Spin-wave Instability Threshold Research Articles

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.

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 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.

Spin-wave Instability Theory for Ferromagnetic Nanostructures

A microscopic, or Hamiltonian-based, theory is outlined for studying the spin-wave instability thresholds of the parametric processes occurring in ferromagnetic nanostructures under conditions of pumping with a microwave eld. Most previous work has concentrated on spheres or lms with dimensions of order several μm or more, with the theoretical interpretation being made in terms of macroscopic (or continuum) methods. At smaller length scales, as in ultrathin lms and nanowires with thickness or lateral dimensions less than about 100 nm, the discreteness of the quantized spin waves and their spatial distributions become modi ed, making it more appropriate to employ a microscopic approach to the nonlinear dynamics with a lattice of e ective spins interacting through the magnetic dipole dipole and exchange interactions. E ects of microwave pumping (in either the parallel or perpendicular con guration) are incorporated in calculations for the instability thresholds of the quantized spin-wave bands in di erent nanostructures and materials.

Theory of spin-wave instability thresholds for ultrathin ferromagnetic films under parallel pumping

A microscopic, or Hamiltonian-based, theory is developed to study the spin-wave instability thresholds for the parametric processes occurring in ultrathin ferromagnetic films under conditions of parallel pumping with a microwave field. Most previous work has focused on spheres or films with dimensions of order several microns or more, and the theoretical interpretation has been in terms of macroscopic (continuum) methods. At smaller size scales, as in ultrathin films with thickness less than about 100 nm, the discreteness of the quantized spin waves and their spatial distributions become modified, making it more appropriate (particularly for the nonlinear dynamics) to employ a microscopic or Hamiltonian-based approach with a lattice of effective spins interacting with one another through the magnetic dipole-dipole and exchange interactions. This work utilizes a similar microscopic approach, but with the effects of microwave pumping included, to calculate the spin-wave instability thresholds for the bands of quantized spin waves in ultrathin films with the saturation magnetization parallel to their surface. Magnetic materials with different ratios of the exchange to dipole-dipole strengths are considered, taking examples for relatively strong, intermediate, and weak exchange. In the case of parallel pumping it is found that the shape of the typical ``butterfly curve,'' as conventionally obtained with macroscopic samples of YIG, becomes modified in these ultrathin films due to the occurrence of several quantized spin-wave bands and their spatial properties.

Electrical detection of nonlinear ferromagnetic resonance in single elliptical permalloy thin film using a magnetic tunnel junction

A quantitative method to detect ferromagnetic resonance using magnetic tunnel junction structure has been developed. Experimental results reveal three distinct regions for single elliptical permalloy film of micrometer lateral size. Above the spin wave instability threshold, the experimental results show a linear response of the longitudinal magnetization component to the microwave field amplitude over a large range rather than a lock-up phenomenon appeared in macroscopic permalloy films and then a phase limiting behavior. The linear behavior can be described by the theoretical model describing subsidiary resonance.

Field-induced transition from parallel to perpendicular parametric pumping for a microstrip transducer

Microstrip transducers used for the excitation of spin waves in magnetic films possess two characteristic properties: high spatial localization of the microwave magnetic field and the presence of field components parallel and perpendicular to the bias field. Here, the effects of these features on the process of parametric pumping are presented. By microwave measurements of the spin-wave instability threshold a transition from parallel pumping to perpendicular pumping at the critical field with the minimal threshold is observed. This transition is accompanied by a sharp threshold increase above the critical field due to the spatial confinement of the pump region.

Ferromagnetic resonance saturation and second order Suhl spin wave instability processes in thin Permalloy films

High power ferromagnetic resonance (FMR) loss versus static field H profiles and the corresponding spin wave instability threshold microwave field amplitude hcrit vs H butterfly curves were measured for in-plane magnetized thin Permalloy films of thicknesses 35, 57, 74, 104, and 123nm at a nominal pumping frequency of 9.11GHz. Cavity loading and calibration issues that proved to be problematic in past attempts to obtain accurate resonance saturation data over the full FMR profile in ferrites and metal films were resolved through a careful decoupling of the pump field and a full cavity response calibration. The FMR profiles show a drop in the loss peak, a shift in the peak to lower field, a broadening, and the development of a foldover-like asymmetry as the power is increased. The butterfly curves show a minimum hcrit at the low power FMR field and a smooth rounded increase on either side, except for a small kink on the low field side associated with the shift and asymmetry development. Apart from the kink, the second order Suhl spin wave instability theory, suitably modified for thin films, provided good fits to the butterfly curve data through the use of a single spin wave linewidth ΔHk value for each data set. The ΔHk values ranged from 16to35Oe, with the implied critical mode in-plane wave vectors always directed parallel to the static field. These spin wave linewidths translate into Gilbert damping parameter αk values in the 0.002–0.005 range, the same order as expected for intrinsic magnon-electron scattering losses in metal ferromagnets. These αk values are about a factor of 2 smaller than those implied by the low power FMR linewidths. The FMR in-plane precession cone angles at threshold were on the order of 3°–6°.

High power ferromagnetic resonance and spin wave instability processes in Permalloy thin films

The high power ferromagnetic resonance (FMR) response, as well as butterfly curves of the spin wave instability threshold microwave field amplitude hcrit versus in-plane static field H profiles, have been measured for Permalloy films with thicknesses of 104, 128, and 270nm at a nominal pumping frequency of 9.37GHz. The hcrit values range from about 1 to 7Oe. Both the resonance saturation response at the FMR field and the subsidiary absorption (SA) response for static fields below the FMR field are similar in appearance to those for bulk ferrites. Butterfly curves over the SA response region, while similar to those for ferrites, exhibit a film thickness dependent band edge cutoff effect not found in bulk ferrites. The SA butterfly curve data were analyzed on the basis of a spin wave instability theory adapted to thin films. The observed shift in the SA band edge cutoff with thickness agrees with calculations based on the thin film dispersion response and the assumption of first order instability processes with critical modes at one half the pumping frequency. The fitted SA spin wave linewidths give values consistent with metallic relaxation processes, but indicate critical modes with wave vectors that always make relatively small 0°–20° angles with the static field, very different from the critical modes for bulk ferrites. Three key conclusions from this work are (1) the nonlinear microwave FMR response in Permalloy films is a threshold effect related to well established spin wave instability processes, (2) the details of the SA response are controlled largely by the thin film spin wave dispersion, and (3) these nonlinear processes occur for very small precession angles.

Effect of large magnetocrystalline anisotropy on the spin wave linewidth in Zn–Y hexagonal ferrite

The oblique pumping spin wave instability threshold microwave field amplitude hcrit was measured as a function of the static field for both in-plane and out-of-plane static fields for a thin disk of Mn substituted Zn–Y (Ba2Zn2Fe12O22) easy plane hexagonal ferrite at 16.7 GHz. Theoretical fits to the in-plane static field data gave a single value of 12.8 Oe for the spin wave linewidth ΔHk. The best overall fits were for a critical spin wave mode wave number k close to zero and there was no correlation with the critical mode propagation directions. The fitted ΔHk for the out-of-plane static field geometry was found to increase with the out-of-plane magnetization angle, but showed no correlation with the critical mode propagation directions. These critical modes had k≈0 as well. The fitted ΔHk increased from the in-plane field value of 12.8 Oe to a value of 21 Oe at the maximum accessible magnetization angle of 70° relative to the disk plane. This increase in spin wave damping with the out-of-plane angle is attributed to spin orbit coupling.

Control of spin-wave instability threshold in YIG sphere

Spin-wave instability threshold under multiple drive excitations is studied in an yttrium iron garnet sphere at 4.2 K . Both a static magnetic field and a parallel RF field are applied along the [1 1 1] direction. Another perpendicular RF field excites magnetostatic modes through the first-order Suhl process. Interactions between spin-waves and magneostatic modes cause a change of instability thresholds.

High power microwave properties of Zn-Y hexagonal ferrite—parallel pumping size effects

The parallel pump spin wave instability threshold field hcrit was measured as a function of static field for various size in-plane magnetized thin plates of single crystal Mn substituted Zn-Y at both 9 and 16.7 GHz. The 9 GHz data indicate that (1) the critical modes consist of standing magnetostatic waves and (2) the hcrit thresholds depend on the lateral dimensions of the sample. The minimum parallel pumping spin wave linewidths were in the range 3–10 Oe and increased with a decrease in the sample lateral dimensions. These data are consistent with a transit time model and a size limited spin wave linewidth for low wave number critical modes. At 16.7 GHz, thresholds and spin wave linewidths are consistent with the 17.5 GHz and 9.5 GHz ferromagnetic resonance linewidth results and are sample size independent. The data indicate that exchange dominated spin waves are excited for fields below the butterfly curve minimum. These data give a k-dependent spin wave linewidth. The minimum parallel pumping spin wave linewidths were in the range 12–13 Oe.

Spin wave instability in single crystal Zn–Y hexagonal ferrite at 8.93 GHz

Resonance saturation (RS), subsidiary absorption (SA), and parallel pump (PP) spin wave instability threshold measurements have been made on single crystal easy plane disks of Mn substituted Zn–Y type hexagonal ferrite materials at 8.93 GHz and room temperature. For each configuration, “butterfly curves” of the spin wave instability threshold microwave field amplitude hcrit as a function of the static field applied in the disk plane were obtained. The previous theory for these instability processes was also extended to include planar magnetocrystalline anisotropy and a wave vector k dependent spin wave linewidth, ΔHk. The RS butterfly curve had a characteristic “V” shape with a rounded minimum at the ferromagnetic resonance (FMR) field. The nominal ΔHk needed to fit the data at the ferromagnetic resonance field was 7 Oe, but the butterfly curve shape indicated a k-dependent ΔHk. The butterfly curves for the PP configuration were flat at low field and then diverged rapidly at the cutoff field for first order instability processes, Hcut. The SA butterfly curves were also flat over the field interval for first order processes, but then decreased as the field was increased above Hcut. This decrease is attributed to the onset of second order processes due to the proximity of the FMR and additional magnetostatic mode peaks as one moves to and then above Hcut. The flat portions of the PP and SA butterfly curves could be fitted with a single k-independent ΔHk value of 18 Oe.

Effect of rare-earth Gd3+ on instability threshold of YIG

Development of low-loss microwave ferrite material (gadolinium-substituted yttrium iron garnet) for high-power microwave device is reported from the studies of spin-wave instability threshold (hcrit) in parallel and perpendicular pumping configurations at 9.4 GHz and room temperature. Room-temperature ferromagnetic resonance linewidth (ΔH) and spin wave linewidth (ΔHk) show marked effect with various Gd3+ substitution. The experimental instability threshold results show strong variation with Gd3+ substitution. Parallel pump experimental butterfly curves are reproduced theoretically from our revised pore-scattering model, taking into account the k dependence of spin-wave linewidth from a trial function ΔHk = A + BΔHk(p) + Ck, whereas the perpendicular pump butterfly curves are reproduced from a sin θk function in conjunction with the k dependence of spin-wave linewidth similar to Patton's model.

Effect of the strong relaxer cobalt on the parallel and perpendicular pumping spin-wave instability threshold of LiTi ferrites

Room temperature data on the parallel and perpendicular pumping instability threshold at 9.4 GHz, using a reflection-type microwave spectrometer, are reported for a series of polycrystalline LiTi ferrites substituted with the strong relaxing ion cobalt. The experimental instability threshold results show strong variation with cobalt substitution. The experimental butterfly curves are reproduced theoretically from the revised pore-scattering model, taking into account the k dependence of the spin-wave linewidth from a trial function: Δ H k = A + BΔ H k ( p) + Ck.

Butterfly curves and critical modes for second-order spin-wave instability processes in yttrium iron garnet films

Combined Brillouin light-scattering (BLS) and microwave pumping techniques were used to measure the second-order spin-wave instability threshold microwave field amplitudes and characterize the critical modes for ferromagnetic resonance (FMR) saturation in 4.15 μm-thick yttrium iron garnet films at 8.47 GHz with the static magnetic field in-plane. To the best of our knowledge, this work represents the first BLS measurements for second-order FMR saturation processes in ferrite materials. Several new results were obtained: (1) A new type of butterfly curve for second-order processes. (2) Strong scattering from modes at low wave numbers in the 104 rad/cm range. (3) An observed in-plane propagation direction for these low wave number modes at 90° to the in-plane static field direction. These results differ significantly from the behavior expected from the bulk sample instability theories of Suhl and Schlömann, which predict critical modes at wave numbers and propagation directions in the 105–106 rad/cm and 0° ranges, respectively, and a sharp cusplike response centered at FMR. These results indicate that significant modifications of the bulk theory, which take into account the real modes supported by the film, are needed to realistically model second-order instability processes in films.

Parallel pump spin wave instability threshold in thin ferromagnetic films

A rigorous theory of parallel pump instability threshold of spin waves in ferromagnetic films is developed. Dipole and exchange interactions, the dipole-dipole hybridization of spin wave branches, and the magnetocrystalline and induced anisotropies are taken into account. Expressions for the parallel pump instability threshold are obtained in general form which can be used to calculate the threshold of a single ferromagnetic layer or a multilayered structure containing an arbitrary number of ferromagnetic films. The influences of the dipole-dipole hybridization of parametrically generated spin waves and of their nonreciprocal propagation properties on the threshold are discussed.

Intermittency Observed in Yttrium Iron Garnet under Parallel Pumping

Parallel pumping experiments in yttrium iron garnet have been performed at a pumping frequency 9.45 GHz and at a temperature 4.2 K. Above the spin-wave instability threshold, auto-oscillations of magnon amplitude are observed. Just above the onset of the auto-oscillations, signal has character of intermittent. From time-series data, Poincare return maps and distribution of laminar period lengths are obtained. These results are in agreement with the theory based on symmetrical mapping that describes the dynamics of Lorentz type flows. Bifurcation parameters obtained by the best fit with the theoretical relation are presented as a function of the microwave power. Relationship between the average of the laminar lengths and the bifurcation parameter is in good agreement with the theoretical prediction.

Brillouin light scattering study of spin wave instability magnon distributions in yttrium iron garnet thin films (abstract)

There has been increased interest recently in nonlinear microwave phenomena in bulk and thin film single crystal ferrite materials. These nonlinear phenomena show a variety of novel effects such as spin wave instability, auto-oscillation, multistability, period multiplication, intermittency, and chaos. Emerging theories to explain these phenomena have generally been based on simple two mode models. It is clear that an experimental determination of the number and distribution of the modes excited at and above the spin wave instability threshold could play a key role in the refinement of these theories. This work is concerned with a Brillouin light scattering (BLS) experimental study of the wave vector distribution of the parametric spin wave modes excited at and above the subsidiary absorption spin wave instability threshold in yttrium iron garnet (YIG) films. The in-plane magnetized 4.15-μm-thick films were transverse pumped at 8.47 GHz, with the microwave field also in-plane. The BLS data were obtained with a tandem, multipassed, high contrast Sandercock Fabry–Perot interferometer. The data show a complicated wave vector distribution for the excited modes. The spin wave propagation direction is sharply peaked at the value expected from standard instability theory. However, the wave number distribution is quite broad, even at threshold. For power levels above threshold, this distribution evolves in a complicated manner that depends on field and propagation direction. These results show that simple two mode models are inadequate to deal with high frequency nonlinear processes in ferrite thin films.

Measurement of spin wave instability magnon distributions for subsidiary absorption in yttrium iron garnet films by Brillouin light scattering.

The first evidence for a wide distribution in the critical mode wave vectors above the spin wave instability threshold for subsidiary absorption is reported. The Brillouin light scattering BLS measurements were done on 4.15 \ensuremath{\mu}m thick yttrium iron garnet films with the static field and the 8.47 GHz linearly polarized microwave field in plane. The distribution in the critical mode wave number is broad, with widths of about 0.5\ifmmode\times\else\texttimes\fi{}${10}^{4}$--2\ifmmode\times\else\texttimes\fi{}${10}^{4}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ and shapes which change with field and power. These results cast doubts on the validity of simple two mode models for the analysis of self-oscillation, chaos, and related effects above threshold.