Analyzing and controlling chaos in spin-wave instabilities
H. Benner
Institut für Festkörperphysik,
Technische Hochschule Darmstadt and SFB 185,
D-64289 Darmstadt, Germany
Ferromagnetic samples excited by strong microwave fields show a variety
of nonlinear phenomena. We report on magnetic resonance experiments in
yttrium iron garnet (YIG) spheres probing spin-wave instabilities above the
first-order Suhl threshold. Various scenarios, such as period doubling
routes, quasiperiodicity, different types of intermittency together with
a very complex multistability have been found and analyzed [1]. In the
case of nonresonant excitation of the uniform mode ('subsidiary absorption')
the observed chaotic autooscillations correspond to a low-dimensional
attractor ( 
) with a characteristic time scale of microseconds,
whereas for resonant excitation ('coincidence regime') very high-dimensional
attractors ( 
) are obtained.
Intermittency, so far, was found rather seldom in magnetic systems, and only the occurrance of Pomeau-Manneville type III has been reported in literature [2]. We observed various kinds of intermittency starting from a fixed point, a limit cycle, a 2-torus, or even alternating between different chaotic states. From analyzing the distribution and scaling behaviour of the 'laminar' lengths, the observed signals could clearly be attributed to each of the classical Pomeau-Manneville types I, II or III and to crises [3]. A particular case of chaos-chaos intermittency identified as 'on-off intermittency' was very recently observed by us in the case of high-dimensional chaotic attractors within the coincidence regime. This specific behaviour, which was interpreted in terms of a global symmetry-breaking bifurcation, could be attributed to the excitation of an additional spin-wave mode [4].
A general problem of current interest concerns the possibility of controlling
the chaotic behaviour of nonlinear systems, which means to change the
irregular into a regular behaviour, without drastically affecting the
system parameters. The practical use of such a control would be to suppress
undesired irregularity and to select among a large number of possible
regular oscillations by just applying rather small controlling power.
We used different strategies to achieve such a control: (i) non-feedback
modulation methods, which are either based on the synchronization to an
external periodic force with a frequency close to an intrinsic system
frequency or on the change of stability induced by fast modulation of
some system parameter [5]; (ii) more sophisticated feedback control methods
aiming at the stabilization of existing, system inherent unstable periodic
orbits. This can be achieved by a simple time-delayed feedback [6] or
by calculated time-dependent corrections on one of the system parameters
as proposed by Ott, Grebogi, and Yorke (OGY) [7]. Since the latter techniques
make use of the intrinsic properties of the underlying chaotic attractor
they can, in principle, be run with very small controlling power. E. g.
in order to stabilize unstable periodic orbits on a timescale of microseconds
we developed an analog feedback device which implements the controlling
scheme of OGY. We succeeded in suppressing low-dimensional
chaos by applying a very small time-dependent feedback signal of only 
the amplitude of the input microwave field.