Large Precession Angles Research Articles

Interplay Between Nonlinear Spectral Shift and Nonlinear Damping of Spin Waves in Ultrathin Yttrium Iron Garnet Waveguides

We use the phase-resolved imaging to directly study the nonlinear modification of the wavelength of spin waves propagating in 100-nm thick, in-plane magnetized YIG waveguides. We show that, by using moderate microwave powers, one can realize spin waves with large amplitudes corresponding to precession angles in excess of 10 degrees and nonlinear wavelength variation of up to 18 percent in this system. We also find that, at large precession angles, the propagation of spin waves is strongly affected by the onset of nonlinear damping, which results in a strong spatial dependence of the wavelength. This effect leads to a spatially dependent controllability of the wavelength by the microwave power. Furthermore, it leads to the saturation of nonlinear spectral shift's effects several micrometers away from the excitation point. These findings are important for the development of nonlinear, integrated spin-wave signal processing devices and can be used to optimize their characteristics.

Ising Machine Based on Electrically Coupled Spin Hall Nano-Oscillators

The Ising machine is an unconventional computing architecture that can be used to solve NP-hard combinatorial optimization problems more efficiently than traditional von Neumann architectures. Fast, compact oscillator networks that provide programmable connectivities among arbitrary pairs of nodes are highly desirable for the development of practical oscillator-based Ising machines. Here we propose using an electrically coupled array of gigahertz spin Hall nano-oscillators to realize such a network. By developing a general analytical framework that describes injection locking of spin Hall oscillators with large precession angles, we explicitly show the mapping between the coupled oscillators' properties and the Ising model. We integrate our analytical model into a versatile Verilog-A device that can emulate the coupled dynamics of spin Hall oscillators in circuit simulators. With this abstract model, we analyze the performance of the spin Hall oscillator network at the circuit level using conventional electronic components and considering phase noise and scalability. Our results provide design insights and analysis tools toward the realization of a CMOS-integrated spin Hall oscillator Ising machine operating with a high degree of time, space, and energy efficiency.

Resonant dynamics of the magnetization of uniaxial nanoparticle

Analysis of equilibrium conditions was carried out and resonant precessional dynamics of magnetization of a single-domain magnetically uniaxial ellipsoidal particle. Considered the case when magnetic field is along the easy magnetization axis. the easy magnetization axis is directed parallel to the axis of symmetry of the ellipsoid and transverse to pumping by a weak high-frequency field. Features of the behavior of the magnetization were discovered. It has been revealed that the magnetization has features of resonant behavior: large resonant precession angles with amplitude 0.5M0, elliptical deviations of the precession trajectory from circular at a negative value of the effective anisotropy field, and the presence of a frequency region with nonlinear precession for an oblate nanoparticle. Keywords: ferromagnetic resonance, elliptical nanoparticles, transverse bias field, effective anisotropy, bistability, easy magnetization axis, nonlinear effects.

Резонансная динамика намагниченности одноосной наночастицы

Analysis of equilibrium conditions was carried out and resonant precessional dynamics of magnetization of a single-domain magnetically uniaxial ellipsoidal particle. Сonsidered the case when magnetic field is along the easy magnetization axis. the easy magnetization axis is directed parallel to the axis of symmetry of the ellipsoid and transverse to pumping by a weak high-frequency field. Features of the behavior of the magnetization were discovered. It has been revealed that the magnetization has features of resonant behavior: large resonant precession angles with amplitude , elliptical deviations of the precession trajectory from circular at a negative value of the effective anisotropy field, and the presence of a frequency region with nonlinear precession for an oblate nanoparticle.

Imparting memory functionality to planar waveguide structures with photo-magnetic materials

A waveguide-type Mach–Zehnder interferometer (WG-MZI) incorporating a magnetic layer on each of two WG branches is proposed for use in an all-optical memory cell. The key concept is switching the relative magnetization configuration between parallel and anti-parallel with photonic or electronic excitation, which alters the interference condition of the WG-MZI and thus varies the intensity of its output light. In the present work, photo-excited precession of magnetization is assumed as a trigger for magnetization switching. The magnitude of changes in the effective refractive index (ΔnM) in the WG region optically coupled with magnetization and the output light intensity (ΔI) are studied theoretically by model calculation based on magneto-optical (MO) phase delay, through which target and practical values of ΔnM and ΔI are examined. Experimental works on the preparation and characterization of ultra-thin Co/Pd multi-layers are described as a prototype magnetic system for the proposed optical memory due to their large photo-induced precession angle.

Neutron spin-turning reflectors

The purely quantum aspects of the neutron interaction with magnetic layers are revealing new possibilities for spin manipulations. Neutron spin-turning reflectors (π/2 and π turners, in particular) are suggested on the basis of magnetic single layers as well as multilayer structures that increase manifold the value and/or the range of the working angles. Larmor and quantum spin precessors inducing large precession angles are also considered.

Nonlinear scattering in nanoscale magnetic elements: Overpopulation of the lowest-frequency magnon state

We utilized Brillouin light-scattering spectroscopy to study the magnetization dynamics in nanoscale permalloy elements driven by a large microwave magnetic field. We demonstrate that at large precession angles, the magnons excited by the microwaves scatter into the lowest-frequency state by a process similar to the scattering that leads to the Bose-Einstein condensation of magnons in the low-loss garnet films. The discovered effect is important for understanding the nonlinear processes in strongly driven nanomagnetic devices such as spin-torque nano-oscillators and magnetic memory.

Is precession electron diffraction kinematical? Part II: A practical method to determine the optimum precession angle

A series of experiments was undertaken to investigate the kinematical nature of precession electron diffraction data and to gauge the optimum precession angle for a particular system. Kinematically forbidden reflections in silicon were used to show how a large precession angle is needed to minimise multi-beam conditions for specific reflections and so reduce the contribution from dynamical diffraction. Small precession angles were shown to be detrimental to the kinematical nature of some low-order reflections. By varying precession angles, precession electron diffraction data for erbium pyrogermanate were used to investigate the effect of dynamical diffraction on the output from structure solution algorithms. A good correlation was noted between the precession angle at which the rate of change of relative intensities is small and the angle at which the recovered structure factor phases matched the theoretical kinematical structure factor phases.

Identification of the kinematical forbidden reflections from precession electron diffraction

AbstractThe visibility of the kinematical forbidden reflections due to glide planes, screw axes and Wyckoff positions is considered both on experimental and theoretical electron precession patterns as a function of the precession angle. The forbidden reflections due to glide planes and screw axes become very weak and disappear at large precession angle so that they can be distinguished from the allowed reflections and used to deduce the space groups. Contrarily, those due to Wyckoff positions remain visible and strong provided they are located on a major systematic row. This difference of behavior between the forbidden reflections is confirmed by observation of the corresponding dark-field LACBED patterns and is interpreted using the Ewald sphere and the Laue circles from the availability of double diffraction paths. This study also proves that dynamical interactions remain strong along the main systematic rows present on precession patterns.

Nonlinear phenomenological model of magnetic dissipation for large precession angles: Generalization of the Gilbert model

A nonlinear phenomenological model of magnetic dissipation is proposed. This model is a generalization of a standard Gilbert model, where the constant Gilbert damping parameter ${\ensuremath{\alpha}}_{G}$ is replaced by a function ${\ensuremath{\alpha}}_{G}(\ensuremath{\xi})$ of the dimensionless scalar quantity $\ensuremath{\xi}$ proportional to the square of the time rate of change of the magnetization vector ${(\ensuremath{\partial}\mathbit{M}∕\ensuremath{\partial}t)}^{2}$. The proposed model is illustrated for the example of magnetization precession excited by spin-polarized current in an in-plane magnetized nanopillar---the case where the standard Gilbert model leads to qualitatively incorrect results that contradict experiments.

Outflows from the high-mass protostars NGC 7538 IRS1/2 observed with bispectrum speckle interferometry

NGC 7538 IRS1 is a high-mass (approx. 30 M_sun) protostar with a CO outflow, an associated UCHII region, and a linear methanol maser structure, which might trace a Keplerian-rotating circumstellar disk. The directions of the various associated axes are misaligned with each other. We investigate the near-infrared morphology of the source to clarify the relations among the various axes. K'-band bispectrum speckle interferometry was performed at two 6-meter-class telescopes -- the BTA 6m telescope and the 6.5m MMT. Complementary IRAC images from the Spitzer Space Telescope Archive were used to relate the structures detected with the outflow at larger scales. High-dynamic range images show fan-shaped outflow structure in which we detect 18 stars and several blobs of diffuse emission. We interpret the misalignment of various outflow axes in the context of a disk precession model, including numerical hydrodynamic simulations of the molecular emission. The precession period is approx. 280 years and its half-opening angle is 40 degrees. A possible triggering mechanism is non-coplanar tidal interaction of an (undiscovered) close companion with the circumbinary protostellar disk. Our observations resolve the nearby massive protostar NGC 7538 IRS2 as a close binary with separation of 195 mas. We find indications for shock interaction between the outflow activities in IRS1 and IRS2. Indications of outflow precession have been discovered to date in a number of massive protostars, all with large precession angles 20--45 degrees. This might explain the difference between the outflow widths in low- and high-mass stars and add support to a common collimation mechanism.

Structure analysis of embedded nano-sized particles by precession electron diffraction. η′-precipitate in an Al–Zn–Mg alloy as example

The Vincent-Midgley precession technique has been used to collect three-dimensional electron diffraction intensity data from a dispersion of coherent precipitates in a matrix. In order to suppress severe effects from multiple diffraction via matrix reflections, a fairly large precession (tilt) angle had to be used. This implied a high background from the surrounding matrix, and limited the number of reflections that could be measured from patterns on image plates. The heavily faulted hexagonal η′-precipitates ( a = 0.496 nm , c = 1.405 nm ) with thickness 3–5 nm occur in four equivalent orientations relative to the aluminium matrix; with frequent overlap of reflections. A model of the average structure in the space group P6 3 /mmc with assumed composition Mg 2Zn 5− x Al 2+ x , have been derived by Patterson analysis and intensity comparisons.

Pumping-field-induced dynamic effects in micron-sized permalloy lines and their influence on HF filter applications

We present a combined time- and frequency-domain study on the dynamic properties of 2-/spl mu/m-wide Permalloy (Py) lines with different shape anisotropies placed on top of coplanar waveguides. The observed results are compared to numerical simulations of the magnetization dynamics using a macrospin model. For small-angle excitation, the inductive measurement of the resonance frequency in the frequency domain is equal to that in the time domain. However, if high pumping field amplitudes are used in the time-domain measurements, additional effects appear that shift the resonance frequency. They are caused by the large precession angle of the magnetization and the tilting of the equilibrium angle of the magnetization due to the presence of the pumping field. Depending on whether the shape anisotropy of the Py line is larger or smaller than the pumping field, the direction of this shift is either to low or to high frequencies. The simulations qualitatively confirm these experimental observations.

Multiwavelength Imaging and Long-Slit Spectroscopy of the Planetary Nebula NGC 6884: The Discovery of a Fast Precessing, Bipolar Collimated Outflow

We present Hα, [N II] λ6583, [O III] λ5007 ground-based images, Hubble Space Telescope (HST) (V band) archival images, VLA-A 3.6 cm continuum data, and high-resolution long-slit spectra of the planetary nebula NGC 6884. The VLA and HST images show an extremely knotty and filamentary nebula with an elliptical central structure also recognizable in Hα and [O III]. The [N II] image is different and is dominated by two bright arclike structures. The image ratio maps indicate a complex ionization structure within the nebula with low-excitation filaments surrounded by high-excitation regions. The spectra make it possible to distinguish three basic structural components in NGC 6884: (1) a compact (38 × 28, P.A. 32°), high-excitation ([N II] λ6583/Hα ≤ 0.15) ellipsoidal shell seen almost pole-on with polar and equatorial expansion velocities in the Hα line of 25 and 19 km s-1, respectively; (2) two point-symmetric, low-excitation ([N II]/Hα 0.6–1) spirals in which the distance to the central star and the radial velocity exhibit systematic variations; (3) two compact, apparently isolated, low-excitation bipolar knots. All data agree that the spirals represent precessing bipolar jetlike outflows. The observational properties of these precessing outflows can satisfactorily be explained with an approximately constant ejection velocity (55 km s-1) and a large precession angle (2 120°). The deduced precession period (500 × [D(kpc)/2] yr) is the shortest one measured so far in this kind of structure in planetary nebulae. The image ratio maps and the [N II]/Hα intensity ratio suggest shock excitation in the precessing jets. A general discussion of NGC 6884 is presented within the context of planetary nebulae with jetlike components.

New Class of High Frequency Nonlinear Magnetic Oscillations in Epitaxial Garnet Films

We performed magneto-optical investigations of the shape of the magnetization precession trajectory in garnet films at large precession angle. To describe the precession in asymmetric potential well the second order terms of small magnetization deflections are taken into account in the expansion of the thermodynamical potential. It is shown, that zero and second harmonic appear in the magnetization oscillations spectrum. The amplitude of this harmonics are proportional to the square of the exciting field amplitude. The dependence of asymmetric precession degree upon applied field and film parameters is found. The reported effects are like second harmonic generation and light detection effects in nonlinear optics.

Nonlinearities in the ferrimagnetic resonance in epitaxial garnet films

The ferrimagnetic resonance of magnetic garnet films has been measured at foldover and instability conditions. The resonance is excited locally within a region of about 50 μm diameter. Large precession angles of more than 80° can be achieved within this region, if the saturation magnetization M s is small. If M s is large, the precession spreads out far beyond the excitation region while simultaneously the maximum of the precession angle is reduced. For instability oscillations the time variations of the polar and azimuthal angle are determined separately. It turns out that the polar angle variation lags behind the variation of the azimuthal angle and that its amplitude is small compared to that of the azimuthal angle.

Chaos in magnetic garnet thin films

Ferromagnetic resonance in thin magnetic garnet films has been studied at excitation frequencies of 10 GHz and from room temperature to 4.2 K. Powers sufficient to drive the magnetization to large precession angles have been studied. Second-order Suhl instabilities of the main resonance have been observed as an onset of auto-oscillations of the magnetization. These oscillations include regular and irregular oscillations, very noisy collective oscillations, as well as spiking. They have been observed in real time and by spectral analysis. In pure yttrium iron garnet (YIG) films the oscillations have been observed in the frequency range from 0.5 to 2 MHz at 300 and 4.2 K. In going from 300 to 4.2 K the threshold power level pth in YIG films is lowered by three orders of magnitude, while the frequency of the regular oscillations are nearly independent of temperature. If pth is connected to the intrinsic damping parameter γ, then γ is temperature dependent, which is in fair agreement with the large number of narrow resonance features observed in the films. Preliminary simulations using a model extending the S theory of Zakharov and Nakamura for large precession angles give time evolutions that are qualitatively similar to the experimental observations. Regular and weekly irregular oscillations are found for one spin-wave mode coupled to a linear resonance circuit, i.e., a phonon mode. More irregularity is found for two coupled spin-wave modes excited to large precession angles.

A 'stroboscopic model' for nonlinear ferromagnetic resonance phenomena

Nonlinear ferromagnetic resonance phenomena are described by a simple classical 'stroboscopic model' (SM), which integrates the spin precession between the strobing times analytically. For small polar angles of the spin precession, the SM is equivalent to the S theory of Zakharov et al. (1975), which uses the Holstein-Primakoff transformation in the classical limit. In contrast with the S theory, the SM is also valid for large precession angles.

Ferrimagnetic resonance in garnet films at large precession angles

Perpendicular ferrimagnetic resonance in (111) oriented epitaxial garnet films is excited by strong rf drive fields causing large foldover effects. The precession angle of the magnetization is derived from the measured change of Faraday rotation of linearly polarized light passing through the films. Precession angles of over 60° have been observed. Measurements of the steady-state precession angles are in good agreement with calculations on the basis of Gilbert equations. The transient behavior of the precession, however, is slower than calculated. Conditions to achieve large precession angles are given.

GFactors of High-Spin Yrast States inTh232andU238

Extremely large precession angles (0.24 rad) have been observed when Coulomb-excited, 2-MeV/A actinide recoils decelerate in ferromagnetic Gd. In both $^{232}\mathrm{Th}$ and $^{238}\mathrm{U}$ the $g$ factors increase above spin $I=18\ensuremath{\hbar}$. This is the first direct evidence for rotation alignment of ${i}_{\frac{13}{2}}$ protons in the actinides. In $^{232}\mathrm{Th}$ there is also evidence for alignment of ${j}_{\frac{15}{2}}$ neutrons below $I=16\ensuremath{\hbar}$.