Brillouin Light-scattering Technique Research Articles

Brillouin Light Scattering from Magnetic Excitations.

Brillouin light scattering (BLS) has been established as a standard technique to study thermally excited sound waves with frequencies up to ~100 GHz in transparent materials. In BLS experiments, one usually uses a Fabry-Pérot interferometer (FPI) as a spectrometer. The drastic improvement of the FPI contrast factor over 1010 by the development of the multipass type and the tandem multipass type FPIs opened a gateway to investigate low energy excitations (ħω ≤ 1 meV) in various research fields of condensed matter physics, including surface acoustic waves and spin waves from opaque surfaces. Over the last four decades, the BLS technique has been successfully applied to study collective spin waves (SWs) in various types of magnetic structures including thin films, ultrathin films, multilayers, superlattices, and artificially arranged dots and wires using high-contrast FPIs. Now, the BLS technique has been fully established as a unique and powerful technique not only for determination of the basic magnetic constants, including the gyromagnetic ratio, the magnetic anisotropy constants, the magnetization, the SW stiffness constant, and other features of various magnetic materials and structures, but also for investigations into coupling phenomena and surface and interface phenomena in artificial magnetic structures. BLS investigations on the Fe/Cr multilayers, which exhibit ferromagnetic-antiferromagnetic arrangements of the adjacent Fe layer's magnetizations depending on the Cr layer's thickness, played an important role to open the new field known as "spintronics" through the discovery of the giant magnetoresistance (GMR) effect. In this review, I briefly surveyed the historical development of SW studies using the BLS technique and theoretical background, and I concentrated our BLS SW studies performed at Tohoku University and Ishinomaki Senshu University over the last thirty five years. In addition to the ferromagnetic SW studies, the BLS technique can be also applied to investigations of high-frequency magnetization dynamics in superparamagnetic (SPM) nanogranular films in the frequency domain above 10 GHz. One can excite dipole-coupled SPM excitations under external magnetic fields and observe them via the BLS technique. The external field strength determines the SPM excitations' frequencies. By performing a numerical analysis of the BLS spectrum as a function of the external magnetic field and temperature, one can investigate the high-frequency magnetization dynamics in the SPM state and determine the magnetization relaxation parameters.

Modulation of interfacial magnetic relaxation timeframes by partially uncoupled exchange bias

A set of partially uncoupled NiFe/Cu/IrMn exchange biased thin films with variable thickness of non-magnetic Cu spacer is characterized by ferromagnetic resonance (FMR) and Brillouin light scattering (BLS) techniques applied complementary to reveal time-scale dependent effects of uncoupling between ferromagnetic and antiferromagnetic layers on high-frequency magnetization dynamics. The results correlate with interfacial grain texture variations and static magnetization behavior. Two types of crystalline phases with correlated microwave response are revealed at the ferro–antiferromagnet interface in NiFe/Cu/IrMn thin films. The 1st phase forms well-textured NiFe/IrMn grains with NiFe (111)/IrMn (111) interface. The 2nd phase consists of amorphous NiFe/IrMn grains. Intercalation of NiFe/IrMn by Cu clusters results in relaxation of tensile strains at the NiFe/IrMn interface leading to larger size of grains in both the NiFe and IrMn layers. The contributions of well-textured and amorphous grains to the high-frequency magnetization reversal behavior are distinguished by FMR and BLS techniques. Generation of a spin-wave mode is revealed in the well-textured phase, whereas microwave response of the amorphous phase is found to originate from magnetization rotation dominated by a rotatable magnetic anisotropy term. Under fixed FMR frequency, the increase of Cu thickness results in higher magnetization rotation frequencies in the amorphous grains.

Perpendicular magnetic anisotropy and interfacial Dzyaloshinskii–Moriya interaction in as grown and annealed X/Co/Y ultrathin systems

The perpendicular magnetic anisotropy (PMA) and the interfacial Dzyaloshinskii–Moriya interaction (iDMI) are investigated in as grown and 300 °C annealed Co-based ultrathin systems. For this, Co films of various thicknesses (0.8 nm ⩽ tCo ⩽ 5.7 nm) were deposited by magnetron sputtering on thermally oxidized Si substrates using Pt, W, Ir, Ti, Ru and MgO buffer or/and capping layers. X-ray diffraction was used to investigate their structural properties and vibrating sample magnetometry (VSM) was used to determine the magnetic dead layer thickness and the magnetization at saturation (Ms). VSM revealed that the Ms for the Pt and the Ir buffered and capped films is the largest. Microstrip line ferromagnetic resonance (MS-FMR), used to extract the gyromagnetic ratio of the thicker Co films, revealed the existence of a second order PMA term, which is thickness dependent. Brillouin light scattering (BLS) in the Damon–Eshbach configuration was used to investigate the thickness dependence of the iDMI effective constant from the spin wave vector dependence of the frequency difference between Stokes and anti-Stokes lines. BLS and MS-FMR techniques were combined to measure the spin wave frequency variation as a function of the in-plane applied magnetic field (where the second order PMA contribution vanishes). The thickness dependence of the effective magnetization was then deduced and used to investigate PMA. For all the systems, PMA results from interface and volume contributions that we determined. The largest interface PMA constants were obtained for Pt- and Ir-based systems due to the electron hybridization of Co with these heavy metals having high spin orbit coupling. Annealing at 300 °C increases both the interface PMA and iDMI for the Pt/Co/MgO most probably due to de-mixing of interpenetrating oxygen atoms from the Co layer and the formation of a sharp Co/O interface.

Dzyaloshinskii-Moriya interaction induced asymmetry in dispersion of magnonic Bloch modes

We report the results of the experimental investigation of magnonic Bloch modes in the presence of asymmetric dispersion induced by the interfacial Dzyaloshinskii-Moriya interaction by means of Brillouin light-scattering technique. It was realized in a specially designed ultrathin CoFeB/Pt periodic structure consisting of an array of rectangular nanostrips separated by half-etched grooves. The proposed theory based on the coupled mode approach explains the major features observed experimentally, such as Brillouin zone folding and the asymmetry of the magnonic band-gap points in the reciprocal $k$ space.

Effect of exchange and dipolar interlayer interactions on the magnonic band structure of dense Fe/Cu/Py nanowires with symmetric and asymmetric layer widths

We present a systematic experimental and theoretical investigation of the magnonic band structure in dense arrays of both asymmetric and symmetric cross-section trilayered Fe(10 nm)/Cu( $t$)/Py(10 nm) nanowires (NWs). The Cu spacer thickness ($t$) is varied in the range between 0 and 10 nm. The frequency dispersion of collective spin-wave excitations in the above trilayered NW arrays has been studied by the Brillouin light-scattering technique while sweeping the wave vector perpendicularly to the nanowire length over four Brillouin zones of the reciprocal space. The experimental results have been quantitatively reproduced by an original numerical model that includes a two-dimensional Green's function description of the dipole field of the dynamic magnetization and exchange coupling between the layers. We found that, depending on $t$, the Py and Fe magnetic layers within the same nanowire are coupled by either the interlayer exchange or dipolar interactions. This has an impact on both the magnetization reversal and the collective dynamical properties of the artificial crystal. In particular, it is possible to stabilize a magnetization configuration where the layer magnetization vectors point in the same or in the opposite direction over a field range that varies with the Cu thickness. In addition, several modes are detected whose propagation properties (i.e., stationary or dispersive) through the array depend on static magnetization configuration as well as on the relative phase (in-phase or out-of-phase) of dynamic magnetizations between the two layers within the same nanowire.

P0666BRILLOUIN AND RAMAN SPECTROSCOPIES FOR NON-CONTACT ASSESSMENT OF MECHANO-CHEMICAL PROPORTIES OF URINARY PROTEINS: A PROOF OF CONCEPT STUDY

Abstract Background and Aims Proteinuria is a major marker of chronic kidney disease (CKD) severity, the predictor of renal function decline and cardiovascular mortality. The main pathway of CKD progressive is caused by tubular toxicity of filtering proteins, so more, the rapid development of renal failure is expected in those patients who have higher level of proteinuria. However, despite high level of proteinuria, paradoxically, some patients may have slow decline of renal function compared to those patients with lower level of urinary protein excretion. This may possibly due to their different mechanical (visco-elastic) and chemical properties, as well as the proteomics of excreting urinary proteins. Brillouin light scattering (BLS) and surface enhanced Raman scattering (SERS) spectroscopies are non-contact (laser optical-based) techniques providing visco-elastic and chemical property information of probed human biofluids. We aimed to study and compare the visco-elastic and chemical properties of urinary proteins using BLS and SERS spectroscopies in nephrotic patient with high protein excretion and healthy subject. Method Two urine samples from nephrotic patient (proteinuria>3.5 g/24h) and healthy subject (undetectable proteinuria) investigated using BLS and SERS spectroscopies. Brillouin spectroscopy performed using Torus single longitudinal mode laser in conjunction with high contrast JRS Instruments 6-pass tandem Fabry-Perot interferometer coupled with confocal microscope. Using Horiba LabRAM HR Raman microscope with 785 nm laser excitation andx100 microscope objective the SERS spectroscopy was performed on urine samples in contact 60 nm gold nanoparticles placed on gold film. Additionally, reversed-phase liquid chromatography-mass spectrometry (LC-MS) was conducted for profiling of urinary proteins LC-MS data was analysed by Mascot software using the SwissProt protein database. Results We found that elevated protein levels in urine alter the urine fluid elasticity sufficiently to be measurable by BLS spectroscopy, with urine from healthy and proteinuric subjects distinguishable to marked significance, which increases with sample concentration. BLS spectroscopy demonstrated that patients with High Protein Loss, characterized by stiffer urine (i.e. higher Brillouin shift and elastic modulus) and less viscous (i.e. less hypersound attenuation) compared to healthy subject. (Figure 1A). SERS measurements of two urine samples taken from patient with high protein loss in healthy subject (Figure 1B) showed the integrated Raman intensity ratio of 1338 cm-1 and 1002 cm-1 peaks is many times higher for the sample with high protein concentration vs sample with low protein concentration. Urinary protein sequencing and Mascot analysis (Table 1) demonstrated that proteinuric patient had different type of proteins with up to 187k Daltons of molecular weight. Conclusion In this proof of concept study, we demonstrated that laser-optical BLS and SERS techniques combined with LC-MS measurements revealed that human urine fluids of healthy and proteinuric subjects had strong variation in the visco-elastic and chemical properties coupled with various level of protein content.

Anisotropic spin-wave dispersion in two-dimensional Ni80Fe20 diatomic nanodot array

Abstract Artificially patterned magnonic crystals serve as a promising candidate for the emerging research fields of magnonics and spintronics. Here, we investigate the spin-wave dispersion in a diatomic nanodot lattice made of Ni80Fe20 nanodots of two different diameters placed in close proximity to form a binary magnonic crystal with a complex double-dot unit cell. The frequency dispersion of SW eigenmodes experimentally measured by the Brillouin light-scattering technique is in good agreement with the numerically calculated band structure derived from the linearized Landau-Lifshitz equation. Due to the change of the nature of interaction among the dots in two mutually perpendicular orientation of the applied bias magnetic field, magnonic band structure, including the slope of the dispersion curves, varies significantly. The anisotropic SW propagation is also studied numerically by local excitation of spin-wave dynamics in this system. This phenomenon is further explained by the calculated iso-frequency contours. Efficient manipulation of spin waves in this new type of two-dimensional magnonic crystal is promising for the development of nanoscale magnonic and spintronic devices.

Reciprocal excitation of propagating spin waves by a laser pulse and their reciprocal mapping in magnetic metal films

Focused pulse-laser-induced propagating magnetostatic surface spin waves (MSSWs) were investigated using an all-optical space-time-resolved magneto-optical Kerr effect microscope in 20-nm-thick permalloy thin films to clarify reciprocity and symmetry of MSSW emission. The microscope setup was constructed with variable direction of the applied magnetic field, and the corresponding angular dependence was examined. MSSWs were reciprocally emitted from the laser spot, in contrast to the nonreciprocal emission obtained by the antenna method. Specifically, the observed excitation amplitude and phase were independent of the propagation and magnetization directions within experimental error. By transforming the data into wave number--frequency space, the MSSW dispersion relation was clearly identified within the wave number of 2--3 rad/$\ensuremath{\mu}\mathrm{m}$ and frequency of 10 GHz. These observations are consistent with the model of ultrafast modulation of out-of-plane shape magnetic anisotropy inside the focused laser spot. In addition to confirming the symmetric and reciprocal emission of laser-induced MSSWs, the study demonstrated that this technique can provide all-optical microscopic spectroscopy for MSSW in metals, such as Brillouin light-scattering technique.

Low-damping spin-wave propagation in a micro-structured Co2Mn0.6Fe0.4Si Heusler waveguide

We report on the investigation of spin-wave propagation in a micro-structured Co2Mn0.6Fe0.4Si (CMFS) Heusler waveguide. The reduced magnetic losses of this compound compared to the commonly used Ni81Fe19 allow for the observation of spin-wave propagation over distances as high as 75 μm via Brillouin light scattering (BLS) microscopy. In the linear regime, a maximum decay length of 16.7 μm of the spin-wave amplitude was found. The coherence length of the observed spin-wave modes was estimated to be at least 16 μm via phase-resolved BLS techniques.

Collective spin modes in chains of dipolarly interacting rectangular magnetic dots

We present a combined experimental and micromagnetic study of spin excitations in chains of dense magnetic dots. The samples consist of long chains of rectangular dots with rounded corners having lateral dimensions of 715 \ifmmode\times\else\texttimes\fi{} 450 nm${}^{2}$ and 1025 \ifmmode\times\else\texttimes\fi{} 450 nm${}^{2}$, respectively. Chains are composed of magnetic elements put side by side along either their major or minor axis with edge-to-edge separation below 100 nm. The frequency dispersion of the spin-wave excitations was measured by Brillouin light-scattering technique as a function of the transferred wave vector directed along the chains of dots and for an external magnetic field applied perpendicularly to the transferred wave vector in the dots plane. Evidence is given of collective excitations in the form of Bloch waves propagating through the chains characterized by magnonic energy bands. Micromagnetic calculations, performed by using the dynamical matrix method, enable us to satisfactorily reproduce the frequency dispersion of collective spin modes as well as to visualize the spatial profile of the dynamic magnetization inside the dots. We also propose a general rule to understand the frequency dispersion of collective modes starting from the relative phase of dynamic magnetization in the facing sides of adjacent dots.

Analysis of collective spin-wave modes at different points within the hysteresis loop of a one-dimensional magnonic crystal comprising alternative-width nanostripes

The Brillouin light-scattering technique has been applied to study collective spin waves in a dense array of dipolarly coupled ${\text{Ni}}_{80}{\text{Fe}}_{20}$ stripes of alternating widths, during the magnetization reversal process. Both the saturated ``ferromagnetic'' state, where the magnetizations of wide and narrow stripes are parallel, and the ``antiferromagnetic'' state, characterized by an antiparallel alignment of the static magnetization in adjacent stripes, have been analyzed. The experimental data provide strong evidence of sustained collective excitations in the form of Bloch waves with permitted and forbidden magnonic energy bands. The measured frequencies as a function of the exchanged wave vector have been satisfactorily reproduced by numerical simulations which enabled us to calculate the spatial profiles of the Bloch waves, showing that some of the modes are preferentially localized in either the wide or the narrow stripes. We estimated the expected light-scattering cross section for each mode at different magnetic ground states, achieving a good agreement with the measured intensities. The alternating-width stripes system studied here represents a one-dimensional artificial magnonic crystal with a complex base and can be considered as a model system for reprogrammable dynamical response, where the band structure of collective spin waves can be tailored by changing the applied magnetic field.

Anisotropic dynamical coupling for propagating collective modes in a two-dimensional magnonic crystal consisting of interacting squared nanodots

Collective spin excitations in a planar array of interacting submicron magnetic squared dots have been studied by the Brillouin light-scattering technique. The dispersion curves of collective spin modes are characterized by periodical oscillations determined by the width of the artificial Brillouin zone. Because of the uniaxial symmetry introduced by the application of an external magnetic field ${H}_{0}$, the dynamical coupling and the frequency dispersion of collective modes are different when the wave vector is perpendicular or parallel to ${H}_{0}$. An analytical model has been exploited to calculate the dispersion of collective spin modes by numerically solving eigenvalue/eigenfunction problem for a band matrix which originates from linearized Landau-Lifshitz magnetic torque equation. A very good agreement between calculation and experiment was found. In addition, a micromagnetic approach has been exploited to achieve an independent evaluation of the collective modes frequency and a visualization of their spatial profile on a limited $(3\ifmmode\times\else\texttimes\fi{}3)$ array of dots.

Three-magnon splitting and confluence processes for spin-wave excitations in yttrium iron garnet films: Wave vector selective Brillouin light scattering measurements and analysis

Brillouin light scattering (BLS) has been used to observe and confirm the existence of nonlinear three magnon splitting and confluence processes for propagating spin waves in the magnetostatic backward volume wave configuration. Wave vector and frequency selective BLS techniques were also used to provide a quantitative map of the wave vector make-up for the parametrically excited half-frequency dipole-exchange spin wave (DESW) split magnons and the confluence magnons that result from the recombination of these DESW modes. The experimental wave vector maps for the product splitting and confluence magnons matched nicely with those expected from spin-wave theory. The data were obtained with (1) a strip line excitation/detection transducer structure, (2) forward-scattering BLS optics, (3) a fixed magnetic field of 352 Oe applied along the propagation direction, (4) pumping frequencies from 2.5 down to 2.1 GHz, (5) and cw input powers from $200\text{ }\ensuremath{\mu}\text{W}$ to 6 mW. The wave vector selective measurements utilized variable diameter circular diaphragms, rotatable slit apertures, and circular light blocks to access spin waves with wave numbers from about 100 to $3.6\ifmmode\times\else\texttimes\fi{}{10}^{4}\text{ }\text{rad}/\text{cm}$ and the full $360\ifmmode^\circ\else\textdegree\fi{}$ range of propagation angles.

Discrete modes of a ferromagnetic stripe dipolarly coupled to a ferromagnetic film: aBrillouin light scattering study

Spin wave excitations in a magnetic structure consisting of a series of long permalloystripes of a rectangular cross section magnetized along the stripe length and situated abovea continuous permalloy film are studied both experimentally and theoretically. Stripes andcontinuous film are coupled by dipole–dipole interaction across 10 nm thick Cuspacers. Experimental measurements made using the Brillouin light scatteringtechnique (with the light wavevector oriented along the stripe width) provideevidence for one dispersive spin wave mode associated with the continuous film andseveral discrete non-dispersive modes resonating within the finite width of thestripes.To interpret the experimental spectra, an analytic theory based on the spin wave formalismfor finite-width magnetic stripes has been developed, achieving a good qualitative andpartly quantitative description of the experimentally observed spin wave spectrum of thesystem. In particular, it is explained why the presence of a continuous magnetic film nearthe magnetic stripe leads to a substantial decrease of the frequencies of the discrete dipolarspin wave modes localized within the stripes. A more quantitative description of themeasured frequencies and of the spatial profiles of the spin wave eigenmodes has beenobtained by numerical calculations performed using a finite element method.

Brillouin scattering study on the single-crystal elastic properties of natrolite and analcime zeolites

The Brillouin light-scattering technique was used to investigate the single-crystal elastic properties of two aluminosilicate zeolites, natrolite (NAT) and analcime (ANA), at ambient conditions. An inversion of the acoustic velocity data results in the full set of elastic stiffness moduli (Cij’s) for both materials. From the single-crystal moduli the aggregate adiabatic bulk moduli (Ks), shear moduli (G), and Poisson’s ratios (ν) were found to be Ks=48.5(1.0)GPa, G=31.6(1.0)GPa, and ν=0.232(5) for NAT, and Ks=59.8(1.2)GPa, G=32.1(1.0)GPa, and ν=0.272(5) for ANA (Voigt-Reuss-Hill averages). The bulk and shear moduli of both zeolites are relatively low compared with those of densely packed aluminosilicates, reflecting an open framework structure of (Al,SiO4) tetrahedra which is easily deformed by bending the Si–O–Al angles. As expected for a less dense crystal, NAT is softer and more compressible than ANA. An evaluation of the directional Young’s moduli shows that the compressibility of NAT is nearly uniform along the [100] and [010] axes, while [001] is stiffer, in agreement with previous compression studies. We do not find experimental evidence of negative Poisson’s ratios for NAT zeolites as predicted by recent theoretical calculations.

Brillouin light scattering analysis of three-magnon splitting processes in yttrium iron garnet films

Wave vector and frequency selective Brillouin light scattering (BLS) has been used to measure the wave vector make up for the dipole exchange spin wave (DESW) modes which are parametrically excited by propagating magnetostatic surface wave (MSSW) pulse signals in a long and narrow yttrium iron garnet film strip through three magnon splitting processes. The signal frequency ${f}_{s}$ was 2.65 GHz, the input pulse width was 100 ns, and the in-plane applied field was 340 Oe. In addition, time and space resolved (TSR) BLS techniques were used to map the spatio-temporal propagation properties of the MSSW and DESW modes as they evolve as a result of three magnon processes. The film thicknesses were 5--10 \ensuremath{\mu}m. Specific data are reported for an 8.7 \ensuremath{\mu}m thick film. The DESW mode frequencies are at about ${f}_{s}/2.$ The DESW wave vector k directions form lobes at in-plane angles of 5\ifmmode^\circ\else\textdegree\fi{}--15\ifmmode^\circ\else\textdegree\fi{} relative to the field. The k values are in the ${10}^{4}\mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{c}\mathrm{m}$ range and are quantized. The frequencies and k values match those predicted from the dispersion relations and energy and momentum conservation. Specific critical powers are associated with particular k values. The TSR data show that the MSSW pulses propagate with a wedge shaped wave front and quench in such a way as to produce the ultra short 1--2 ns wide output pulses reported previously. The quench is connected with the appearance of a corresponding half frequency DESW wedge which is nearly stationary, has a response time of a few nanoseconds, and has a decay time in excess of the 100 ns MSSW pulse width.

Anomalous spin-wave damping in exchange-biased films

Ferromagnetic resonance and Brillouin light-scattering techniques have been used to investigate the spin-wave damping in ferromagnetic (FM)/antiferromagnetic bilayers exhibiting exchange bias. The measurements were done in the prototype system NiFe/NiO sputtered on Si(100) as a function of the NiFe film thickness. The linewidths measured with both techniques are more than one order of magnitude larger than in similar NiFe films without exchange bias and increase dramatically with decreasing FM film thickness. The data are consistently explained by a relaxation mechanism based on two-magnon scattering processes due to the local fluctuation of the exchange coupling caused by interface roughness. The local interface energy necessary to account for the measured linewidths is on the same order of the atomic exchange coupling.

Linear and nonlinear diffraction of dipolar spin waves in yttrium iron garnet films observed by space- and time-resolved Brillouin light scattering

An advanced space- and time-resolved Brillouin light-scattering technique is used to study diffraction of two-dimensional beams and pulses of dipolar spin waves excited by strip-line antennas in tangentially magnetized garnet films. The technique is an effective tool for investigation of two-dimensional spin-wave propagation with high spatial and temporal resolution. Linear effects, such as the unidirectional excitation of magnetostatic surface waves and the propagation of backward volume magnetostatic waves (BVMSW) in two preferential directions due to the noncollinearity of their phase and group velocities, are investigated in detail. In the nonlinear regime, stationary and nonstationary self-focusing effects are studied. It is shown that nonlinear evolution of a stationary BVMSW beam, having a finite transverse aperture, leads to self-focusing of the beam at one spatial point. Evolution of a finite-duration (nonstationary) BVMSW pulse leads to space-time self-focusing and formation of a strongly localized two-dimensional wave packet (spin-wave bullet). Theoretical modeling of the self-focusing and diffraction processes by using a variational approach and direct numerical integration of the two-dimensional nonlinear Schr\"odinger equation provides a good qualitative description of the observed phenomena.

Brillouin light-scattering observation of the nonlinear spin-wave decay in yttrium iron garnet thin films

The direct observation of nonlinear spin-wave decay in thin yttrium iron garnet (YIG) films is reported. The second-order parametric spin waves were excited by a series of nonlinear magnetostatic backward volume wave (MSBVW) pulses propagated in a microstrip structure at 5 GHz. Brillouin light-scattering techniques were used to detect spin waves in the YIG at a point along the propagation path. Data were obtained as a function of the input pulse duty cycle and peak power level. These data yielded the decay rate ${\ensuremath{\eta}}_{\mathrm{eff}}$ for the parametric spin waves vs input power ${P}_{\mathrm{in}}.$ This ${\ensuremath{\eta}}_{\mathrm{eff}}$ was equal to the usual spin-wave relaxation rate at low power, but decreased rapidly with increasing ${P}_{\mathrm{in}}.$ As ${P}_{\mathrm{in}}$ approached the threshold power for complete MSBVW soliton formation at the observation point, ${\ensuremath{\eta}}_{\mathrm{eff}}$ leveled off to a relatively constant value that was about a factor of 5--10 smaller than the low power value. The initial decrease in ${\ensuremath{\eta}}_{\mathrm{eff}}$ with power is due to the compensation of the usual spin-wave decay by the simultaneous parametric pumping of the spin waves by Suhl processes. The leveling off in ${\ensuremath{\eta}}_{\mathrm{eff}}$ at the soliton threshold is due to the spin-wave shedding that is needed to maintain order one eigenmode soliton propagation at high input power levels. These experiments demonstrate the reduction in the spin-wave decay rate with power below the threshold for spin-wave instability. This reduction is a key element in spin-wave instability theory that has never been observed directly. The data also demonstrate the enhanced production of parametric spin waves that accompanies microwave magnetic envelope soliton formation.

Spin-wave instability magnon distribution for parallel pumping in yttrium iron garnet films at 9.5 GHz

Parallel-pumping spin-wave instability processes for 2-, 4.15-, and 6-\ensuremath{\mu}m-thick yttrium iron garnet films have been studied by microwave and Brillouin light-scattering techniques. The pump frequency was 9.5 GHz. The static and linearly polarized microwave fields were in plane. Butterfly curves of the instability threshold microwave-field amplitude vs the static field H were measured, along with companion determinations of the critical mode in-plane spin-wave polar-angle ${\mathrm{\ensuremath{\theta}}}_{\mathrm{k}}$ and in-plane wave-number k distributions vs H. The 4.15- and 6-\ensuremath{\mu}m-thick films show narrow distributions in the critical-mode ${\mathrm{\ensuremath{\theta}}}_{\mathrm{k}}$ values and broad distributions in the critical-mode k values which appear at threshold and extend to high power. For the 2-\ensuremath{\mu}m film, the critical-mode ${\mathrm{\ensuremath{\theta}}}_{\mathrm{k}}$ distribution is narrow just at the instability threshold. As the power is increased, the critical-mode ${\mathrm{\ensuremath{\theta}}}_{\mathrm{k}}$ distribution broadens and develops a bimodal character indicative of a splitting into two critical modes. These distributions also show considerable fine structure. The basic shape of the butterfly curve and the measured ${\mathrm{\ensuremath{\theta}}}_{\mathrm{k}}$ values for the 4.15- and 6-\ensuremath{\mu}m-thick films are in rough agreement with predictions from bulk theory, except that the measured k values are in the ${10}^{4}$ rad/cm range rather than near zero. These measured k distributions are quite broad and also show significant structure.