Spin Wave Linewidth Research Articles

Scattering of spin waves by pores in ferrimagnetic materials

The differential cross section of spherical pores in ferrimagnetic materials is calculated by using the Born approximation in scattering theory. Using this scattering cross section, the theory is developed for evaluating the wave-vector dependence of the spin-wave linewidth. The wave-vector dependence of the spin-wave linewidth is 1/k in the long-wavelength region and is proportional to k for the short-wavelength region, where k is the wave vector of the spin waves. It is concluded that the spin-wave linewidth is a function of both the number of pores and their radius. Agreement between the theoretical formula and the experimental results is good except in the region of very long wavelength.

Comparison of rare earth relaxation effects in YIG from perpendicular and parallel-pump measurements

Samples of polycrystalline YIG have been doped at various concentrations with terbium and dysprosium. The effects on spin wave linewidth, ΔH k , effective linewidth, W, and resonance field shift, S, have been measured and compared. An empirical relation between the spin wave linewidth, the spin wave vector, and doping concentration is given with rare earth dependent constants. It has been observed that in the low field region the behaviour of W is consistent with coupling to high k spin waves (wavelength \sim0.1 \mu m). Almost exactly the same behaviour has been observed in the high field region. Within the degenerate region the relative effects of the two rare earths were reduced. No changes in either the shape or magnitude of the S behaviour were observed. The conclusions are that the rare earth doping does not affect the degenerate coupling and that within the degenerate region both rare earth relaxation and polycrystalline inhomogeneity relaxation are effective. It is suggested that the high and low field behaviour of W can be explained if there exist localised, near atomic scale inhomogeneities producing coupling to very high k vector spin waves. More detailed quantitative analysis is required to verify this.

Temperature dependence of the magnetic excitations in iron

The neutron coherent inelastic-scattering technique has been used to study the temperature dependence of the magnetic excitations in iron from room temperature to well above the ferromagnetic transition temperature. Most of the measurements were taken on a large single crystal of $^{54}\mathrm{Fe}$ (12-at.% Si), although a less extensive set of data was obtained with a single crystal of pure iron. In contrast to the behavior previously observed in the small-wave-vector region, we find that the spin waves at larger values of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$ are only moderately renormalized up to ${T}_{C}$, and persist as excitations up to the highest temperature measured ($\ensuremath{\sim}1.4{T}_{C}$). No further renormalization of the dispersion relation is observed above ${T}_{C}$. Measurements of the spin-wave linewidths show that as the temperature increases to ${T}_{C}$ the widths rapidly increase, but above ${T}_{C}$ no additional broadening occurs. In the paramagnetic phase the ratios of the energy widths divided by the excitation energies for $E\ensuremath{\gtrsim}8$ meV are found to be less than one ($\frac{\ensuremath{\Delta}E}{E}l1$), which has been used as the criterion for the definition of a spin-wave excitation. As the energy decreases below \ensuremath{\sim} 8 meV, the scattering evolves continuously into the critical scattering around the origin ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}=0$, $\ensuremath{\omega}=0$), whereas with increasing energy $\frac{\ensuremath{\Delta}E}{E}$ decreases. The dynamical correlation range corresponds to a sphere with a diameter \ensuremath{\sim} 10 \AA{}, and this correlation range is, within experimental error, independent of the temperature. The over-all spin-wave intensities are reduced at elevated temperatures, but the abrupt decrease in the spin-wave intensity at high energies, interpreted in terms of the band model of magnetism as the intersection of the spin-wave spectrum with the Stoner continuum of spin-flip excitations, is found to be independent of the temperature. The spin-wave energies, as well as the linewidths, are isotropic in $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$ over the entire temperature range covered, and no interaction of the spin waves with the phonons is observed. These experimental results are in disagreement with present theoretical estimates of the generalized susceptbility at elevated temperatures.

Relaxation of rare earth and cobalt ions in polycrystalline yttrium iron garnet

Relaxation at room temperature of rare earths and cobalt ions in ferrimagnetic garnets has been studied by measuring the three linewidths : ΔH, resonance linewidth, Δ H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eff</inf> , effective linewidth, ΔH <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</inf> , spinwave linewidth. These linewidths have been measured at 9 GHz Δ H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eff</inf> , far from resonance, Δ H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</inf> in perpendicular and in parallel pumps. From experimental results, relations between ΔH, Δ H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eff</inf> and Δ H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</inf> have been found which are in good agreement with the theory. The broadening δ (ΔH), due to the introduction of rare earths ions, allows the relaxation time τ (about 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-13</sup> sec) of some rare earths ions to be deduced from Kittel's theory. At room temperature, this theory explains the gyromagnetic properties of Sm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> , Tb <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> , Dy <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> , Ho <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> and Er <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> ions. An adaptation of this theory allows us to explain also the behaviour of Gd <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> ions. Relation between δ (ΔH) and the saturation magnetization 4π M <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</inf> are explained for the Sm, Dy, Ho and Er ions by an extension of Kittel's theory, but this explanation is not unique.

Interesting microwave ferrites of polycrystalline Y Gd I G's with both octahedral and tetrahedral substitutions

The influences of simultaneous tetrahedral (aluminium) and octahedral substitutions (tin or indium) upon the magnetic and microwave properties of various YGdFe polycrystalline garnets have been studied. We have obtained interesting new materials with saturation magnetizations between 200 and 900 G which exhibit higher temperature stabilities of the magnetization than those of classical garnets. In addition they have fairly narrow gyromagnetic linewidths, weak dielectric losses and relatively high values of spin-wave linewidths. These properties, obtained by a judicious balance between both substitutions, make these materials suitable for applications in the lower frequency range of the microwave spectrum when high peak and average powers are needed.

Microwave Lithium Ferrites: An Overview

Lithium ferrites are discussed and compared with other spinel microwave ferrites and rare earth-iron garnets. Points of comparison are saturation magnetization, temperature performance, hysteresis loop properties, stress sensitivity, insertion loss, power handling capability, resonance linewidth, and cost. The main points of discussion deal with the relative effectiveness of lithium ferrites, nickel ferrites, magnesium ferrites, and garnets as elements employed in latching applications at frequencies in the S, C, X, and K/sub u/ bands. A section is devoted to the compositional modifications necessary for: 1) adjusting magnetization, spin-wave line width, coercive force, and magnetic anisotropy; 2) the minimization of stress sensitivity and dielectric loss; and 3) the improvement of microstructural characteristics.

A possibility of identifying the surface spin-wave mode from spin-wave resonance linewidth

Spin-wave resonance linewidth is calculated from the Landau-Lifshits equation including dipole interactions. The graph of the linewidthΔH p vs. the square of the SWR peak number is a straight line for spin-wave space modes, whereas for the peak corresponding to surface spin-wave excitationΔH lies beyond it, thus providing a criterion for distinguishing the surface peak from the others.

Wave-vector dependence of rare-earth relaxation in yttrium iron garnet

A wave-vector dependence of the parallel-pump spin-wave linewidth in rare earth doped YIG is reported. The spin-wave linewidth (ΔHk) has the form ΔHk = a + a′c + (b + b′c)k. The a's and b's are constants with the primed values dependent on the particular rare earth and c is the rare-earth doping level. Values of b′ are 1.8±0.2, 3.55±0.3, and (11.6±0.5)×105 Oe cm/at.% rare-earth doping level for samarium, holmium, and terbium, respectively. The k dependence may be due either to a k dependence of the longitudinal relaxation mechanism or to a transit-time phenomena. These results show that the rare earths are more effective at increasing the high-power capability of ferrites than the extrapolated ΔHk→0 results would suggest.

Some features of Gd substituted garnet containing Co2+for latching phase shifter

One of the authors has demonstrated that the high-power capability of a latching phase shifter was remarkably enhanced by employing Co2+doped Gd YIG without any increase in the insertion loss. Investigations done so far on the insertion loss are not sufficient to describe this fact. A part of the results of the investigation concerning Co2+doped Gd YIG has been presented by Nicolas et al. The characteristics of the Co2+, doped Gd YIG have been studied in regard to a latching phase shifter by way of the precise measurement of the complex permeabilities. For the samples containing an appropriate amount of Co2+, the part of the insertion loss due to the anisotropy field has been proved to be eliminated, and the value of the spin-wave linewidth has suggested that high-power capability is enhanced. The coercive force indicates the minimum value at that content of Co2+, while the remanence ratio remains fairly constant. It is concluded that the materials containing an appropriate amount of Co2+are superior to those materials without Co2+in both the insertion loss and high-power capability.

Parallel Pumping of Spin-Waves in an Orthorhombic Antiferromagnet

By means of the parallel pumping technique, unstable growths of spin-waves are observed in antiferromagnetic CuCl 2 2H 2 O at a pumping frequency of 8.912 GHz. The threshold r f -field h c for the onset of parallel pumped spin-wave instability is theoretically obtained for antiferromagnets with the anisotropy of orthorhombic type. In addition to excitation of two spin-waves of the same branch in the spin-wave spectrum, excitation of two spin-waves of the different branches is also considered. The threshold field h c is experimentally obtained for the low-frequency branch when the static and the r f -fields are both applied parallel to the spin easy axis. Using the theoretical expression for h c , the experimental data are deduced to the spin-wave linewidth Δ H k which increases linearly with k 2 for small k and is proportional to T 4.6 in the temperature range from 1.2 to 1.8 K.

Fabrication and properties of microwave lithium ferrites

Lithium ferrites are low-cost materials which are attractive for microwave device applications. For a number of years these materials have been prominent in the computer core industry because of excellent temperature performance and the squareness of their hysteresis loops. Previous attempts at exploiting lithium ferrites for microwave applications have met with limited success. Properties which required further improvements were the dielectric and magnetic loss tangents, anisotropy, coercive force, and density. This paper reports primarily the development of microwave S - and C -band lithium ferrites with substantially improved properties, comparable to those of the more expensive ferrimagnetic garnets currently in use. Extensive applications are also expected for higher frequencies up to and including K u band. Because a number of factors can affect the performance of microwave devices, the lithium ferrites reported herein are heavily doped to optimize the numerous properties of interest. The following additives were employed: 1) Ti-to tailor saturation magnetization for various frequencies; 2) Zn-for its beneficial effects on coercive force, magnetic loss, and densification; 3) Mn-to decrease the dielectric loss, improve the remanence, and reduce the stress sensitivity of the remanence; 4) Co-to provide a range of spinwave linewidths ; 5) Ni-for increased remanence ; and 6) Bi (the most important additive)-to increase the densification at low firing temperatures and thereby provide low dielectric loss and low coercive force. The microwave lithium ferrites offer a high degree of latitude for tailoring various parameters for special device requirements. However, the optimization of selected properties is sometimes accomplished at the expense of other properties. Although this investigation was directed mainly toward applications for latching devices, lithium ferrites have been altered for use in a variety of devices such as limiters and circulators. The requirements for ferrite materials in latching phasers are reviewed, the compositional factors which result in useful properties are discussed, and performance in circulators and latching phasers is reported.

Spin-Wave Resonance Fields, Linewidths, and Intensities of a Permalloy Film: Theory and Experiment

Spin-Wave Resonance Fields, Linewidths, and Intensities of a Permalloy Film: Theory and Experiment

Effect of Nonmagnetic Inclusions on the Spin-Wave Linewidth in Polycrystalline YIG

Nonmagnetic second-phase inclusions of two different average sizes (2.5 ± 0.5 and 1.2 ± 0.5 μ m) were produced in specimens of polycrystalline YIG. A dependence of spin-wave linewidth on inclusion size was observed. The linear relationship between spin-wave linewidth and the concentration of second-phase inclusions was dependent on the wave vector k. At k ≈ 2 × 105 cm−1, the relationship was 0.15 Oe and 0.075 Oe per % second-phase concentration for the samples with the smaller and larger inclusions, respectively. It is suggested that in porous specimens the average size of the pores may affect the spin-wave linewidth and that this effect is similar to the transit-time effect produced by finite grain sizes.

Experimental dependence of the SSW linewidth with wavenumber in permalloy films

Films of Permalloy for which standing spin-wave (SSW) linewidths do not increase with wavenumber have been experimentally obtained. It is shown that the broadening of the linewidth with wavenumber in the case of oblique incidence evaporation is quantitatively explained by a calculation of ΔH <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</inf> taking into account the gradient of film thickness determined by the evaporation law. It is concluded that the interactions between different regions of the film do not appreciably influence the SSW linewidth, and that the effect of the thickness dropoff which appears at the edge of the films is negligible. In addition, it is shown that films of relatively large dimensions with a constant and small linewidth can be obtained by a careful arrangement of the evaporation system.

Spin-Wave Linewidth of Ruthenium and Iridium-Substituted Yttrium-Iron-Garnet

physica status solidi (a)Volume 6, Issue 1 p. K11-K13 Short Note Spin-Wave Linewidth of Ruthenium and Iridium-Substituted Yttrium-Iron-Garnet P. Hansen, P. Hansen Philips Forschungslaboratorium Hamburg GmbHSearch for more papers by this authorW. Tolksdorf, W. Tolksdorf Philips Forschungslaboratorium Hamburg GmbHSearch for more papers by this author P. Hansen, P. Hansen Philips Forschungslaboratorium Hamburg GmbHSearch for more papers by this authorW. Tolksdorf, W. Tolksdorf Philips Forschungslaboratorium Hamburg GmbHSearch for more papers by this author First published: 16 July 1971 https://doi.org/10.1002/pssa.2210060142Citations: 7AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Citing Literature Volume6, Issue116 July 1971Pages K11-K13 RelatedInformation

Relationship between spinwave linewidth Δ H k and the effective linewidth Δ H eff in ferrites

The spinwave linewidth ΔHk and effective linewidth ΔHeff were measured on y.i.g., Ni ferrites and Mg, Mn ferrites, fine-grained and strong-relaxer-doped. It is seen that ΔHkalways increases with ΔHeff

Temperature dependence of SSW linewidth in metallic thin films

Measurements of the standing spin wave linewidth ΔH n at 17·6 GHz from 6 °K to 400 °K are presented for two permalloy films whose structure is either polycrystalline or epitaxial. It is shown that in both films, ΔH n is proportional ton 2 (n is the mode number). Although ΔH n is little modified by temperature (20% variation maximum over the entire temperature range), we experimentally state that the slopep of ΔH n (n 2) is a linear function of the saturation magnetizationM which agrees with a planar inhomogeneity model.

Enhancement of Mode Locking of Spin Waves at Low Temperatures

Investigations of mode locking of spin waves in YIG by nonlinear magnetoelastic coupling have been extended to low temperatures. Due to an increase of the spin-wave linewidth of YIG at low temperature, more spin-wave modes can be excited and, consequently, stronger mode-locking effects are observed. In our experiment more than 10 modes of spin waves have been mode locked. The variation of number of modes as a function of temperature is presented. In addition, a pickup coil is placed near the sample to measure any changes in mz. Since, for small perturbations, mz = 1 − ½ (mx1+my2), beating among different spin-wave modes will cause time variations of mz at the various beat frequencies. An enchancement of the harmonic content is observed upon the application of a mode-locking acoustic wave.

BEHAVIOR OF FERRITES IN THE MICROWAVE FREQUENCY RANGE

Present and foreseen applications of ferrites in the microwave frequency range are reviewed. The material parameters that are required or desirable for these applications are discussed. Special attention is given to the losses observed in polycrystals at biasing fields much smaller or much larger than the field for resonance. The loss may be characterized by an effective linewidth ƊHeff, which is a function of frequency and dc magnetic fieldstrength. In low loss polycrystals ƊHeff is typically much smaller in the off-resonance regions than near resonance, but even in the best polycrystals it is considerably larger than in good single crystals. The near-resonance behavior of ƊHeff can be explained quite well in terms of inhomogeneity induced scattering of energy into spin waves, having wavenumbers comparable to the inverse grain size. The off-resonance behavior is less well understood. Inhomogeneity induced scattering into phonons is discussed as a possible loss mechanism. For fine-grain ferrites the observed dependence of ƊHeff upon grain size and that of the spinwave linewidth (inferred from the instability threshold) upon grain size and frequency is in rough agreement with .the behavior expected theoretically for this mechanism. The microwave properties of partially magnetized ferrites are discussed. A simple theoretical formula, applicable in the demagnetized state, is derived. It is shown to agree reasonably well with the observed behavior both at high frequencies (where the losses are low) and at intermediate frequencies (0.1-3 GHz) (where the losses are high).

Possible relation between the low-level attenuation constant or Δ H eff and Δ H k

It is deduced from a theoretical model that the effective linewidth or low-level attenuation constant increases in proportion to the reciprocal of the spin-wave linewidth when the latter exceeds a certain minimum.