The radiation dynamics of a magnetic dipole located inside a photonic crystal has been considered as an analogue for optical emission of a point-like emitter in such a crystal. We have experimentally realized this situation by fixing a single crystal yttrium iron garnet (YIG) sphere of 1.7 mm diameter inside a photonic crystal consisting of dielectric alumina rods. These rods form a woodpile structure of size 16 × 6 × 6 cm3 . The photonic crystal shows a band gap at microwave frequencies between 12.9 and 14.3 GHz as calculated and verified from the transmission characteristics of the crystal. The radiation feedback of the YIG sphere was probed by ferromagnetic resonance experiments covering a large frequency range from 8 to 17 GHz. Whereas outside the band gap the radiation-induced linewidth amounts up to 30 Oe, it is almost completely suppressed inside the gap. From the full analysis of linewidth and resonance shift, we could clearly prove the non-Markovian character of the radiation dynamics at the edges of the gap as expected from theory. The experimental control of spontaneous emission, as realized in our experiment, is a very promising step towards future optical applications in low threshold lasers, highly efficient light emitting diodes or photovoltaic solar modules.

The temperature dependence of the spin susceptibilities of S = 1, 3/2, 2, 5/2 and 7/2 Heisenberg antiferromagnetic 1D spins chains with nearest-neighbor coupling was simulated via quantum Monte Carlo calculations, within the reduced temperature range of 0.005 ≤ T* ≤ 100, and fitted to a Padé approximation with deviations between the simulated and fitted data of the same order of magnitude as or smaller than the quantum Monte Carlo simulation error. To demonstrate the practicality of our theoretical findings, we compare these results with the susceptibility of the well known 1D chain compound TMMC ([(CH(3))(4)N[MnCl(3)]], d(5), S = 5/2) and find that different intra-chain spin-exchange parameters result if we consider the data above and below the structural phase transition reported for TMMC at ~126 K. The structural phase transition, which gives rise to an anomaly in the magnetic susceptibility, is independent of the magnetic field up to magnetic fields of 7 T. Additionally, we show that the S = 1 system NiTa(2)O(6) with tri-rutile crystal structure can be very well described as a Heisenberg S = 1 spin chain.

The phenomenon of chaotic microwave self-generation under conditions of a four-wave parametric spin wave interaction in active resonance rings based on ferromagnetic films has been studied for the first time. It is shown that microwave signals of various types-in particular, monochromatic, stationary soliton-like pulse trains, and dynamic chaos-can be generated by controlling the gain level in the active ring. Parameters characterizing the chaotic signal generated in the ring are determined.

Intense soliton-like spin wave pulses were parametrically generated in ferromagnetic thin-film ring resonators under the action of periodic parallel magnetic pulse pumping. Various types of nonlinear pulse sequences were observed depending on the pump pulse repetition period and the position of the pulse carrier frequency with respect to the ring resonator frequency spectrum. A theoretical model is suggested and calculations are performed that give a detailed explanation of the observed phenomena.

We generate experimentally spin-wave envelope dark solitons from rectangular high-frequency dark input pulses with externally introduced phase shifts in yttrium-iron garnet magnetic fims. We observe the generation of both odd and even numbers of magnetic dark solitons when the external phase shift varies. The experimental results are in a good qualitative agreement with the theory of the dark-soliton generation in magnetic films developed earlier [Phys. Rev. Lett. 82, 2583 (1999)].

The theoretical approach of two-magnon scattering in polycrystalline ferrites by Sparks, Loudon, and Kittel [Phys. Rev. 122, 791 (1961)] aiming at the microstructure-related relaxation of the uniform precession mode is extended to describe the relaxation of spin-wave modes. Within this framework we introduce a unified model that describes the influence of pores and microdomains on the relaxation of both the uniform precession and spin-wave modes. It is shown that the spin-wave linewidth does not only depend on the wave number-as assumed in conventional theory-but also on the propagation direction of the spin waves. This will, in particular, affect the damping of the critical modes at spin-wave instabilities, when probed in different experimental configurations. The effect of the number and size of pores as well as the influence of domain size and anisotropy is studied in detail, and as will be shown, this results in quite different parameter dependencies. Good qualitative and even quantitative agreement with previous experimental data is achieved without using any fit parameter.

We show by means of theoretical considerations and electronic circuit experiments that time-delayed feedback control suffers from severe global constraints if transitions at the control boundaries are discontinuous. Subcritical behavior gives rise to small basins of attraction and thus limits the control performance. The reported properties are, on the one hand, universal since the mechanism is based on general arguments borrowed from bifurcation theory and, on the other hand, directly visible in experimental time series.

We address the problem which type of initial state yields successful stabilisation when time-delayed feedback control is applied. Using well known concepts from bifurcation theory we provide a general mechanism that limits the corresponding basins of attraction. Application of normal form analysis to general delay-differential equations proves the universality of our results. The empirical criteria which determine the prospective size of the basin are easily accessible and a demonstration in terms of a simple numerical simulation is provided.

We review recent developments for the control of chaos by time-delayed feedback methods. While such methods are easily applied even in quite complex experimental context the theoretical analysis yields infinite-dimensional differential-difference systems which are hard to tackle. The essential ideas for a general theoretical approach are sketched and the results are compared to electronic circuits and to high power ferromagnetic resonance experiments. Our results show that the control performance can be understood on the basis of experimentally accessible quantities without resort to any model for the internal dynamics.

The influence of dissipation on the process of formation and propagation of envelope solitons is considered on the example of spin wave envelope solitons in yttrium iron garnet (YIG) film waveguides. It is shown that the measurements of attenuation of the peak power of a propagating nonlinear wave packet in a weakly dissipative medium can be used to determine the soliton formation length. This length turns out to be smaller than the characteristic dispersion length calculated for a given shape and duration of the input pulse. A simple approximate analytic expression for the soliton formation time in a dissipative medium is introduced and confirmed by both numerical calculations and preliminary laboratory experiments on dipolar spin waves in YIG waveguides.

Parametric generation of intense solitonlike spin-wave pulses is experimentally observed in ring resonators based on ferromagnetic films under the effect of a periodic parallel pulsed magnetic pumping. Depending on the repetition rate of the pumping pulses and the position of their carrier frequency about the eigenfrequency spectrum of the ring resonator, different types of nonlinear pulse sequences are obtained. The theoretical explanation of this phenomenon is proposed.

The basic features of time-delayed feedback schemes for the control of chaos are reviewed, The method is applied to high-power ferromagnetic resonance experiments in YIG spheres beyond the Suhl threshold. Chaotic motion is suppressed, and regular periodic states are stabilized.

The self-generation of periodic spin-wave envelope soliton trains of microwave spin waves in active rings based on ferromagnetic films is studied experimentally. The trains of bright solitons with different periods are self-generated in the same ring due to the frequency-selective control of the attenuation of spin waves circulating in an active ring.

The performance of time-delayed feedback control is studied by linear stability analysis. Analytical approximations for the resulting eigenvalue spectrum are proposed. Our investigations demonstrate that eigenbranches that develop from the stable Lyapunov exponents of the free system also have a strong influence on the control properties, either by hybridization or by a crossing of branches which interchanges the role of the leading eigenvalue. Our findings are confirmed by numerical analysis of two particular examples, the Toda and the Rossler models. More important is the verification by actual electronic circuit experiments. Here, the observed reduction of control domains can be attributed to these additional eigenvalue branches. The investigations lead to a thorough analytical understanding of the stability properties in time-delayed feedback systems.

The parametric generation of bright spin-wave soliton-like pulse trains by microwave parallel pumping has been realized in an yttrium iron garnet film. Two intrinsically different types of the stationary soliton trains were obtained. Theoretical explanation for the observed phenomena is suggested.

The problem of internal oscillations of kink-type solitons in a one-dimensional easy-plane antiferromagnet is studied by analytical methods. Apart from the Goldstone mode a second local mode which is due to the coupling between in-plane and out-of-plane spin components has been derived. For typical experimental conditions in a model system like (TMMC) the frequency of this mode is very close to the bottom of the magnon band. Considering both a twofold and a weak sixfold in-plane crystal field anisotropy we found that close to the spin-flop transition the separation of this local mode from the magnon band is increased and dramatically affected by the sixfold anisotropy. We show that quantum properties of this mode are not important.

We report low-temperature measurements of the specific heat, thermal expansion, and thermal conductivity on the quasi-one-dimensional, effective S = 1/2 Heisenberg antiferromagnet Yb4As3. Distinct field-induced anomalies were found in the above quantities which are well described by the classical sine-Gordon soliton solution for an easy-plane Heisenberg antiferromagnet. Our findings strongly suggest that Yb4As3 represents the first example of an antiferromagnetic S = 1/2 spin-chain system where this type of nonlinear excitation could be identified. [S0031-9007(99)09295-9].

The dynamics of the magnetization of yttrium iron garnet spheres was studied by ferromagnetic resonance both within the subsidiary absorption regime and the coincidence regime of the first-order Suhl instability. The absorption signal shows auto-oscillations with a rich variety of nonlinear behavior. Along with other routes to chaos we observed intermittency and identified each of the Pomeau-Manneville types I-III. Within the chaotic regime crisis-induced intermittency, on-off intermittency, and noise-induced intermittent behavior were observed. [S1063-651X(99)00602-9].

Numerical simulations of noise-free stochastic resonance and aperiodic stochastic resonance in chaotic ferromagnetic resonance are presented. The model, based on three-magnon interactions between the externally excited uniform mode and pairs of spin waves, shows on-off intermittency. The rf magnetic field amplitude is slowly modulated by a small periodic or aperiodic signal, and the output signal, which reflects the occurrence of laminar phases and bursts in the time series of spin-wave amplitudes, is analyzed. On variation of the de magnetic field the signal-to-noise ratio of the output signal and the correlation function between modulation and output signal pass a maximum, which indicates the occurrence of periodic and aperiodic stochastic resonance, respectively. The role of thermal magnon excitations in the occurrence of this maximum is clarified. The results are compared with experimental findings obtained in other types of intermittency.

This chapter contains sections titled: Introduction Ferromagnetic Resonance in Spin-Wave Instabilities Experimental Set-Up Observed Phenomena Routes to Chaos Nonresonant Parametric Modulation Analytical and Numerical Approach Experimental Suppression of Spin-Wave Chaos Occasional Proportional Feedback The OGY Concept Experimental Control by an Analog Feedback Device Time-Delayed Feedback Control Principles of Control Application to Spin-Wave Chaos Conclusions