential barrier may be accurately described by a single Lorentzian with characteristic frequency given by the quantum mechanical reaction rate. [ABSTRACT FROM AUTHOR]