Spin Wave Linewidth Research Articles

Parallel Pumping in Hexagonal Ferrites with the Dc Field Off the Easy Plane

This paper gives the theory of spinwave instability under parallel pumping in hexagonal Zn/sub 2/Y ferrites with planar anisotropy in the case of a sphere. The configuration considered in this paper is the one in which the dc field makes an angle /spl beta/ with the easy plane and the resultant magnetization lies at an angle /spl alpha/ to it. To obtain parallel pumping with this arrangement it is necessfly to align the RF field along the magnetization. This leads to a new spinwave spectrometer which allows the dependence of the spinwave linewidth upon the angle /spl alpha/ which the unstable spinwave makes with the c axis of the crystal to be determined. The experimental results obtained on two Mn-Zn/sub 2/Y single-crystal ferrite spheres show that the spinwave linewidth increases with the angle /spl alpha/.

Spinwave Linewidth Measurements with Low-Power RF Sources (Correspondence)

This correspondence describes a perturbation technique for obtaining the spinwave linewidth of polycrystalline garnet spheres with large values of /spl Delta/H/sub k/. Conventions waveguide cavity techniques require power levels in the kilowatt region to excite the parallel-pump instability. By using a dielectric resonator, large RF magnetic field intensities can be generated using relatively low-power levels, and the presently available low-loss dielectric materials enable high Q-values to be attained in the resonator. Since the sensitivity of cavity perturbation techniques depend on high Q-values, the ferrite sphere can be made small enough so that perturbation assumptions apply. Results are presented for some representative polycrystalline samples. The largest spinwave linewidth measurement required a RF magnetic field intensity of approximately 27.0 Oe.

Effect of Grain Size on the Microwave Properties of Polycrystalline Yttrium Iron Garnet

Data on the parallel pump and subsidiary absorption threshold at 9.1 GHz and effective linewidth ΔHeff at 9.9 GHz have been obtained for polycrystalline YIG materials with an average grain diameter a0 from 1 to 30 μ. The fine-grain samples (1–10 μ) were made by hot pressing. The parallel pump spin-wave line-widths extrapolated to zero wavenumber, ΔHk→0, vary as a0−1, with ΔHk→0=25 Oe at a0=1 μ. The ΔHk for the fine-grain samples (a0 ≈ 1 μ) show an inverse k-dependence. A simple model in which the spin-wave transit time across individual grains limits ΔHk appears to explain the a0−1 dependence but not the observed k-dependences for ΔHk. The high-field ΔHeff is 5.5 Oe for a0=1 μ and varies as a0−1/2. The low-field values are slightly larger, due to a small two-magnon contribution arising from coupling to degenerate short-wavelength spin waves. Even though the high-field ΔHeff contains no two-magnon contribution, it is significantly larger than linewidths in single crystals. A recently proposed magnetostriction mechanism is consistent with the a0−1/2 dependence, but the predicted magnitude of ΔHeff is much smaller than observed.

General Critical Field Expression for the Parallel-Pumped Magnetoelastic Instability

A general expression is derived for the critical parallel-pump-field strength for magnetoelastic waves. This expression can be used for all wave propagation directions, bias field directions, and crystal symmetries. In contrast to previous treatments, certain critical field results can be obtained without extensive numerical computation. It is found, for example, that when spin wave damping of elastic modes is dominant, these elastic modes have a critical pump field strength simply equal to twice the spin wave linewidth.

Ferromagnetic Resonance and Nonlinear Effects in Ferrites with Uniaxial Anisotropy

A study of the ferromagnetic resonance properties in single crystal Zn2+–Ti4+ substituted barium ferrite (BaZnxTixFe12–2xO19) with uniaxial anisotropy has been performed over the frequency range 23.2–37.6 GHz. By varying the amount of zinc and titanium substitution, the anisotropy field can be varied from 17 000 to 5000 Oe. This investigation concentrated on the composition in which x=2.25. These samples had an anisotropy field of 6590 Oe and a saturation magnetization of 2300 G. Cavity perturbation techniques were used with polished spherical samples 15–20 mils in diameter. The measured resonance linewidth along the easy axis was 43.2 Oe at 23.2 GHz and increased to 82.5 Oe at 37.6 GHz. Extrapolation of resonance data gave γ=2.75 MHz/Oe. As the incident rf power was increased at 36.1 GHz, nonlinear effects were observed. The threshold field for spin wave excitation was 0.86 Oe. Using an extension of nonlinear spin-wave theory to include uniaxial anisotropy, an intrinsic spin-wave linewidth of 0.97 Oe was calculated.

Microwave Properties of Fine Grain Polycrystalline Yttrium Iron Garnet

Parallel pump and subsidiary absorption thresholds at 9.1 GHz and effective linewidth (ΔHeff) at 9.9 GHz have been measured for polycrystalline YIG samples with average grain diameter a0 from 1 to 30 μ. The spin-wave linewidths extrapolated to zero wavenumber, ΔHk→0, vary as a0−1. The ΔHk for a0=1 μ shows an inverse k dependence. A simple model in which the spin-wave transit time across individual grains limits ΔHk explains the a0−1 dependence but not the observed k dependences for ΔHk. The high-field ΔHeff is 5.5 Oe for a0=1 μ and varies as a0−1/2. These ΔHeff are significantly larger than single-crystal linewidths. Two-magnon interactions cannot contribute to the high-field ΔHeff. A recently proposed magnetostriction mechanism is consistent with the a0−1/2 dependence, but the predicted magnitudes are much smaller than observed.

Possible relation between the low-level attenuation constant or ΔHeff and ΔHk

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.

Nonlinear Properties of Magnesium Manganese Ferrite

Measurements have been taken on the ferromagnetic resonance properties of narrow-linewidth single-crystal magnesium manganese ferrite spheres at 9100 MHz and between 77°K and room temperature. The composition of the melt in mole percent was as follows: MgO 11.60%; MnO2 4.5%; Fe2O3 15.08%; PbO 34.41%; and PbF2 34.41%. This particular ratio of constituents was chosen in order to obtain an equal percentage of magnesium and manganese in the final samples. The actual composition of the samples investigated in this report was the following: Mg0.53Mn0.47Fe2O4. The low-power resonance linewidth (ΔH) measured along the easy axis [111] was 8.4 Oe at 295°K and rises to 24.7 Oe at 77°K. The threshold field (hc) for spin-wave excitation at 77°K was 250 mOe, while at room temperature it dropped to 100 mOe. From the room temperature threshold field, an intrinsic spin-wave linewidth (ΔHk) of 270 mOe was calculated.

Nuclear and Electronic Spin-Wave Relaxation Rates in the Hexagonal Antiferromagnet CsMnF3

Nuclear and electronic spin-wave relaxation rates have been measured in the hexagonal antiferromagnet CsMnF3 in the flopped state using two kinds of parallel pumping experiments. In the first experiment, previously performed by Hinderks and Richards for RbMnF3, values of the product ηknηke are obtained from critical field data for simultaneous nuclear-electronic spin-wave instability using a 9.35 GHz pump. In the second experiment values of ηke are obtained by pumping at 17.5 GHz, twice the electronic spin-wave frequency. Reasonable agreement with a theory of Richards is obtained at 4.2° and 1.7°K for relaxation rates of the nuclear spin-waves having k ≈ 105 cm−1. For k ≈ 0 there is an order-of-magnitude discrepancy which may be accounted for if it is assumed that inhomogeneities strongly mix modes for k<105 cm−1. The electronic spin-wave linewidths for k ≈ 0 are much smaller than the AFMR which is independent of temperature from 4.2°–1.7°K. These results are consistent with a random strain-broadening interpretation of the AFMR width.

Second-order spin-wave instability in Mn-Zn2Y planar hexagonal ferrites

The letter describes some measurements of the decline of the main resonance under 2nd-order pumping in an Mn-Zn2Y single-crystal hexagonal ferrite biased in the easy plane. Measurements were carried out with the r.f. field in the easy plane and also with the r.f. field perpendicular to it. The ratio of the two responses in the linear region is e02, which is the ratio of the susceptibilities for the two excitations. The ratio of the two r.f. threshold fields is also approximately e. Here e02 is the uniform-mode ellipticity. For the samples used, the critical r.f. threshold field was 41A/m in the easy plane and the spinwave linewidth was 565A/m.

FMR studies of Ag-doped CdCr 2Se 4

The ferromagnetic linewidth, spin-wave linewidth, and crystalline anisotropy are changed significantly when CdCr 2Se 4 is doped with Ag. These changes are discussed.

Spin-Wave Relaxation in Ferromagnetic CdCr2Se4

The rather simple magnetic structure of the ferromagnetic insulator CdCr2Se4 makes it an attractive substance for the study of magnetic relaxation mechanisms in general, but in particular those mechanisms of importance in the vicinity of the ordering temperature. The ferromagnetic relaxation has been studied here by means of both FMR and high-power parallel-pump techniques. Using the latter technique, the intrinsic spin-wave linewidth was measured up to temperatures within a few degrees of the Curie temperature. Near the Curie temperature the linewidth diverges as (T0-T)−1 with T0=133°K. This value of T0 is in close agreement with our measured value of the Curie temperature 130°K. At low temperatures, up to 30°K, the relaxation appears to result from two-magnon coupling of the k=0 mode to modes of higher k, which relax by the three-magnon confluence process.

Excitation of Nuclear and Electronic Spin Waves in RbMnF3 by Parallel Pumping

We report observation of the simultaneous excitation of nuclear and electronic spin waves by parallel pumping, an effect predicted by Ninio and Keffer, in RbMnF3 at a pumping frequency of 8.56 GHz. Wavevectors between near zero and 105 cm−1 are excited by varying H. We operate with H and hrf in a [100] direction and H greater than the value required for flopping. From threshold fields, which are about 1.2 Oe minimum, we calculate, at 4.2°K, ηknηke = 6.1×1010 sec−2 for k→0 and 9.5×1010 sec−2 for k = 1.05×105 cm−1 (n stands for nuclear mode, e for electronic). These figures are smaller by two orders of magnitude than what is obtained from ηke inferred by Cole and Courtney from saturation of the main resonance and the value of ηn taken from the half-width of NMR absorption. To reduce critical-field data to spin-wave linewidths we have applied the methods of Ninio and Keffer to obtain a theoretical expression for hcrit in the case of a flopped antiferromagnet.

Operating Dynamics and Performance Limitations of Ferrite Digital Phase Shifters

Performance capabilities and limitations of nonreciprocal waveguide ferrite digital phase shifters are discussed. A computer-aided solution of the boundary value problem facilitates the optimization of both device geometry and material properties. Experimental results are in excellent agreement with predicted loss and phase shift values. Maximum figures of merit of the order of 1000 deg/dB have been realized. When high peak powers must be accommodated, some sacrifice in low-power performance is necessary. Operating peak power levels can be increased by lowering the saturation magnetization of the ferrite or by raising its spinwave linewidth. Peak power levels above 150 kW at X band and 350 kW at C and S bands have been attained in laboratory models with less than 1 dB loss for a 360 degree differential phase shift. When high-average power levels must be handled, various material and geometric considerations can be incorporated to minimize loss per unit length and to increase heat dissipation capabilities. Units have been successfully operated at S-band frequencies with only a five percent decrease in phase shift when carrying 900 watts average power. The various tradeoffs necessary to achieve high peak and average power performance are discussed.

Low-Temperature Nonlinear Effects in High-Saturation Magnetization Ferrites

Single-crystal nickel zinc (Ni0.5Zn0.5Fe2O4) and lithium zinc (Li0.35Fe2.35Zn0.5O4) ferrite were used in an experimental investigation of ferromagnetic nonlinear effects with incident power at both room temperature and 77°K. All data were taken at a constant frequency of 9.0 GHz. The lowest measured linewidths (ΔH) were 10 and 15 Oe at room temperature on nickel zinc and lithium zinc, respectively. These linewidths are reduced approximately 50% at 77°K. The saturation magnetization of the samples was in the order of 5000 ±150G at room temperature. This magnetization is increased approximately 20% above the room temperature value at 77°K. Variation of the incident power in oersteds over the range 1×10−6 to 10 Oe yielded the following general results: A substantial reduction in threshold field for nonlinear effects was measured on both lithium and nickel zinc ferrite at 77°K. Spin-wave linewidths (ΔHk) calculated at 77°K also yielded large reductions from those observed at room temperature. These enhanced values of saturation magnetization, along with the low threshold fields observed in nickel zinc ferrite, have important applications in the design of microwave-power limiters operating in the coincidence mode.

Anisotropy and temperature dependence of the spin-wave attenuation parameter in ferrite single crystals

Results are presented for ferromagnetic resonance in Mg-Mn and Li ferrites. The anisotropic part δΔHk of the spin-wave line width is defined as the difference between the spin-wave widths ΔHk as measured on a spherical specimen magnetized along [111] and [100] by parametric excitation of the spin waves by a longitudinal UHF magnetic field. The results are compared with the theory.

Parallel Pumping of Europium and Yttrium Iron Garnets at Low Temperatures

The spin-wave dispersion and relaxation properties as well as magnetoelastic and elastic properties of europium iron garnet (EuIG) and yttrium iron garnet (YIG) are measured at low temperatures and at about 17 Gc/sec using the parallel-pump technique. ${\mathrm{Eu}}^{3+}$ ions have unusual magnetic and relaxation characteristics in large exchange fields, and the effect of these ions on the spin-wave spectrum of the iron lattice is of interest. Also, the large effective magnetoelastic coupling constant of EuIG along [111] should have a marked effect on the character of the threshold curve as well as the magnon-phonon interaction notch. We find that the spin-wave linewidth of YIG is less than that of EuIG and that the three-magnon confluence process does not account quantitatively for the $k$-dependent linewidth at low temperatures. The exchange constant of EuIG is predicted quite well from the known magnetic properties of the ${\mathrm{Eu}}^{3+}$ ion and its expected effect on the spin-wave spectrum of the iron lattice. The large magnetoelastic coupling constant of EuIG along [111] makes the threshold curve quite anomalous. It shifts the longitudinal notch to higher $k$ values, yielding an erroneously high exchange constant. Also, the shear-wave notch is absent, possibly because the spin-wave instability merges smoothly into the elastic-wave instability. Along [100], the coupling constant of EuIG is much smaller and a normal threshold curve is obtained. For YIG, the magnetoelastic coupling constants derived from parallel-pump measurements are significantly higher than those obtained from strain-gauge measurements. This might be due to the lower temperature at which the parallel-pump measurements were done. For EuIG, the agreement between the two kinds of measurements was reasonably good. The elastic $Q$ increases with decreasing temperature for both garnets and is larger for YIG than for EuIG, as expected.

Spin-Wave Anisotropy Effects in Parallel Pumping in YIG

A second ``corner'' has been observed on the ``butterfly curve'' of the parallel pumping experiment on YIG (yttrium iron garnet) at x-band frequency. The extra corner occurs in all crystallographic directions in a (110) plane except the [100] and [111]. The separation between the two corners closely equals the anisotropy-produced azimuthal angle splitting of the top of the spin-wave band. This splitting occurs in cubic YIG in all directions except the [100] and [111]. The shape of the butterfly curve in the region between the corners is partially explained by the variation in spin-wave ellipticity with azimuthal angle. A variation in spin-wave linewidth for k→0 with azimuthal angle may be responsible for the remaining discrepancy.

Effect of Surface Polishing on the Linewidth and High-Power Properties of Single-Crystal Spheres of ZnY

Single-crystal (ZnY) (Ba2Zn2Fe12O22) was used in an investigation of the effects of surface finish on the linewidth and high-power properties. Measurements indicate that by polishing rough-ground spheres with successively finer grit abrasives, the linewidth can be reduced from 50 to 13.8 Oe. From the measured threshold field, the spin-wave linewidth (ΔHK) of 6.6 Oe has been calculated, in good agreement with that obtained by Green and Healy who used the parallel pump technique. Experiments indicate a threshold field an order-of-magnitude lower than for yttrium iron garnet with a comparable linewidth.

Spin-Wave Instability and Premature Saturation in Antiferromagnetic Resonance

A semiclassical theory of spin-wave instability in antiferromagnetic resonance is developed. The calculation is valid both for simple antiferromagnets and for canted systems when the canting is due either to single ion magnetocrystalline anisotropy or anisotropic exchange. The nonlinear terms leading to the instability are found to originate in the anisotropy and exchange energies. The critical radio frequency field for the onset of instability is calculated and in general is given by ${h}_{c}=4\ensuremath{\Delta}{H}_{0}{(\frac{\ensuremath{\gamma}\ensuremath{\Delta}{H}_{k}}{{\ensuremath{\omega}}_{0}})}^{\frac{1}{2}}$, where $\ensuremath{\Delta}{H}_{0}$ and $\ensuremath{\Delta}{H}_{k}$ are, respectively, the uniform mode and spin-wave linewidths; and ${\ensuremath{\omega}}_{0}$ is the zero-field antiferromagnetic resonance frequency. Experimental evidence for the existence of spin-wave instability in the canted antiferromagnet, KMn${\mathrm{F}}_{3}$, is presented and discussed. An anomalous low-level saturation of the rf susceptibility is attributed to the onset of spin-wave instability. A new technique for the measurement of spin-wave linewidths is described. This technique, which is based on the response of the resonant system to amplitude modulated microwave power, yields results in agreement with the instability theory. The spin-wave linewidth as determined by these experiments is approximately three orders of magnitude narrower than the linewidth of the uniform mode, indicating that the broadening mechanisms are grossly different in the two cases.