Spin-wave Instability Research Articles

Parametric Excitation and Instabilities of Spin Waves Driven by Surface Acoustic Waves

AbstractThe parametric excitation of spin waves by coherent surface acoustic waves in metallic magnetic thin film structures is demonstrated experimentally using Brillouin light scattering spectroscopy. Complementary micromagnetic simulations and analytical modeling reveal that, depending on the experimental conditions, the spin‐wave instabilities originate from different phonon‐magnon and magnon‐magnon scattering processes. This opens novel ways to create micro‐scaled nonlinear magnonic systems for logic and data processing that profit from the efficient excitation of phonons using piezoelectricity.

Instability of Magnetic Skyrmion Strings Induced by Longitudinal Spin Currents.

It is well established that spin-transfer torques exerted by in-plane spin currents give rise to a motion of magnetic skyrmions resulting in a skyrmion Hall effect. In films of finite thickness or in three-dimensional bulk samples the skyrmions extend in the third direction forming a string. We demonstrate that a spin current flowing longitudinally along the skyrmion string instead induces a Goldstone spin wave instability. Our analytical results are confirmed by micromagnetic simulations of both a single string as well as string lattices, suggesting that the instability eventually breaks the strings. A longitudinal current is thus able to melt the skyrmion string lattice via a nonequilibrium phase transition. For films of finite thickness or in the presence of disorder a threshold current will be required, and we estimate the latter assuming weak collective pinning.

Parallel-Pumped Spin-Wave Instability Threshold Characteristics in Polycrystalline Yttrium Iron Garnet Excited by the Varied Rising-Edge Microwave Pulses

The parallel-pumped spin-wave instability (SWI) threshold power, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$P_{\mathrm {th}}$ </tex-math></inline-formula> , of polycrystalline yttrium iron garnet (YIG) excited by microwave pulses with the varied rising-edge time was investigated theoretically and experimentally. The SWI threshold model associated with the rising-edge time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{r}$ </tex-math></inline-formula> is developed in terms of the attributes of half-frequency spin waves in the applied static fields <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\mathrm {ext}}$ </tex-math></inline-formula> . The results manifest a significant increase in microwave-excited SWI threshold power level when the rising-edge time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{r}$ </tex-math></inline-formula> is shortened from 600 to 100 ns at the X-band. In addition, the rising-edge microwave pulses with different time scale distinctly present different threshold responses under the left-wing field region of the butterfly curves. The SWI thresholds associated with the spin-wave initial amplitude grow with increasing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\mathrm {ext}}$ </tex-math></inline-formula> when <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{r}$ </tex-math></inline-formula> is smaller than the spin-wave relaxation time ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{r}~ \boldsymbol {\le }~200$ </tex-math></inline-formula> ns), while SWI thresholds are more sensitive to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -dependent spin-wave linewidth, which decreases with the increasing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\mathrm {ext}}$ </tex-math></inline-formula> as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{r}$ </tex-math></inline-formula> exceeds the spin-wave relaxation time ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{r} ~ \boldsymbol {\ge }~400$ </tex-math></inline-formula> ns). The calculated responses of the SWI threshold are in close agreement with the measurements.

Experimental methods for the study of spin waves

Purpose of this paper is to give an overview of various experimental methods for investigation of spin waves characteristics. Methods. The paper presents a description of a number of experimental techniques, such as the probing method, the phase shift method, the method of measure of equiphase dependences, the method of intersecting wave beams, and the use of Fourier analysis of the complex transfer coefficient of spin waves to determine their spatial spectrum. The conditions for using the listed methods and the characteristics of spin waves that one can measure by means of these methods are discussed in detail. Results. The paper presents a number of fundamental results that have been obtained on the basis of described methods. For example, the probing method was successfully used to visualize the amplitude and phase distribution of spin waves in the ferrite film plane and, in particular, it was used to experimentally confirm the previously predicted appearance of super-directed propagation of surface and backward volume spin wave beams. The phase-shift measurement method made it possible to measure the dispersion dependence of spin waves in ferrite structures such as ferrite – metal and ferrite – dielectric – metal, where measurements cannot be made by the probing method. The method of measuring equiphase dependences of spin waves made it possible, in particular, to measure for the first time with great accuracy the value of an external magnetic field magnetizing an yttrium iron garnet film to saturation in various crystallographic directions. The method of intersecting wave beams has made it possible to clarify the mechanism of parametric instability of surface spin waves. Fourier analysis of the complex transfer coefficient of spin waves allowed to determine the spatial spectrum of these waves; in particular, dispersion dependences of higher modes of the backward volume spin wave were first measured using this method. Conclusion. The methods described in this paper may continue to be successfully used for investigations of spin waves characteristics in various magnon crystals, ferrite structures and meta-structures.

Second harmonic generation as a probe of parametric spin wave instability processes in thin magnetic films

We have explored the dynamic response of in-plane magnetized thin permalloy films excited by microwave fields of high amplitudes (up to 3 Oe) at 1 GHz. The response was detected using a microstrip line by measuring the second harmonic signal generated by the dynamic components of the uniform magnetization. The data measured at ferromagnetic resonance showed the threshold effect of the Suhl parametric instability process. With the increase of the microwave power above the threshold value, the dynamic response revealed an intricate nonlinear behavior, including the emergence of an additional threshold. This second threshold can be explained in terms of the ``stage by stage'' process of parametric spin wave excitation following the $S$ theory of Zakharov, L'vov, and Starobinets.

Spin-Wave Doppler Shift by Magnon Drag in Magnetic Insulators.

The Doppler shift of the quasiparticle dispersion by charge currents is responsible for the critical supercurrents in superconductors and instabilities of the magnetic ground state of metallic ferromagnets. Here we predict an analogous effect in thin films of magnetic insulators in which microwaves emitted by a proximity stripline generate coherent chiral spin currents that cause a Doppler shift in the magnon dispersion. The spin-wave instability is suppressed by magnon-magnon interactions that limit spin currents to values close to but below the threshold for the instability. The spin current limitations by the backaction of magnon currents on the magnetic order should be considered as design parameters in magnonic devices.

Quantum hydrodynamics description of spin-1 Bose–Einstein condensates

We develop a novel model of the magnetized spin-1 Bose–Einstein condensate (BEC) of neutral atoms, using the method of many-particle quantum hydrodynamic (QHD) and propose an original derivation of the system of continual equations. We consider bosons with a spin-spin interaction and a short range interaction in the first order in the interaction radius, on the of basis of the self-consistent field approximation of the QHD equations. We demonstrate that the dynamics of the fluid velocity and magnetization is determined by a nontrivial modification of the Euler and Landau–Lifshitz equation, and show that a nontrivial modification of the spin density evolution equation contains the spin torque effect that arises from the self-interactions between spins of the bosons. The properties of the dispersion spectrum of collective excitations are described. We obtain the new contribution of the self-interaction of spins in the spin wave spectrum together with the influence of an external magnetic field and spin-spin interactions between polarized particles. The anisotropic spin wave instability is predicted.

Influence of Mach-Zehnder modulator bias point on chaotic dynamics in spin-wave optoelectronic oscillator

In this paper we investigate in details the scenario of a transition to chaos in the spin-wave optoelectronic oscillator. The feature of the investigated circuit is the presence of two nonlinearities with different nature – modulation instability of spin waves and nonlinearity of the transmission characteristic of the electro-optical modulator. The influence of a position of the modulator bias point on the scenario of chaos development is experimentally investigated.

Broadband multi-magnon relaxometry using a quantum spin sensor for high frequency ferromagnetic dynamics sensing

Development of sensitive local probes of magnon dynamics is essential to further understand the physical processes that govern magnon generation, propagation, scattering, and relaxation. Quantum spin sensors like the NV center in diamond have long spin lifetimes and their relaxation can be used to sense magnetic field noise at gigahertz frequencies. Thus far, NV sensing of ferromagnetic dynamics has been constrained to the case where the NV spin is resonant with a magnon mode in the sample meaning that the NV frequency provides an upper bound to detection. In this work we demonstrate ensemble NV detection of spinwaves generated via a nonlinear instability process where spinwaves of nonzero wavevector are parametrically driven by a high amplitude microwave field. NV relaxation caused by these driven spinwaves can be divided into two regimes; one- and multi-magnon NV relaxometry. In the one-magnon NV relaxometry regime the driven spinwave frequency is below the NV frequencies. The driven spinwave undergoes four-magnon scattering resulting in an increase in the population of magnons which are frequency matched to the NVs. The dipole magnetic fields of the NV-resonant magnons couple to and relax nearby NV spins. The amplitude of the NV relaxation increases with the wavevector of the driven spinwave mode which we are able to vary up to 3 × 106 m−1, well into the part of the spinwave spectrum dominated by the exchange interaction. Increasing the strength of the applied magnetic field brings all spinwave modes to higher frequencies than the NV frequencies. We find that the NVs are relaxed by the driven spinwave instability despite the absence of any individual NV-resonant magnons, suggesting that multiple magnons participate in creating magnetic field noise below the ferromagnetic gap frequency which causes NV spin relaxation.

Modulation of the longitudinal pumping in quantum spin systems

The effect of the modulation of a high-frequency ac magnetic field parallel to the dc one (longitudinal pumping) by the lower-frequency ac field acting on quantum spin systems is considered for closed and open systems. For most magnetically ordered spin systems, the modulation causes the oscillation of the threshold of the parametric instability of spin waves as a function of the amplitude and the frequency of the modulation. On the other hand, our results for quantum spin systems with fermionic eigenstates imply that the modulating field causes the combined resonance and the modulation of the magnitude of time-dependent oscillations of the magnetization and the absorbed by the system power of the ac field for the closed system and for the open system in the dynamical and the steady-state regimes.

Nutation Spectroscopy of a Nanomagnet Driven into Deeply Nonlinear Ferromagnetic Resonance

Strongly out-of-equilibrium regimes in magnetic nanostructures exhibit novel properties, linked to the nonlinear nature of magnetization dynamics, which are of great fundamental and practical interest. Here, we demonstrate that field-driven ferromagnetic resonance can occur with substantial spatial coherency at unprecedented large angle of magnetization precessions, which is normally prevented by the onset of spin-wave instabilities and magnetization turbulent dynamics. Our results show that this limitation can be overcome in nanomagnets, where the geometric confinement drastically reduces the density of spin-wave modes. The obtained deeply nonlinear ferromagnetic resonance regime is probed by a new spectroscopic technique based on the application of a second excitation field. This enables to resonantly drive slow coherent magnetization nutations around the large angle periodic trajectory. Our experimental findings are well accounted for by an analytical model derived for systems with uniaxial symmetry. They also provide new means for controlling highly nonlinear magnetization dynamics in nanostructures, which open interesting applicative opportunities in the context of magnetic nanotechnologies.

Magnetoelastic parametric instabilities of localized spin waves induced by traveling elastic waves

A theory of parametric interaction between spin waves localized in a waveguide and traveling elastic waves is developed for ferromagnetic thin films. The presented theoretical formalism takes into account an arbitrary spatial distribution of the displacement field in the acoustic waves and an arbitrary magnetization in spin waves. Using the theory, we examine interaction of forward-volume spin waves (FVSW) localized in a narrow waveguide and Rayleigh surface acoustic waves traveling in a substrate underneath the waveguide. We show that, in contrast to classical electromagnetic pumping, the symmetry of the magnetoelastic interaction allows for the generation of first-order parametric instabilities in spin waves with circular precession, such as FVSW. At the same time the localization of spin waves modifies the momentum conservation law for the parametric process to include the transfer of momentum to the waveguide, which allows for a frequency separation of the interacting counterpropagating spin waves. The frequency separation enables amplification of a localized spin wave without generation of a traveling idler wave, which results in a greater amplification efficiency.

Anisotropic-Exchange Magnets on a Triangular Lattice: Spin Waves, Accidental Degeneracies, and Dual Spin Liquids

We present an extensive overview of the phase diagram, spin-wave excitations, and finite-temperature transitions of the anisotropic-exchange magnets on an ideal nearest-neighbor triangular lattice. We investigate transitions between five principal classical phases of the corresponding model: ferromagnetic, N\'{e}el, its dual, and the two stripe phases. Transitions are identified by the spin-wave instabilities and by the Luttinger-Tisza approach. Some of the transitions are direct and others occur via intermediate phases with more complicated forms of ordering. In a portion of the N\'{e}el phase, we find spin-wave instabilities to a long-range spiral-like state. In the stripe phases, quantum fluctuations are mostly negligible, leaving the ordered moment nearly saturated even for the $S=1/2$ case. However, for a two-dimensional surface of the full 3D parameter space, the spin-wave spectrum in one of the stripe phases exhibits an enigmatic accidental degeneracy manifested by pseudo-Goldstone modes. As a result, despite the nearly classical ground state, the ordering transition temperature in a wide region of the phase diagram is significantly suppressed from the mean-field expectation. We identify this accidental degeneracy as due to an exact correspondence to an extended Kitaev-Heisenberg model with emergent symmetries that naturally lead to the pseudo-Goldstone modes. There are previously studied dualities within the Kitaev-Heisenberg model on the triangular lattice that are exposed here in a wider parameter space. One important implication of this correspondence for the $S=1/2$ case is the existence of a region of the spin-liquid phase that is dual to the spin-liquid phase discovered recently by us. We complement our studies by the density-matrix renormalization group of the $S=1/2$ model to confirm some of the duality relations and to verify the existence of the dual spin-liquid phase.

Intrinsic Localized Spin Wave Modes and Modulational Instability in a Two-Dimensional Heisenberg Ferromagnet

An analytical study on the properties of intrinsic localized modes and modulational instability in a quantum two-dimensional ferromagnet with single-ion uniaxial anisotropy is completed in the semiclassical limit. By making use of the semidiscrete multiple-scale method, we obtain a line localized solution and a radially symmetric localized solution, and analyze their existence conditions. Taking into account that the existence of bright localized solutions is closely linked to the modulational instability of plane waves, we analytically study the discrete modulational instability of plane spin waves. The result of the modulational instability analysis show that the uniaxial anisotropy plays a key role in the appearance of our intrinsic localized spin wave modes.

Density wave instabilities and surface state evolution in interacting Weyl semimetals

We investigate the interplay of many-body and band structure effects of interacting Weyl semimetals (WSM). Attractive and repulsive Hubbard interactions are studied within a model for a time-reversal-breaking WSM with tetragonal symmetry, where we can approach the limit of weakly coupled planes and coupled chains by varying the hopping amplitudes. Using a slab geometry, we employ the variational cluster approach to describe the evolution of WSM Fermi arc surface states as a function of interaction strength. We find spin and charge density wave instabilities which can gap out Weyl nodes. We identify scenarios where the bulk Weyl nodes are gapped while the Fermi arcs still persist, hence realizing a quantum anomalous Hall state.

Suhl instabilities for spin waves in ferromagnetic nanostripes and ultrathin films

A microscopic (or Hamiltonian-based) theory is employed for the spin-wave instability thresholds of nonlinear processes in ultrathin ferromagnetic stripes and films under perpendicular pumping with an intense microwave field. The spatially-quantized linear spin waves in these nanostructures may participate in parametric processes through the three-magnon interactions (the first-order Suhl process) and the four-magnon interactions (the second-order Suhl process) when pumped. By contrast with most previous studies of spin-wave instabilities made for larger samples, where macroscopic (or continuum) theories involving Maxwell's equations for magnetic dipolar effects are used, a discrete lattice of effective spins is employed. Then a dipole-exchange spin Hamiltonian is employed to investigate the behavior of the quantized spin waves under perpendicular pumping, when modifications due to the more extensive spatial confinement and edges effects in these nanostructures become pronounced. The instability thresholds versus applied magnetic field are calculated, with emphasis on the size effects and geometries of the nanostructures and on the different relative strengths of the magnetic dipole-dipole and exchange interactions in materials. Numerical results are presented using parameters for Permalloy, YIG, and EuS.

Spin-wave self-modulation instability in a perpendicularly magnetized magnonic crystal

Self-modulation instability of microwave spin waves monochromatically excited in a periodic magnetic film structure, a magnonic crystal, has been observed. The phenomena occurs only at the frequencies corresponding to the band gaps of the spin-wave spectrum of the magnonic crystal. Depending on the frequency within the band gap the nonlinear waveforms have a shape of bright or dark pulses.

A nonlinear lattice model for Heisenberg helimagnet and spin wave instabilities

We study the dynamics of a Heisenberg helimagnet by presenting a square lattice model and proposing the Hamiltonian associated with it. The corresponding equation of motion is constructed after averaging the Hamiltonian using a suitable wavefunction. The stability of the spin wave is discussed by means of Modulational Instability (MI) analysis. The influence of various types of inhomogeneities in the lattice is also investigated by improving the model.

Quantum Lifshitz Field Theory of a Frustrated Ferromagnet.

We propose a universal nonlinear sigma model field theory for one-dimensional frustrated ferromagnets, which applies in the vicinity of a "quantum Lifshitz point," at which the ferromagnetic state develops a spin wave instability. We investigate the phase diagram resulting from perturbations of the exchange and of magnetic field away from the Lifshitz point, and uncover a rich structure with two distinct regimes of different properties, depending upon the value of a marginal, dimensionless, parameter of the theory. In the regime relevant for one-dimensional systems with low spin, we find a metamagnetic transition line to a vector chiral phase. This line terminates in a critical end point, beyond which there is at least one multipolar or "spin nematic" phase. We show that the field theory is asymptotically exactly soluble near the Lifshitz point.

Spin-wave instabilities of ferromagnetic nanowire stripes under parallel pumping

A microscopic (or Hamiltonian-based) theory is presented for the spin-wave instability thresholds in ferromagnetic nanowires under conditions of parallel pumping with a microwave field. A dipole-exchange Hamiltonian is employed in which the external magnetic field is either longitudinal or transverse to the length of the nanowire. This contrasts with most previous work on nonlinear spin waves which concentrate on situations where a macroscopic (or continuum) theory is appropriate. In nanowire stripes with lateral dimensions of order 100 nm or less, the quantization of the eigenmodes becomes modified due to strong spatial confinement and edge effects, making it appropriate to employ a microscopic dipole-exchange approach analogous to that used recently for ultrathin films. Numerical applications are presented for the dependence of the threshold microwave field amplitude for instability on the static applied field (the analog of the butterfly curves). The cases of longitudinal and transverse applied fields are found to lead to distinctly different behaviors, which are illustrated using EuS and permalloy as materials with different ratios of dipolar to exchange interactions. Structural effects due to the discrete spin-wave branches lead to structural aspects of the butterfly curves that are significantly modified compared with those for ultrathin films due to the edge modes in the nanowires.