Nonlinear Spin Waves Research Articles

Nonlinear effective spin-mixing conductance in Pt/Ni80Fe20/Pt thin films

In this study, the effective spin-mixing conductance in Ni80Fe20/Pt was investigated by measuring the interface-induced enhancement of the Gilbert damping constant. Ferromagnetic resonance spectra were measured in coplanar waveguide geometry with different incident microwave powers. The nonlinear behavior of normal Gilbert damping G0 and effective spin-mixing conductance g↑↓ have been observed when the incident microwave power is above a critical ac field hrf of 1.6 Oe. Both phenomena are explained by considering the coupling between spin coherent precession and spin wave modes. This work demonstrates the nonlinear behavior of the effective spin-mixing conductance g↑↓. It suggests that the nonlinear spin wave modes excited at high incident microwave power are detrimental to the spin pumping effect and should be avoided in future spin battery designs. The capability of tuning G0 and g↑↓ through the microwave power is also useful for the fundamental study on the damping mechanism.

Linear and nonlinear spin-wave dynamics in macro- and microscopic magnetic confined structures

We present an investigation of the propagation of spin waves in macro- and microscopic laterally confined magnetic structures and the influence of direct spin-polarized current on spin-wave radiation by nanocontacts. For detection of spin waves the space-resolved Brillouin light scattering technique is used. Nonlinear effects modifying the spin-wave propagation and eigenmodes are studied experimentally and analysed theoretically. We show that the spin-polarized current changes the effective damping constant of the ferromagnet. The dependence of the damping constant is linear for one direction of the current, in agreement with existing theoretical models. For the opposite direction of the current the dependence is strongly nonlinear showing saturation.

‘Off-shell’ nonlinear spin waves for the Heisenberg model

We consider the general classical Heisenberg model (HM) with a z-axis anisotropic Hamiltonian. The ferromagnetic (FR) (antiferromagnetic (AF)) nonlinear spin waves (NLSWs), also called finite-amplitude spin waves, are well-known solutions of the equations of motion and are characterized by constant and equal (in each sublattice, in the AF case) z-components of the spins. In this paper, we present general analytical solutions which share this property, but do not necessarily reside on the equal-spins shell in phase space (spins can be unequal) and hence will be termed ‘off-shell’ NLSWs. For periodic lattices, we find that these solutions are linear combinations of standard FR (generalized AF) NLSWs. For a Heisenberg ring, in particular, we prove that the ‘off-shell’ solution is the sum of only two FR (generalized AF) NLSWs of opposite momenta. In this case, we show that the standard NLSWs are the only ‘on-shell’ solutions with the property that the z-components of the spins (in each sublattice, in the AF case) are all equal to the same nonzero constant. Novel standing-wave solutions with planar spins are also presented.

Nonlinear mode conversion in monodomain magnetic squares

Modifications of the spatial distributions of dynamic magnetization corresponding to spin-wave eigenmodes of magnetic squares subjected to a strong microwave excitation field have been studied experimentally and theoretically. We show that an increase of the excitation power leads to nonlinear generation of long-wavelength spatial harmonics caused by the nonlinear cross coupling between the eigenmodes. The analysis of the experimental data shows that this process is mainly governed by the action of the nonlinear spin-wave damping. This conclusion is further supported by numerical calculations based on the complex Ginzburg-Landau equation, phenomenologically taking into account the nonlinear damping.

Modulational instability of nonlinear spin waves in an atomic chain of spinor Bose-Einstein condensates

The modulational instability of coherently excited spin waves is studied in an atomic spin chain of spinor Bose-Einstein condensates (BECs) confined in an optical lattice. We examine the dependence of the stability on the long-range nonlinear interaction of spin waves excited at different lattice sites. The long-range nonlinear spin coupling in the optical lattice is due to light-induced and static magnetic dipole-dipole interaction between atoms. We compare the spin wave dynamics in an atomic spin chain of spinor BECs formed in an optical lattice with that in a Heisenberg-like spin chain in solid-state physics. This reveals the important differences of the spin chain with long-range spin coupling from that with the short-range one.

Quantum and classical spins on the spatially distorted kagomé lattice: Applications to volborthiteCu3V2O7(OH)2∙2H2O

In volborthite, spin-$1∕2$ moments form a distorted kagom\'e lattice of corner sharing isosceles triangles with exchange constants $J$ on two bonds and ${J}^{\ensuremath{'}}$ on the third bond. We study the properties of such spin systems and show that despite the distortion, the lattice retains a great deal of frustration. Although subextensive, the classical ground state degeneracy remains very large, growing exponentially with the system perimeter. We consider degeneracy lifting by thermal and quantum fluctuations. To linear (spin wave) order, the degeneracy is found to stay intact. Two complementary approaches are therefore introduced, appropriate to low and high temperatures, which point to the same ordered pattern for ${J}^{\ensuremath{'}}gJ$. In the low-temperature limit, an effective chirality Hamiltonian is derived from nonlinear spin waves, which predicts a transition on increasing ${J}^{\ensuremath{'}}∕J$ from $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$-type order to a ferrimagnetic chirality stripe order with a doubled unit cell. This is confirmed by a large-$n$ approximation on the $\mathrm{O}(n)$ model on this lattice. While the saddle point solution produces a line degeneracy, $\mathrm{O}(1∕n)$ corrections select the nontrivial wave vector of the striped chirality state. The quantum limit of spin $1∕2$ on this lattice is studied via exact small system diagonalization and compares well with experimental results at intermediate temperatures. We suggest that the very-low-temperature spin frozen state seen in NMR experiments may be related to the disconnected nature of classical ground states on this lattice, which leads to a prediction for NMR line shapes.

Angular dependence of the microwave-generation threshold in a nanoscale spin-torque oscillator

It is shown that in a spin-torque microwave oscillator based on a magnetic nanocontact, the nature of the microwave spin wave mode generated at the threshold critically depends on the angle between the external bias magnetic field and the plane of the free layer. When the external bias field is rotating from normal to in-plane orientation, an abrupt transition from a propagating cylindrical wave with the frequency higher than the frequency of the linear ferromagnetic resonance (FMR) to a self-localized standing nonlinear spin wave ``bullet'' with the frequency lower than the FMR frequency takes place at a certain intermediate angle ${\ensuremath{\theta}}_{\mathrm{cr}}$. This transition manifests itself as an abrupt jump (of the order of several gigahertz) in the generated microwave frequency. This mechanism of mode switching might explain abrupt jumps of the generated microwave frequency observed in recent experiments on spin-torque oscillators.

Large-amplitude coherent spin waves excited by spin-polarized current in nanoscale spin valves

We present spectral measurements of spin-wave excitations driven by direct spinpolarized current in the free layer of nanoscale Ir20Mn80/Ni80Fe20/Cu/Ni80Fe20 spin valves. The measurements reveal that large-amplitude coherent spin wave modes are excited over a wide range of bias current. The frequency of these excitations exhibits a series of jumps as a function of current due to transitions between different localized nonlinear spin wave modes of the Ni80Fe20 nanomagnet. We find that micromagnetic simulations employing the Landau-Lifshitz-Gilbert equation of motion augmented by the Slonczewski spin torque term (LLGS) accurately describe the frequency of the current-driven excitations including the mode transition behavior. However LLGS simulations give qualitatively incorrect predictions for the amplitude of excited spin waves as a function of current.

Interaction of a nonlinear spin-wave and magnetic soliton in a uniaxial anisotropic ferromagnet

We study the interaction of a nonlinear spin-wave and magnetic soliton in a uniaxial anisotropic ferromagnet. By means of a reasonable assumption and a straightforward Darboux transformation one- and two-soliton solutions in a nonlinear spin-wave background are obtained analytically, and their properties are discussed in detail. On the background of a nonlinear spin-wave the amplitude of the envelope soliton has the spatial and temporal period, and soliton can be trapped only in space. The amplitude and wave number of spin-wave have the different contribution to the width, velocity, and amplitude of soliton solutions. The envelope of solution hold the shape of soliton, and the amplitude of each envelope soliton keeps invariability before and after collision which shows the elastic collision of two envelope soliton on the background of a nonlinear spin-wave.

Ferrite-film nonlinear spin wave interferometer and its application for power-selective suppression of pulsed microwave signals

A theoretical model of the nonlinear spin wave interferometer has been developed. An experimental prototype of the device has been manufactured and investigated. The device application for power-selective suppression of pulsed microwave signals has been demonstrated. The obtained experimental data are in good agreement with the theory.

Nonlinear spin wave magnetization of solution synthesized Ni nanoparticles

The magnetic properties of Ni nanoparticles synthesized using a soft chemical method followed by heat treatment in H2 atmosphere have been studied in detail. The powder consists of pure Ni with no additional phase and the average crystallite size is 30±5nm, determined using the modified Scherer relation. The crystallites tend to agglomerate into large particles of sizes 50–100nm, as observed by transmission electron microscopy. The saturation magnetization is found to be 46.42emug−1 at 5K, about 80% of the bulk magnetization value. The temperature dependence of saturation magnetization for T<0.5TC is found to deviate from the linear Bloch’s T3∕2 law indicating that spin wave interactions needs to be considered to understand the behavior. The spin wave stiffness constant obtained by fitting the saturation magnetization decay to a nonlinear spin wave model is lower by an order of magnitude compared to that of bulk Ni. The coercivity on the other hand decreases from 67Oe at 5Kto36Oe at 300K with a temperature dependence slower than the T1∕2 behavior predicted for noninteracting superparamagnetic particles.

Nonlinear spin waves in a Bose condensed atomic chain

The modulational instability (MI) of nonlinear coherent spin waves in an atomic spin chain of spinor Bose-Einstein condensates confined in an optical lattice is studied. Analytically we obtained the criteria for the MI of nonlinear coherent spin waves and its relation with the long-range nonlinear spin coupling. We analysed the MI in the case of blue-detuned and red-detuned opctical lattice respectively. It was found that the long-range nonlinear spin coupling in the optical lattice is due to light-induced and static magnetic field-induced dipole-dipole interaction.

Microwave nonlinear spin wave directional coupler

A nonlinear spin-wave directional coupler for the microwave range has been designed, constructed, and studied for the first time. Each of the four ports of the device can be used as the input or output for a microwave signal. The role of a control element in the coupler is played by a nonlinear spin wave shifter based on a thin ferromagnetic film. A distinctive feature of the proposed device is that an increase in the input power level leads to the signal switching from one to another output, which is caused by a power-dependent variation in the spin wave phase shift.

Nonlinear Ferrite Film Microwave Signal Processing for Advanced Communications—Physics and Devices

Microwave ferrite devices, including circulators, isolators, and phase shifters, have played a crucial role in the development of radar and other microwave signal processing applications. Recent work has advanced the basic understanding and applications for a wide range of new nonlinear spin wave phenomena in ferrite films. With the help of feedback and parametric pumping interactions, these spin wave phenomena can serve as the basis for phase locked frequency comb generators, wideband chaotic microwave oscillators, and microwave pulse multiplexers, among other devices.

Formation of longitudinal patterns and dimensionality crossover of nonlinear spin waves in ferromagnetic stripes

Formation of stationary longitudinal amplitude patterns by propagating nonlinear spin waves has been discovered and studied experimentally by means of space-resolved Brillouin light scattering spectroscopy. The pattern formation is observed for spin waves propagating in narrow, longitudinally magnetized yttrium iron garnet stripes, characterized by attractive nonlinearity in both the longitudinal and transverse directions. A clear crossover of the effective dimensionality describing the propagation of spin waves in the stripe is observed with increase of the wave amplitude.

Amplitude-frequency characteristic of a nonlinear spin wave interferometer operating in a quasi-nonlinear regime

A thin-film nonlinear spin wave interferometer has been experimentally studied. The concept of a quasi-nonlinear operation regime is introduced for the first time and the boundaries of the quasi-nonlinear dynamic range of the interferometer are experimentally determined. It is shown that the nonlinear spin wave interferometer operating in the quasi-nonlinear regime can be characterized, like linear devices, by the amplitude-frequency characteristic (AFC). However, an increase in the signal power level within the quasi-nonlinear dynamic range at the input of the nonlinear interferometer leads, in contrast to the case of a linear device, to a frequency shift of the AFC. An analysis of the AFC shift indicates that a 180° change in the phase difference between the interfering signals at each separate frequency is achieved for the input power varied within the limits of the quasi-nonlinear dynamic range. This behavior shows the possibility of using the nonlinear interferometer for the processing of microwave signals without undesired distortion of the signal waveform.

On modulational instability of nonlinear waves in 1D ferromagnetic spin chains

We report a theoretical study of modulational instability of extended nonlinearspin waves in a one-dimensional ferromagnetic chain. The investigation is madeboth analytically within the framework of the linear stability analysis and alsonumerically by means of molecular dynamics simulations. Using a Holstein–Primakofftransformation for the spin operators, the Hamiltonian, which is constituted by aHeisenberg exchange term, a biquadratic exchange energy, an anisotropic energy and aZeeman term, is bosonized. Then we derive a discrete nonlinear Schrödinger-likeequation for the spin-wave motion. Using a linear stability analysis, we establish thestability criteria of the spin waves in such a ferromagnetic chain. From our numericalsimulations of the discrete spin chain for the onset of instability, it emerges that theanalytical predictions are correctly verified. For a long timescale, depending on thestrength of the biquadratic exchange interaction relative to the exchange energy andthe anisotropy energy, on the one hand an intrinsic localized wave train can becreated displaying properties of the breather motion. On the other hand, due to theincreasing size of the instability domain, with increase of the biquadratic parameter,the instability can fully develop and the linear stability fails; consequently, thetime evolution of the modulated spin waves can show both regular and chaoticbehaviour.

Static, periodic, and chaotic magnetization behavior induced by spin-transfer torque in magnetic nanopillars

The magnetization dynamics of a square magnet in a pillar structure under the influence of a dc spin current is studied by micromagnetic simulation based on the modified Landau-Lifshitz-Gilbert equation. Even in the situation with neither external field perturbation nor thermal activation, the magnetization exhibits intricate behaviors ranging from static configurations to periodic domain wall rotations to chaotic processes. It arises from the nonlinearity of the spin-transfer torque and is explained by the excitation of nonlinear spin waves in the magnet.

Nonlinear spin waves for the Heisenberg model and the ferromagnetic–antiferromagnetic bifurcations

We present finite-amplitude spin-wave solutions for the nonlinear equations of the classical Heisenberg model on a general periodic lattice. These are families of periodic solutions bifurcating from the ferromagnetic (FR) and antiferromagnetic (AF or Neel) states which are fixed points of the flow. We allow for longitudinal anisotropy and constant uniform magnetic field in the direction of anisotropy. We find analytical expressions for the energy–frequency (e–w) curves of these families. In particular, we show that the AF families come in pairs of vertical lines. In the expression of both the FR and AF nonlinear spin waves (NLSWs), we are able to eliminate the amplitude in favour of the frequency and/or energy. All special cases of solutions are carefully analysed. We discover that the two AF families end on the FR family of a corresponding wavevector. This correspondence can be made precise without compromising the generality of the lattice. Our major point is the proof that these FR–AF intersections on the e–w plot are isochronous branchings. Hence, we establish a novel view of the AF NLSWs as bifurcations of the FR NLSWs.

Ferrimagnetic resonance in films of vanadium[tetracyanoethanide]x, grown by chemical vapor deposition

Ferrimagnetic resonance (FMR) measurements in thin films of $\mathrm{V}{[\mathrm{TCNE}]}_{x}$ grown by chemical vapor deposition exhibit a series of sharp lines at $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The orientational dependence of these lines is a result of the sample geometry provided the magnetization tracks the applied magnetic field. The FMR intensities scale with the temperature dependence of the magnetization as measured by SQUID magnetometry. The temperature dependence of the FMR at various orientations yields an estimate of the local, negative anisotropy field, which is approximately $200\phantom{\rule{0.3em}{0ex}}\text{Oe}$ at zero temperature and decreases linearly with increasing temperature and is well fit by a model developed for spin glasses. The widths of the FMR lines track the temperature dependence of the magnetization, which suggests that they are determined by density fluctuations. The spacings between the individual FMR lines and their temperature dependence are consistent with the presence of nonlinear spin waves, whose critical microwave field is approximately ${10}^{\ensuremath{-}2}\phantom{\rule{0.3em}{0ex}}\text{Oe}$. A rough estimate of the exchange stiffness constant is $A={10}^{\ensuremath{-}10}\phantom{\rule{0.3em}{0ex}}\mathrm{erg}∕\mathrm{cm}$. The small value of $A$ may be due to the magnitude of the antiferromagnetic exchange between V and adjacent TCNE and the frustration of AFM exchange between adjacent TCNE radicals.