Probabilistic aspects of magnetization relaxation in single-domain nanomagnets.

A single-domain nanomagnet is a basic example of a system where relaxation from high to low energy is probabilistic in nature even when thermal fluctuations are neglected. The reason is the presence of multiple stable states combined with extreme sensitivity to initial conditions. It is demonstrated that for this system the probability of relaxing from high energies to one of the stable magnetization orientations can be tuned to any desired value between 0 and 1 by applying a small transverse magnetic field of appropriate amplitude.

Dispersion in the SERS enhancement with silver nanocube dimers.

The SERS phenomenon was studied using a large set of silver nanocube dimers programmed to self-assemble in preset locations of a patterned substrate. This SERS substrate made it possible to demonstrate the dependence of the SERS enhancement on the geometry of the silver nanocube dimers and to quantify the dispersion in the SERS enhancement obtained in an ensemble of dimers. In addition to the effects of the gap distance of the dimer and the orientation of the dimer axis relative to the laser polarization on SERS enhancement, the data reveal an interesting dependence of the site-to-site variations of the enhancement on the relative orientation of the nanocubes in the dimer.

Analysis of dynamics of excitation and dephasing of plasmon resonance modes in nanoparticles.

A novel theoretical approach to the dynamics analysis of excitation and dephasing of plasmon modes in nanoparticles is presented. This approach is based on the biorthogonal plasmon mode expansion, and it leads to the predictions of time dynamics of excitation of specific plasmon modes as well as their steady state amplitude and their decay. Temporal characteristics of plasmon modes in nanoparticles are expressed in terms of their shapes, permittivity dispersion relations, and excitation conditions.

Magnetization switching and microwave oscillations in nanomagnets driven by spin-polarized currents.

A novel theoretical approach to magnetization dynamics driven by spin-polarized currents is presented. Complete stability diagrams are obtained for the case where spin torques and external magnetic fields are simultaneously present. Quantitative predictions are made for the critical currents and fields inducing magnetization switching, for the amplitude and frequency of magnetization self-oscillations, and for the conditions leading to hysteretic transitions between self-oscillations and stationary states.

Spectral density analysis of nonlinear hysteretic systems.

A method for the analysis of spectral densities of hysteretic nonlinearities driven by diffusion processes is presented. This method is based on the Preisach formalism for the description of hysteresis and the mathematical machinery of diffusion processes on graphs. The calculations are appreciably simplified by the introduction of the "effective" distribution function.

Resonant behavior of dielectric objects (electrostatic resonances).

Resonant behavior of dielectric objects occurs at certain frequencies for which the object permittivity is negative and the free-space wavelength is large in comparison with the object dimensions. Unique physical features of these resonances are studied and a novel technique for the calculation of resonance values of permittivity, and hence resonance frequencies, is proposed. Scale invariance of resonance frequencies, unusually strong orthogonality properties of resonance modes, and a two-dimensional phenomenon of "twin" spectra are reported.

Functional integration approach to hysteresis.

A general formulation of scalar hysteresis is proposed. This formulation is based on two steps. First, a generating function g(x) is associated with an individual system, and a hysteresis evolution operator is defined by an appropriate envelope construction applied to g(x), inspired by the overdamped dynamics of systems evolving in multistable free-energy landscapes.

Spin-wave instabilities in large-scale nonlinear magnetization dynamics.

The stability of large magnetization motions in systems with uniaxial symmetry subject to a circularly polarized radio-frequency field is analytically studied. Instability conditions valid for arbitrary values of the amplitude and frequency of the driving field are derived. In the limit of small motions, these conditions yield Suhl's theory of spin-wave instabilities for the case of ferromagnetic resonance.

Nonlinear magnetization dynamics under circularly polarized field.

Exact analytical results are presented for the nonlinear large motion of the magnetization vector in a body with uniaxial symmetry subject to a circularly polarized field. The absence of chaos, the existence of pure time-harmonic magnetization modes with no generation of higher-order harmonics, and the existence of quasiperiodic magnetization modes with spontaneous breaking of the rotational symmetry are proven. Application to ferromagnetic resonance and connection with the Stoner-Wohlfarth model are discussed.

Noise in hysteretic systems and stochastic processes on graphs.

It is shown that the theory of stochastic diffusion processes on graphs is a natural tool for the analysis of noise in hysteretic systems. In particular, by using this theory, analytical expressions for stationary characteristics of random outputs of some hysteretic systems are derived.