Parametric Excitation Of Spin Waves Research Articles

Temperature dependence of the magnon-phonon energy relaxation time in a ferromagnetic insulator

We have used the Boltzmann kinetic equation for the phonon distribution function to analyze the relaxation kinetics of the spin system of a ferromagnetic insulator (F) lying on a massive dielectric substrate with high thermal conductivity. Under periodic heating of the spin system, the relaxation depends on the thickness of the F layer and on the frequency of the thermal source $\ensuremath{\omega}$. When the thickness of the F layer is much greater than the phonon-magnon scattering length, the magnon temperature dependence on the frequency has two features related to specific characteristic times of the system. One of them determines the dependence in the low-frequency regime and is related to the average phonon escape time from the F layer to the substrate ${\ensuremath{\tau}}_{\mathrm{es}}$. In turn, the high-frequency behavior is determined by the magnon-phonon collisions time ${\ensuremath{\tau}}_{mp}$. From the latter, the time of phonon-magnon collisions ${\ensuremath{\tau}}_{pm}$ can be found. In contrast, the response of effectively thin F layers is characterized by just one feature, which is determined by the time ${\ensuremath{\tau}}_{mp}$. Thus, based on the obtained theoretical results, the times ${\ensuremath{\tau}}_{\mathrm{es}},{\ensuremath{\tau}}_{mp}$, and ${\ensuremath{\tau}}_{pm}$ can be deduced from experiments on the parametric excitation of spin waves by electromagnetic radiation modulated at frequency $\ensuremath{\omega}$.

Parallel pumping of a ferromagnetic nanostripe: Confinement quantization and off-resonant driving

The parametric excitation of spin waves in a rectangular, ferromagnetic nanowire in the parallel pump configuration and with an applied field along the long axis of the wire is studied theoretically, using a semi-classical and semi-analytic Hamiltonian approach. We find that as a function of static applied field strength, there are jumps in the pump power needed to excite thermal spin waves. At these jumps, there is the possibility to non-resonantly excite spin waves near kz = 0. Spin waves with negative or positive group velocity and with different standing wave structures across the wire width can be excited by tuning the applied field. By using a magnetostatic Green's function that depends on both the nanowire's width and thickness—rather than just its aspect ratio—we also find that the threshold field strength varies considerably for nanowires with the same aspect ratio but of different sizes. Comparisons between different methods of calculations are made and the advantages and disadvantages of each are discussed.

Excitation of propagating spin waves in ferromagnetic nanowires by microwave voltage-controlled magnetic anisotropy.

The voltage-controlled magnetic anisotropy (VCMA) effect, which manifests itself as variation of anisotropy of a thin layer of a conductive ferromagnet on a dielectric substrate under the influence of an external electric voltage, can be used for the development of novel information storage and signal processing devices with low power consumption. Here it is demonstrated by micromagnetic simulations that the application of a microwave voltage to a nanosized VCMA gate in an ultrathin ferromagnetic nanowire results in the parametric excitation of a propagating spin wave, which could serve as a carrier of information. The frequency of the excited spin wave is twice smaller than the frequency of the applied voltage while its amplitude is limited by 2 mechanisms: (i) the so-called “phase mechanism” described by the Zakharov-L’vov-Starobinets “S-theory” and (ii) the saturation mechanism associated with the nonlinear frequency shift of the excited spin wave. The developed extension of the “S-theory”, which takes into account the second limitation mechanism, allowed us to estimate theoretically the efficiency of the parametric excitation of spin waves by the VCMA effect.

Parametric Excitation of Spin Waves by Voltage-Controlled Magnetic Anisotropy

The storage and transport of spin currents in spintronic devices are typically controlled by inputs of electrical current. This work instead proposes applying a voltage to excite a propagating spin wave in an ultrathin ferromagnetic heterostructure. This so-called ``voltage-controlled magnetic anisotropy'' technology could lead to significantly decreased power consumption and improved compatibility with conventional semiconductor devices.

Application of the smith chart in the analysis of the relaxation properties of magnetostatic oscillations and spin waves in ferrite films

The relaxation properties of three main types of magnetostatic oscillations in a magnetostatic film resonator and nonlinear processes (parametric excitation of spin waves in the first and second bands in the presence of the tangential magnetization of the gallium-substituted yttrium-iron garnet film and foldover in the regime of normal magnetization) are studied in the frequency range 0.8–4.5 GHz. An original method is proposed for the determination of thresholds of the parametric excitation of spin waves using the deformations of Smith chart caused by variations in the measurement power level. The method is used in the highaccuracy analysis of the frequency dependences of threshold power in the presence of tangential magnetization in the regimes of resonances of both surface and backward volume magnetostatic waves. The frequencyfield dependences of the absorption spectra of three main types of magnetostatic oscillations in the linear regime are used to determine the saturation magnetization, anisotropy fields, and unloaded Q factors of resonator at each mode and to calculate the relaxation parameters of the corresponding magnetostatic oscillations. The experimentally measured threshold pump powers are used to calculate the relaxation line widths of the parametrically excited spin waves with the aid of the improved theory of parametric processes that takes into account both cubic and uniaxial anisotropy of the film.

Parametric instability in uniform spin precession in superfluid 3He-B

In order to explain the “catastrophic spin relaxation” observed in superfluid 3He-B, the stability of spatially uniform spin precession in this liquid relative to the parametric excitation of spin waves has been analyzed. It is shown that uniform spin precession becomes unstable at low temperatures (Suhl instability). At zero temperature, the growth increments are determined for all spin wave branches. The temperature at which the transition from stable spin precession to instability takes place is estimated.

Induced and parametric excitation of spin waves by a light field with a discrete spectrum and optically induced spin echo

Induced and parametric excitation of spin waves by a light field and light-induced spin echo are considered. The static and steady-state dynamic magnetizations in the light field are determined, and the phase diagrams of the system in magnetic and light fields are constructed. The threshold of parametric excitation, the amplitude of stationary oscillations, and the trajectories described by the end point of the magnetic moment vector are calculated for the case of light-induced nonlinear ferromagnetic resonance. The trajectories can be topologically different. The transition between states with different trajectories occurs as a phase transition. The parameters of the light-induced spin echo are determined.

Parametrically driven first-order Suhl instability and nonlinearities in bismuth-substituted yttrium iron garnet films

We have demonstrated the enhancement of spin-wave nonlinearities in a bismuth-substituted yttrium iron garnet (Bi-YIG) film by parametrically exciting the first-order Suhl instability at the difference frequency of two simultaneous driving frequencies. The results show that parametric excitation of spin waves can cause this instability to grow at low threshold powers, which, in turn, channels power to other nonlinear spin-wave modes. Multiple interactions between spin waves lead to the enhancement of nonlinear processes.

On the transient and stationary parametric excitation of spin waves

Buildup times and the stationary values of spin wave excitations near the Suhl instability threshold are calculated numerically. The study is done in the framework of the two-mode model. The time evolution of the excitation may approach the steady state via oscillations that may last for a very long time. The stationary excitation N 0, and the buildup time τ b depend on the pumping power p, and the pumping field h via power laws: N 0= B( p/ p c−1) δ and τ b= A( h/ h c−1) − Δ . For the case of no de-tuning of the mode frequencies from ω p/2, δ=0.5 and Δ=0.98. In the case of modes that are de-tuned from ω p/2, δ=0.42 and Δ=1.1. The values for δ are consistent with experiments but the values for Δ are in bad agreement with experiment. It is shown that if a finite medium correction term is introduced into the equations of motion the threshold of the pumping field amplitude is below γ/ V where γ is the spin wave relaxation rate and V is the coupling of the spin waves to the pumping field. This result is very strange and raises serious doubts about the justification of the finite medium correction term.

Parametric excitation of spin waves in uniaxial ferrites

Parametric excitation of spin waves in uniaxial ferrites with large anisotropy is investigated theoretically. First-order processes in a sphere with arbitrary orientation of an external static magnetic field, in which case the pumping is oblique, are studied. The threshold field and the parameters of the excited spin waves are calculated numerically for two ferrites — easy-axis and easy-plane.

Stochastic generation accompanying parametric excitation of spin waves in yttrium iron garnet films

We report the results of experimental investigations of chaotic self-modulation of the envelope of surface spin waves as a result of first-order spin-wave parametric instability. The experimental apparatus consisted of a microwave oscillator with a spin-wave delay line in the feedback circuit.

Parametric Pair of Waves as a Nonlinear Oscillator

We considered the process of parametric excitation of spin waves and magnetoelastic waves in magnetoordered crystals in a microwave resonator. From our analysis it follows that for the k and - k wave pair there is a single-mode realization (i.e. the pair can be represented as one oscillator). The theory of parametric resonance of waves constructed in terms of these collective variables provides a new perspective on some old spin-wave experiments and helps explain the recently obtained experimental data.

Parametric excitation of spin waves in ferromagnets by longitudinal pumping localized in space

The equations of motion for the slowly varying complex amplitudes of spin waves parametrically excited by a localized pumping magnetic field have been derived. A solution of these equations satisfying given boundary and initial conditions has been obtained. The energy dissipated by spin waves decreases with the pumping intensity beyond a certain pumping power, which can be termed the regeneration threshold. The losses vanish and change sign at the instability threshold. Both thresholds depend heavily on the linear dimension L of the pumping zone, increasing with decreasing L. Owing to the regeneration process, the dissipation length of spin waves increases without bound as the pumping power approaches the instability threshold. Consequently, perturbations of a uniform state due to the boundary penetrate throughout the pumping zone, regardless of the dimension L. As a result, the full pattern of parametric instability is strongly affected by the zone boundary: 1) the spatial distribution of wave amplitudes becomes nonuniform everywhere inside the zone; 2) the amplitude growth rate in the unstable regime decreases at all points when perturbations due to the boundary reach these points; 3) the instability threshold is independent of the spin-wave frequency offset from the parametric resonance frequency. The calculated minimum instability threshold as a function of the bias magnetic field (the “butterfly” curve) changes shape with L, in agreement with the available experimental data.

Nonlinear radiation damping of parametrically excited spin waves

We consider the process of microwave parametric excitation of spin waves in a resonator. The interaction of the resonator cavity photon with the parametric magnon pair is expected to cause additional nonlinearity: nonlinear radiation damping which is proportional to the quality factor Q of the resonator. Estimations of this positive nonlinear magnon relaxation in ferromagnets and antiferromagnets (for electronic and nuclear spin waves, magnetoelastic waves) show that it can play an important role in forming the stationary state. The threshold of the autooscillations of microwave absorption in a ferromagnet is found to increase with increasing Q.

Origin of the fine structure of subsidiary absorption in tangentially magnetized YIG films

Parametric excitation of spin waves (SWs) under conditions of perpendicular pumping was investigated in epitaxial films of yttrium iron garnet (YIG). The related microwave power absorption was measured at the frequency 9.1 GHz in the magnetic field range 1200–1600 Oe. A series of absorption peaks closely spaced on the magnetic field scale were observed near the threshold of first-order Suhl instability of spin waves. The peaks spaced by 0.2–0.7 Oe originate from the shallow ripple of the butterfly curve. This is the first observation of the fine structure at subsidiary absorption in YIG films. The peak spacing was measured as a function of dc magnetic field H, film thickness d, and in-plane sample dimensions L for square samples. In the field range 1300–1400 Oe the spacing did not depend on H and was inversely proportional to L in the range of 0.6–3 mm. No thickness dependence was found in the range d=3–45 μm. Explanation is given in terms of standing spin waves set in the film plane and related to the exchange part of SW dispersion curves in ferrite film.

Dynamical chaos in magnetic systems

The theoretical and experimental studies on the transition to dynamical chaos in magnetic systems are reviewed. Both dissipative and Hamiltonian systems are discussed, with their fundamental scenarios of the transition to chaos. We discuss the models and characteristics of chaotic oscillations in magnetic materials upon parametric excitation of spin waves, in NMR masers, in the dynamics of spin chains, in the motion of a spin in an external alternating magnetic field, and in nonlinear NMR with dynamic shift of the precession frequency. An analysis of the problems of quantum chaos in spin systems is presented.

The magnon-magnon interactions in easy-plane antiferromagnets

In the framework of the spin-operator diagram technique, the processes of relaxation of lower branch magnons in a two-sublattice easy-plane antiferromagnet are investigated. The procedure of the spin Hamiltonian diagonalization allowing to obtain compact expressions for magnon interaction amplitudes is proposed. The relaxation frequencies due to three- and four-magnon processes, processes of elastic scattering and interbranch transformation by thermal and concentrational magnetization fluctuations as well as the three-magnon confluence processes with rescattering of thermal magnons by fluctuations are calculated. The results obtained are consistent with the experimental data on parametric excitation of spin waves in the low-temperature antiferromagnets MnCO3 and CsMnF3.

Effect of 'hardness' at the parametric excitation of spin-waves in antiferromagnetic MnCO3

The parametric excitation of spin-waves was studied in the easy-plane antiferromagnet MnCO3 at a microwave pumping frequency omega p/2 pi =33.8 GHz and T=1.6 K. The experiments were performed for oblique orientation of the magnetic field H with respect to the based plane of the crystal. The authors found that the two different microwave threshold fields for the appearance (hc1) and disappearance (hc2) of parametric excitation as well as the 'coefficient of hardness' kappa (hc1-hc2)/hc1 strongly depend on the angle theta between H and the basal plane, showing a decrease with increasing theta . The experimental results can be explained by the assumption that some part of the spin-wave relaxation and hardness effect arise from an interaction of spin-waves with 'orthogonal' magnetic impurities.

On the threshold of parametric instability of spin waves in a film with a rough surface

The threshold of parametric excitation of spin waves in a ferrite film with a rough surface is calculated. The influence of the surface on the threshold is twofold: (i) the normal component of the wave vector of a spin wave is quantized and (ii) surface roughnesses scatter a spin wave elastically. The elastic scattering conserves energy of spin waves and mixes phases of spin waves with different wave vectors. The threshold of parametric excitation hth depends on the relationship between the film thickness d and the mean free path l. The threshold in a thick film (d≫l) is close to that in an unbounded sample of ferromagnet hth0: (hth/hth0)2 = 1 + (πl/d)2. In a thin film (d≪l) the threshold is close to that in a randomly inhomogeneous ferromagnet (hth/hth0)2 ∼ γs/γ, where γ is the spin-wave damping and γs is the frequency of elastic scattering of spin waves on surface roughnesses.

Transition to chaotic state in spin-wave turbulence

Parametric excitation of spin-waves in an yttrium iron garnet is studied within the coincidence regime of the first-order Suhl instability. Above the spin-wave instability threshold, a period-doubling cascade is observed. At this onset of chaos, the singularity spectrum f(α) is obtained.