Hartmut Benner

Limits of time-delayed feedback control

Abstract General features of stability domains for time-delayed feedback control exist, which can be predicted analytically. We clarify, why the control scheme with a single delay term can only stabilise orbits with short periods or small Lyapunov exponents, and derive a quantitative estimate. The limitation can be relaxed by employing multiple delay terms. In particular, the extended time delay autosynchronisation method is investigated in detail. Analytic calculations are in good agreement with results of numerical simulations and with experimental data from a nonlinear diode resonator.

Theoretical and experimental aspects of chaos control by time-delayed feedback

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.

Multistability and chaos by parametric excitation of longwave modes in a YIG sphere

Spin-wave instabilities in spheres of yttrium iron garnet have been studied by ferromagnetic resonance within the coincidence regime of the first-order Suhl instability (1.8–3.4 GHz), i.e. both the uniform mode and pairs of spin-waves were simultaneously excited on resonance. From the characteristic behaviour above the threshold, three different regimes of resonance fields (and frequencies) could be distinguished: For low fields (640–680 Oe) and for high fields (950–1210 Oe) the amplitude of magnetization remains time independent and only at high input power becomes suddenly chaotic. In the intermediate regime (680–950 Oe) a very complex multistable behaviour occurs and a variety of oscillations and sequences of bifurcations are observed. We discuss our experimental results in terms of a multi-mode model which, beyond spin-waves, considers the excitation of longwave modes with wavelengths in the order of sample dimension. Magnetostatic modes and spin-waves can be described within a unified picture by introducing “spherical spin-waves” which are classified by symmetry. A new mechanism based on the indirect excitation of the magnetostatic (4,3,0) mode is introduced. Numerical simulations show that this mechanism can explain both the multistability and the complex dynamic behaviour of the system.

Parametric frequency conversion with amplification of a weak spin wave in a ferrite film

We report on experiments of parametric frequency conversion of a weak signal spin wave by a copropagating strong pump spin wave. An effective spin-wave frequency conversion with amplification occurred when the carrier frequencies of the co-propagating waves were in the spectral region of high negative dispersion in the dipole-exchange spin-wave spectrum of the film. A theoretical explanation of the observed phenomenon is given in terms of a four-wave parametric interaction process.

Magnetic solitons investigated by NMR and ESR

Abstract The soliton dynamics in ferro- and antiferromagnetic sine-Gordon chains has been studied by frequency and temperature dependent measurements of the nuclear spin-lattice relaxation time T 1 and of the electron spin resonance linewidth δ H . We report on experiments in CsNiF 3 and TMMC. Particular attention was aimed at the stability of the solitons in high magnetic fields.

Detection of UHF sound in the antiferromagnet FeBO3 by a SQUID magnetometer

The effect of ultra-high-frequency sound on the magnetic moment of an antiferromagnet with strong magnetoelastic interaction is studied. Quasiphonons of frequency approximately 1 GHz were excited by an external piezotransducer or by a microwave field. At liquid nitrogen temperatures the total magnetic moment of the sample is found to decrease with increasing number of quasiphonons, whereas at liquid helium temperatures the magnetic moment increases. This increase can be considered as an effect of dynamic polarization induced by hypersound excitation, which is observed for the first time. The dynamic polarization can be explained in terms of a three-particle process: a quasiphonon and a quasimagnon are annihilated and a new quasimagnon with smaller magnetic moment is created.

Observation of parametric amplification of propagating dipole-exchange spin waves in yttrium iron garnet films

Amplification of a weak-signal spin wave by a strong pump spin wave propagating in an yttrium iron garnet film is observed for the first time. A theoretical explanation of the amplification phenomenon is suggested on the basis of the four-wave parametric processes.

Padé approximations for the magnetic susceptibilities of Heisenberg antiferromagnetic spin chains for various spin values

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.

Parametric generation of solitonlike spin-wave pulses in ring resonators based on ferromagnetic films

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.

Observation of spin-wave envelope dark solitons in ferromagnetic films

Microwave spin-wave envelope dark solitons were experimentally observed for the first time. Dark solitons with zero minimum amplitude were generated by two-frequency excitation of input spin waves with a fixed amplitude. Nonlinear interaction between these two traveling waves gave rise to periodic sequences of dark solitons in a ferromagnetic film.