First-order Suhl Research Articles

Chaos and chaotic transients in an yttrium iron garnet sphere.

We present detailed results of studies of chaos and chaotic transients involving spin waves in an yttrium iron garnet sphere. We drive the ferromagnetic resonance of this system at the first-order Suhl instability using driving frequencies between 2.0 and 3.4 GHz. In some regions of parameter space we see chaotic transients, while in others we see quasiperiodic oscillations or stable chaos. We characterize these states by various means, such as dimension or amplitude. We also present some results of a three-spin-wave-mode calculation based on the Landau-Lifshitz equation. This calculation produces phenomena similar to some of those seen in the experiment but is not sufficient to reproduce all the behavior that we see. We believe that a calculation involving more spin-wave modes is necessary to reproduce many of our experimental results.

Chaos and chaotic transients in yttrium iron garnet (invited)

Long-lived chaotic transients are a prominent feature of the spin-wave behavior of spheres of yttrium iron garnet (YIG) being perpendicularly pumped in the region of the first-order Suhl instability. These transients may appear after a sudden increase in rf pumping power or during transitions between quasiperiodic auto-oscillations. The transients, which result from the collision of a chaotic attractor with the basins of attraction of multiple stable quasiperiodic attractors, vary in lifetime by more than six orders of magnitude, from milliseconds to hours, as a function of the rf driving field. The average lifetimes of these transients fit an extended Grebogi–Ott–Yorke scaling law. Roughening the surface of the YIG sphere drastically changes the behavior of these transients.

Nonlinear dynamics of spin waves (invited)

For a yttrium-iron-garnet sphere at room temperature, an experimental study is made of the first-order Suhl spin-wave instability using perpendicular pumping at 9.2 GHz with the dc field parallel to the [111] crystal axis. The dynamical behavior of the magnetization is observed with high resolution by varying two control parameters, dc field (580<H0<2100 G) and microwave pump power (1<Pin <200 mW). Within this parameter space quite varied behavior is found: (i) onset of the Suhl instability by excitation of a single spin-wave mode with very narrow linewidth (<0.5 G); (ii) when two or more modes are excited, interactions lead to collective oscillations (‘‘auto-oscillations’’) with a systematic dependence of frequency (104–106 Hz) on pump power, these oscillations displaying period-doubling to chaos; (iii) quasiperiodicity, locking, and chaos occur when three or more modes are excited; (iv) abrupt transition to wide band power spectra (i.e., turbulence), with hysteresis; (v) irregular relaxation oscillations and aperiodic spiking behavior. A theoretical model of coupled modes is numerically evaluated and found to exhibit a behavior pattern similar to those observed experimentally.

Antiferromagnetic Resonance and Spin-Wave Instabilities at Spin-Flop Critical Field in (C2H5NH3)2CuCl4

Antiferromagnetic resonance and parametric excitation of spin-waves at spin-flop critical field in (C 2 H 5 NH 3 ) 2 CuCl 4 are studied by perpendicular-pumping technique. Nonlinear absorption which is attributed to the first-order Suhl instability is observed at twice the frequency of the spin-flop critical field resonance. Power dependence of the imaginary part of the susceptibility, χ'', shows the existence of the second threshold which indicates unstable growth of second group of magnon modes.

PARAMETRIC EXCITATION OF SPIN-WAVES THROUGH SPIN-FLOP CRITICAL FIELD RESONANCE IN (C2H5NH3)2 CuCl4

Parametric excitation of spin-waves in antiferromagnetic (C2H5NH3)2 CuCl4 has been studied by the perpendicular-pumping technique. Nonlinear absorption which is attributed to the first-order Suhl instability is observed at twice the frequency of the spin-flop critical field resonance.

Chaotic transients and multiple attractors in spin-wave experiments.

A long-lived transient form of chaos was observed by rf perpendicular pumping of spheres of yttrium iron garnet in the region of the first-order Suhl instability. The average temporal lengths of these transients as functions of pumping power were fitted by a theory involving capture of the chaotic trajectory by multiple periodic attractors.

Spin-Wave Instabilities by Perpendicular Pumping in K2CuF4

The first-order Suhl instability in the two-dimensional ferromagnet K 2 CuF 4 is investigated at the frequency of 8.9 GHz and at the temperature of 1.4 K. The spin-wave relaxation is derived from the threshold for spin-wave instability by the three-magnon splitting process which results in the annihilation of a k =0 magnon and the creation of a pair of magnons having wave vectors k and - k . Spin-wave linewidth in the [100] direction is very large compared with other directions in the c -plane.

Nonlinear phonon generation via localized modes.

A theoretical study of parametric excitation of phonons involving impurities in cubic crystals with NaCl structures is presented. The proposed excitation mechanism which takes place via nonlinear processes involving localized modes is analogous to the first-order Suhl instability in ferromagnetic insulators. Sufficient excitation of impurity lattice vibration by infrared absorption can result in a sudden avalanche of optical and acoustic phonons due to anharmonic interaction. It is shown that the critical power of the laser source necessary to attain the instability threshold is experimentally feasible.

Parametric excitation of phonons in iron borate (FeBO3)

The nonlinear relaxation of the ferromagnetic resonance into short-wavelength phonons is investigated theoretically for weak ferromagnets. A generalized theory of firstorder Suhl instabilities is elaborated showing that the decisive nonlinear term results from the magnetoelastic interaction. Nonlinearities of the dipole-dipole-interaction, generally predominating parametric effects in ferro- and ferrimagnetic materials, can be neglected. The results fit in satisfactorily with the experimental data obtained for FeBO3.

Nonlinear effects involving localized magnon modes in impure ferromagnetic insulators

A simple theoretical treatment for the study of nonlinear processes involving impurities in ferromagnetic insulators is presented. In particular, the possibility of exciting ferromagnetic magnons with very large wave vectors is analyzed theoretically. The proposed excitation mechanism is analogous to the first-order Suhl instability and takes place via nonlinear processes involving localized modes. A rough estimate of the critical power of a far-infrared laser source necessary to attain the instability threshold is given. It is noted that the threshold value is within the power capabilities of present pulsed far-infrared lasers, suggesting that the process is experimentally feasible.

Parametric excitation of spin waves in ferromagnets via localized magnon modes

The possibility to excite ferromagnetic magnons with very large k is analyzed theoretically. The proposed excitation mechanism is analogous to the first-order Suhl instability and takes place via non-linear processes involving localized modes associated with imputities in ferromagnetic insulators. A rough estimate of the critical power of a far-infrared laser source necessary to attain the instability threshold shows that the processes are experimentally feasible.

Green's-Function Theory of Magnon Instabilities

The parallel-pumping and second-order Suhl magnon instabilities are treated by means of the many-time Green's-function method. The criterion for determining the threshold field as the radius of convergence of a series of the physical quantities, established for the first-order Suhl instability, is also found to be valid in these cases.