Nonlinear Spin Waves Research Articles

Self-generation of two-dimensional spin-wave bullets.

The experimental observation of self-generation of two-dimensional, self-focusing nonlinear spin wave packets-spin wave bullets-in an active ring is reported. The ring is composed of a ferrite film with two antennae for excitation and detection of the wave packets, and a microwave amplifier connecting the antennae and closing the ring. Experimental observation has been made by using the time and space resolved Brillouin light scattering technique. The parameters of spin wave bullets self-generated from noise in an active ring are similar to those of bullets coherently excited by external microwave pulses. The observed self-generation process provides unambiguous evidence that wave bullets are intrinsic excitations of a two-dimensional nonlinear medium with dissipation that is focusing in both directions.

Suppressing pulsed microwave signals in a nonlinear spin wave interferometer

The suppression of S-band microwave pulses in a nonlinear spin wave interferometer was experimentally studied for the first time. The microwave interferometer employed a nonlinear spin wave phase shifter based on an yttrium iron garnet film. A signal representing a periodic sequence of rectangular pulses with a power of up to 2.5 mW passes through the nonlinear interferometer without distortion, while an increase in the pulse power to 13.8 mW results in virtually complete suppression of the pulsed signal.

Collision properties of quasi-one-dimensional spin wave solitons and two-dimensional spin wave bullets.

Collision properties of quasi-one-dimensional spin wave envelope solitons propagating in narrow ferrite film waveguides and of two-dimensional self-focused spin wave packets (spin wave bullets) propagating in wide ferrite film samples are studied both experimentally and numerically. The experiments, performed by means of a space- and time-resolved Brillouin light scattering technique, have shown that quasi-one-dimensional spin wave envelope solitons retain their shapes after collisions, while two-dimensional spin wave bullets are destroyed in collisions. The experiments have also shown that the introduction of a fixed phase shift between the colliding envelope solitons leads to a qualitative change in their interaction at the collision point. Numerical modeling of head-on collisions of nonlinear spin wave packets based on two different approaches provides a good qualitative description of the observed collision phenomena.

Modulational instability of nonlinear spin waves in easy-axis antiferromagnetic chains. II. Influence of sample shape on intrinsic localized modes and dynamic spin defects

An indirect method of producing intrinsic localized modes (ILM's) is to drive an unstable uniform mode to large amplitude. In this investigation the intimate connection between the shape-dependent demagnetization factor, the modulation instability, and ILM behavior is established. The stability of the antiferromagnetic resonance (AFMR) against breakup into such ILM's is shown to depend strongly on the frequency difference between the linear AFMR and the long-wavelength limit of the spin-wave dispersion curve. This difference, which stems from the long-range dipole-dipole interactions, depends on the demagnetization factor and hence the sample shape. Here it is demonstrated initially with linear perturbation analysis and later with molecular-dynamics simulations that the instability characteristics and ILM production properties depend strongly on the sign and magnitude of the frequency difference. The simulations show that when the AFMR frequency is coincident with the spin-wave band, a spatially coherent train of ILM's appears, but this coherence is lost at long times. When the AFMR frequency is inside the spin-wave band, the Suhl instability populates the degenerate spin waves, whose subsequent modulational instability leads to traveling and decelerating ILM's. When the AFMR frequency is below the spin-wave band, a large-amplitude threshold for the instability appears. Above this threshold ILM's and localized dynamic spin flops occur, confined to specific lattice regions.

Nonlinear surface spin waves on ferromagnetic media with inhomogeneous exchange anisotropy

The theory of nonlinear surface spin waves in pure-exchange semi-infinite ferrom agnetic media with inhomogeneous exchange anisotropy has been considered by usin g the Landau-Lifshitz equation. For partly pinned pure-exchange ferromagnet, the boun-dary condition for magnatization of this system is derived, and the nonlinear dispersion relation for these waves is obtained. The one-dimensional(stationary wave along the z-direction) and two-dimensional(2D)(travelling wave in the oxy plane) nonlinear Schrdinger equations which are satisfied by the spin -wave envelope amplitude of the magnetization, are derived. It is shown that the amplitude of the magnetization is determined by the 2D nonlinear Schrdinger e quation. From this, we predict that the nonlinear excitation on the surface of m agnetic materials should be of 2D soliton form. For weakly nonlinear spin waves, the possibi-lity of soliton formation on the basis of 2D nonlinear Schrdi nger equation has been discussed in detail.

Theory of Nonlinear Surface Spin Waves on a Pure Exchange Ferromagnet

In terms of the total energy of a ferromagnet and the Landau–Lifshitz equation, the nonlinear surface spin waves in a ferromagnet with pure nonuniform exchange anisotropies are studied. It is found that the nonlinear dispersion relation for these waves is modified by the nonuniform exchange anisotropy comstants, and the nonlinear excitation appears as surface magnetic solitons localized near the surface of a crystal. A two-dimensional nonlinear Schrödinger equation for the spin–wave envelope is obtained and the conditions for the existence of a single soliton solution are discussed.

Nonlinear microwave spin wave interferometer

The characteristics of a nonlinear microwave spin wave interferometer were experimentally studied for the first time. The interferometer was implemented according to a bridge scheme with a nonlinear spin wave phase shifter based on an yttrium-iron garnet film. The maximum sensitivity of the nonlinear interferometer with respect to the input signal level was reached with a phase shifter operating on the forward volume spin waves. In the GHz frequency range, an increase in the microwave power up to a few mW led to a signal phase shift exceeding 180 °.

Spin-wave dynamic magnetization reversal in a quasi-single-domain magnetic grain

Magnetization reversal in a fine ferromagnetic grain is simulated for the case of an instantaneously applied reversal magnetic field. The Hamiltonian of the system contains the exchange interaction, uniaxial anisotropy, Zeeman energy, and dipole-dipole interactions. A cubic grain is discretized into 64 cubic subgrains and the coupled gyromagnetic equations of motion are solved without phenomenological damping. A scheme to solve these equations is developed that utilizes only two variables per sub-cube magnetization and strictly conserves the absolute magnitude. The initial stage of reversal is uniform rotation followed by a nonlinear excitation of nonuniform magnetic oscillations driven by this uniform mode. An excess of the initial Zeeman energy is transformed into nonlinear spin waves, allowing the average magnetization to substantially reverse. The process of magnetization reversal in fine quasi-single-domain grain exhibits general features of Hamiltonian wave systems with nonlinear diffusion. This nonlinear diffusion is forbidden for either a strong reversal field and/or a small grain size.

Nonlinear surface spin waves on ferromagnetic media with inhomogeneous exchange anisotropies: soliton solutions

The nonlinear surface spin waves in ferromagnets with pure inhomogeneous exchange anisotropies have been considered. The boundary condition for magnetization of this system is derived. The nonlinear dispersion relation for these waves is obtained, and the modulation of the inhomogeneous exchange constants is investigated. The two-dimensional nonlinear Schrödinger equation satisfied by the spin-wave envelope amplitude is derived for the first time, and conditions for the existence of a single solitonic solution are discussed. A soliton solution is presented as an example.

Magnetoelastic Interaction in the Heisenberg Magnet Model

We investigate the Heisenberg magnetic chain of spins interacting with the atomic displacement by exchange interaction modulation. By use of the SU(2) generalized coherent states technique we obtain in continual limit the classical description of the model, which is a system of coupled Landau–Lifshitz and Boussinesq equations describing nonlinear spin waves accompanied with sound waves. Domain-walls and soliton type solutions of this system are derived in harmonic phonon approximation. The possibility of energy pumping from the magnon subsystem to the phonon one is shown for the case of near-sonic velocities of motion of the solitons. The model of the multisublattice Heisenberg magnet consisting of p sublattices of ferromagnetic type and q sublattices of antiferromagnetic type is studied taking into consideration the interaction between the sublattices. A system of equations describing this model, which in the small amplitude of spin deviations approximation can be reduced to the nonlinear Schrödinger equation with Yajima–Oikawa potential, is obtained.

Nonlinear spin wave resonance modes

Nonlinear spin wave resonance modes of magnetic films are studied both theoretically and experimentally. In the theoretical analysis the normal modes with arbitrary amplitudes are studied for a film magnetized perpendicular to its plane. The film is assumed to be uniform apart from a layer close to the surfaces, where the spins may be pinned. The spin wave resonance mode of the lowest frequency (principal mode) is considered in detail for the film with arbitrary surface spin pinning. The mode profile changes with increasing amplitude trying to redistribute itself in a more uniform manner across the film thickness. The nonlinear shift of the resonance field depends critically on the pinning. In experiments, we use yttrium–iron–garnet films with a strong gradient in the anisotropy field across the film thickness. With increasing pump power, the principal mode shows a sublinear shift of the resonance field and superlinear growth in the absorption amplitude. These features are explained in terms of the spatial nonuniformity of the mode profile.

Magnetization reversal as a nonlinear multimode process

Dynamic magnetization reversal has been simulated in a single grain for an instantaneously applied reversal magnetic field. The grain was considered as a system of n(=2,4,8) subgrains with uniaxial anisotropy coupled by exchange interaction. The gyromagnetic equations of motion were solved without phenomenological damping terms. The evolution of the magnetization was found to exhibit nonlinear spin wave excitation on a short timescale. The average magnetization significantly decreases and demonstrates irregular oscillations at a well defined mean value. The final stage of reversal is the spin-lattice damping on a longer time scale. The magnetic moment is, thereby, reassembled in a new equilibrium direction.

Solitons of a surface magnetostatic spin wave in a ferrite-insulator-metal structure

The nonlinear Schrodinger equation is analyzed in order to theoretically investigate nonlinear surface magnetostatic spin waves in a planar ferrite-insulator-metal structure. It is shown that for specific distances between the metal screen and the ferromagnetic film, pulses of surface magnetostatic spin waves may propagate as envelope solitons.

Intrinsic localized spin waves in classical one-dimensional spin systems: Studies of their interactions

One-dimensional classical spin systems can support nonlinear excitations referred to as intrinsic localized spin-wave modes. These entities have internal frequencies which lie outside the spin-wave bands of linear theory, and are localized by virtue of the intrinsic nonlinearity present in spin systems. By numerical methods, we have explored collisions between these objects. We explore the influence of a defect on the spectrum of intrinsic nonlinear spin waves, to find a new class of modes localized at the defect. We also examine the interaction of a propagating nonlinear mode with the defect, to find rich behavior. The mode may be transmitted with no reflected component, trapped or reflected depending on the strength of the perturbation associated with the defect spin.

Studies of the modulational instability of antiferromagnetic spin waves in 1D

For antiferromagnetism spin chains the modulational instability of extended nonlinear spin waves has been investigated both analytically within the framework of linear stability analysis and also numerically by means of molecular dynamics simulations. For the particular case of on-site easy-axis anisotropy treated here linear stability analysis predicts the instability region and the growth rates of modulation satellites. Our numerical simulations demonstrate that the analytical predictions correctly describe the onset of instability. For long time scales when the instability is fully developed the linear stability analysis fails and the time evolution of the modulated spin waves can show both regular and chaotic behavior.

Mode beating of spin wave beams in ferrimagnetic Lu/sub 2.04/Bi/sub 0.96/Fe/sub 5/O/sub 12/ films

We report on measurements of the two-dimensional intensity distribution of linear and non-linear spin wave excitations in a LuBiFeO film. The spin wave intensity was detected using a high-resolution Brillouin light scattering spectroscopy setup. The observed snake-like structure of the spin wave intensity distribution is understood as a mode beating between modes with different lateral spin wave amplitude distributions. The theoretical treatment of the linear regime is performed analytically, whereas the propagation of non-linear spin waves is simulated by a numerical solution of a non-linear Schrodinger equation with suitable boundary conditions.

Effect of third-order dispersion on nonlinear magnetostatic spin waves in ferromagnetic films

The effect of high-order dispersion on nonlinear magnetostatic spin waves has been investigated, theoretically, for ferromagnetic films that have metal plates near both surfaces of the film. The conditions under which third-order dispersion has to be considered are thoroughly analyzed and some numerical calculations concerning the propagation of short microwave pulses in ferromagnetic films are presented.

Modulational instability of nonlinear spin waves in easy-axis antiferromagnetic chains

The modulational instability of extended nonlinear spin waves in antiferromagnetic chains with on-site easy-axis anisotropy has been investigated both analytically in the frame of linear-stability analysis and numerically by means of molecular-dynamics simulations. The linear-stability analysis predicts the instability region and the growth rates of modulation satellites. Our numerical simulations demonstrate that the analytical predictions correctly describe the onset of instability. For long-time scales when the instability is fully developed the linear-stability analysis fails and the modulated nonlinear spin waves can evolve into localized excitations. We explore the possibility of generating intrinsic localized spin-wave modes from extended spin waves through modulational instability and find that both discreteness and strong nonlinearity seem to be essential for the creation of long-lived localized excitations. The addition of weak dissipation is found to impose a finite amplitude threshold even for infinite chains.

Non-linear spin waves on topological defects of texture in superfluid He-3-B

We have observed non-linear behaviour of stationary spin waves localised on textural topological defects. We can explain our results in the framework of the Schrodinger equation with feedback. The new method gives us the ability to see many topological defects, which are undistinguished by traditional methods of NMR. We have found that some of the non-linear spin wave modes can be responsible for the extremely long lived induction decay signals called ”Persistent signals”.

Exact nonlinear spin waves in some models of interacting classical spins on a one-dimensional lattice

We present exact finite-amplitude spin wave solutions for the nonlinear differential-difference equations describing the dynamics of spin vectors in a ferromagnetic (FM) and an antiferromagnetic (AFM) classical Heisenberg model of interacting spins on a one-dimensional lattice. We find that the dispersion relation between the frequency and wave vector of the FM nonlinear spin wave has the same form as that of the well-known low-amplitude spin wave, but with a prefactor which is explicitly dependent on its amplitude. This is in contrast with the AFM nonlinear spin wave, where we obtain the following intriguing results: Both the frequency and the wave vector acquire complicated dependences on the sublattice spin wave amplitudes. However, the dispersion relation between them is identical to that of the usual low-amplitude AFM spin wave, with no explicit dependence on the amplitudes. We outline how such solutions can also be supported in certain variants of the above models.