Spin Wave Linewidth Research Articles

In-Plane Anisotropy of Ferromagnetic Resonance and Spin-Wave Relaxation in K2CuF4

Ferromagnetic resonance and parallel pumping experiments in K 2 CuF 4 are investigated at 9 GHz and in the temperature range from 4.2 to 1.4 K. Temperature dependence of a weak fourfold anisotropy in the c -plane is measured. The anisotropy field extrapolated to T =0 K is 5 Oe. Resonance linewidth Δ H 0 and spin-wave linewidth Δ H k have also fourfold anisotropy.

Spin Dynamics in the Amorphous Invar Alloy of Fe86B14

The spin waves in an amorphous Invar alloy Fe 86 B 14 11 , have been studied by inelastic neutron scattering. Well defined magnon groups were detected around (0, 0, 0) up to q =0.12 A -1 for various temperatures below T ≤0.9 T c . The spin waves show the dispersions \( \hbar \omega _{q}(T)=E_{0}(T)+D(T)q^{2}\) with D ( T ) varying with temperature according to D ( T )= D (0)(1- a T 5/2 ) with D (0)=118 ±6 (meV A 2 ). The spin wave stiffness at 0 K, D (0), thus determined is almost twice as large as the value D M (0)=68 ±2 (meV A 2 ) determined for the same sample by a magnetization measurement. The spin wave linewidth \( \varGamma \) varies with wave vector q as \(\varGamma=aq^{2}\) and it shows only limited temperature dependence. All of these features are quite similar to those found in the crystalline Invar alloys as Fe 65 Ni 35 and Fe 3 Pt.

Spin fluctuations in mixed magnetic chains

The dynamic response of ferro- and antiferromagnetically coupled Heisenberg chains containing impurities is calculated in the low temperature and small concentration limit. Particular attention is given to impurity induced effects in the inelastic neutron cross-section, and explicit expressions are given for spin-wave linewidths.

Spin glass-ferromagnetic phase transition in amorphous (FexNi1−x)0.75P0.16B0.06Al0.03

Inelastic neutron scattering studies have been carried out on the magnetically isotropic amorphous system (FexNi1−x)0.75P0.16B0.06Al0.03 in the concentration range (x≳0.17) where both ferromagnetic and spin-glass behavior are observed. For x = 0.4, well defined spin waves which obey the customary quadratic dispersion relation E = DQ2 are observed below the Curie temperature (Tc = 365K) and D is found to increase with decreasing temperature as usual. Below ∼80K, however, D begins to decrease with decreasing temperature as the spin-glass state is approached. Accompanied by this decrease in D is an increase in the spin wave linewidths. Preliminary results for x = 0.3 and x = 0.2 show qualitatively similar behavior.

MEASUREMENT OF SPIN WAVE LINEWIDTH

In this paper, we describe the instrumentation and technique which are suitable for measuring first-Order instability threshold values of microwave field for both configurations of perpendicular and parallel pumping in magnetic order materials. The spin wave linewidth is derived from instability threshold values for parallel pumping. Experimental results are given for a sphere of yttrium iron garnet at room temperature and x-band. These results are in good agreement with those obtained by other researchers.

A broadband microwave signal to noise enhancer

A signal to noise enhancer exhibits a high attenuation to small noise level signals and a lower attenuation to larger above threshold signals. The devices described rely on magnetostatic waves as saturable absorbers of power from a microwave transmission line, typically microstrip. Experiments performed with epitaxial YIG show that instantaneous bandwidths of 900 MHz with threshold levels of less than 0 dBm can be obtained below 4.2 GHz. Enhancement of greater than 20 dB can be achieved for an increase in power level of 20 dB above threshold. Characteristics obtained with lithium ferrite in the 4-8 GHz band are comparable to those obtained with YIG in the 2-4 GHz range. Owing to the increased fmr and spin wave linewidth of the lithium ferrite, the threshold level is higher, + 6 dBm, and the frequency selectivity poorer than observed with YIG.

Spin-Wave Relaxation in the Field-Induced Paramagnetic Phase of the Antiferromagnet (C2H5NH3)2CuCl4

Parallel pumping experiment has been done in the field-induced paramagnetic phase of the antiferromagnet (C 2 H 5 NH 3 ) 2 CuCl 4 at a pumping frequency of 8.9 GHz. Temperature dependence of the spin-wave linewidth Δ H k at the Brillouin-zone-boundary is empirically described as Δ H k =0.1× T 2 Oe in the temperature range from 1.2 to 2.7 K. Wave number dependence of Δ H k is reported as well. Four-magnon relaxation process is appropriate to explain the experimental results.

Wave-vector dependence of spin-wave line-width in yttrium iron garnets

The wave-vector dependence of the spin-wave line-width in yttrium iron garnets has been studied for samples of grain diameter varying from 1·2µm to 12µm. An expression for the spin-wave line-width as a function of wave-vector and grain diameter has been obtained, which agrees satisfactorily with experiment.

Open die hot pressing of yttrium iron garnet

A relatively simple and more economical process of open die hot pressing has been employed in preparing high density yttrium iron garnet samples of fine grain size (∼ 1–2 μM). The samples have been investigated for the microstructure dependent spinwave line-width (ΔH k) and FMR line-width (ΔH). The values of ΔH k and ΔH are in fair agreement with the samples having the same grain size but prepared by the conventional hot pressing using refractory dies.

Anomalous subsidiary absorption in single-crystal YIG and evaluation of spin-wave linewidth

Measurements of the subsidiary absorption spin-wave instability threshold hcrit in high-quality single crystals of yttrium iron garnet reveal anomalous structure over a field interval extending several hundred Oe below the butterfly curve minimum at Hc. Such measurements have now been extended to cover the entire butterfly curve for sphere and plate samples. At the low-field end of the structure region, hcrit increases rapidly as the static field H is decreased to a ’’kink’’ field H′c. As H is reduced further, the increase in hcrit is much more gradual. The nature of the onset changes drastically at H′c, from a gradual increase to an abrupt jump in reflected power at threshold. Theoretical analysis of the data shows: (1) The instability at Hc is for spin waves with a polar angle ϑk of 22° rather than the 35° value often cited. (2) The field interval for the instability of zero wave number (k=0) modes is not confined to H≳Hc, but extends over a wide range down to H′c. (3) The kink at H′c corresponds to an abrupt transition to k≠0 spin waves at lower fields. These features are all due to the effect of the k dependence of ΔHk, the spin-wave linewidth, on hcrit. However, a steplike increase of ΔHk for k≠0 modes, rather than the linear dependence inferred from parallel pumping, is needed for a quantitative fit. This observation, while in partial agreement with the existing three-magnon confluence theory, shows the need for a refined calculation. The structure between Hc and H′c varies with sample shape and appears to be related to low-k magnetostatic mode excitations in the spin-wave spectrum.

Spin waves in static non-periodic magnetic structures

We have studied the propagation of spin waves in a number of static non-periodic magnetic structures. We have established that (1) a ferromagnetic spin wave can ride over a domain wall with little reflection if its wavelength is less than twice the thickness of the wall; (2) in a ferromagnet with a set of parallel but irregularly spaced domain walls the spin wave linewidth is determined by the product of the scattering strength of the walls and the degree of randomness of the wall spacings; and (3) spin waves of rather narrow linewidths can exist in continuously varying irregular spin structures.

Temperature dependence of the parallel-pump spin-wave instability in porous yttrium iron garnet

The parallel-pump spin-wave instability threshold has been measured at 8.88 GHz in porous polycrystalline YIG at temperatures ranging from 88 K to 368 K. Sample porosities ranged from <0.5% to 16.3%. The shapes of the low-temperature butterfly curves suggest that the previously inferred inverse wavenumber dependence of the spin-wave linewidth ΔHk may not be valid in porous YIG. The temperature dependences of the ΔHk are incongruous with those predicted by the various transit-time models of spin-wave relaxation. They are also markedly different from those reported for the off-resonance effective linewidth ΔHeff, which suggests that different mechanisms determine ΔHeff and ΔHk.

Spin-Wave Relaxation in K2CuF4

Spin-wave linewidth Δ H k in a quasi-two-dimensional ferromagnet K 2 CuF 4 has been studied by parallel pumping technique. Wave number dependence of Δ H k from k =0 up to the Brillouin-zone-boundary and temperature dependence of Δ H k ≃0 which is empirically described as Δ H k ≃0 =0.19× T 2.2 Oe at temperatures from 1.2 to 2.2 K are reported. Spin-wave linewidth largely depends on the direction of the static magnetic field applied along the c -plane, which is the easy plane.

The effect of ellipticity on the direction of spinwave rays

Parallel pumping high signal power microwave radiation is a powerful tool to detect spinwave instabilities, since it allows to infer intrinsic damping properties of ferrimagnets. Several experiments of the last years have shown that the spinwave linewidth <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\DeltaH_{k}</tex> does not always follow the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(H_{c}-H_{i})^{1/2}</tex> law for π/2 magnon scattering. This feature is attributed to the existence of a non zero <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\underline{z}</tex> -component of the spinwave propagation vector <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\underline{k}</tex> . Simple formulas, derived from the dispersion relation are presented in this paper, which evidence the dependence on the spinwave ellipticity <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\varepsilon(\vartheta_{k})</tex> of the propagation characteristics of the excited magnons. Also, in the case of three boson processes, the influence of ε on <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\DeltaH_{k}(H_{i})</tex> is briefly discussed in the light of the spinwave transit-time theory.

Influence of the spin-wave linewidth on the spin-wave propagation direction for parallel pumping in single crystal YIG

The peculiar secondary minimum in the parallel pump butterfly curve for [110] magnetized single crystal YIG, originally discovered by Sethares and coworkers, has been experimentally and theoretically investigated Data were obtained for an in-plane [110] magnetized

Operation of High Peak Power Differential Phase Shift Circulators at Direct Magnetic Fields Between Subsidiary and Main Resonances

Instability in high peak power ferrite devices is usually avoided by either widening the spinwave linewidth to move the onset of the subsidiary resonance above the specification of the device, or by using a value of magnetic field below that at which the peak in the subsidiary resonance occurs. A third way to prevent this instability altogether is by adjusting the direct field and material magnetization to prohibit the frequency relation between the microwave signal and the spinwaves. This approach leads to an exceptionally low loss device at both small and large signal levels. The paper describes the experimental development of an 8.5-9.6-GHz 1-MW differential phase shift circulator biased in this way with an insertion loss of less than 0.20 dB.

Spin waves in CsNiF3with an applied magnetic field

The spin wave dispersion in the planar 1D ferromagnet CsNiF3 has been measured by inelastic neutron scattering in an external field. The spin wave linewidths are found to decrease with increasing field and become resolution-limited for H>10 kG at 4.2K. At high fields, H>10 kG, both energies and intensities are found to follow linear spin wave theory. The analysis resolves a discrepancy between the anisotropy constants, A, derived earlier from spin-wave and susceptibility measurements, respectively. It turns out that a quantum correction is necessary in order to get consistent parameters. Two parameters namely the nearest-neighbour exchange, J/k=11.5+or-0.05K and A/k=8.9+or-0.2K, are needed to fully describe the system. The temperature dependence of the spin waves in an external field was also studied.

Interaction of Signals in Ferromagnetic Microwave Limiters

A weak secondary signal is partially absorbed in a ferromagnetic microwave limiter that is saturated by a strong primary signal; the absorption is greatest when the two signals are close in frequency. The width of this absorption is determined here, and is found to be proportional to the spin wave linewidth and to the square root of the excess power in the primary signal. The theory of this effect is presented and is found to agree well with experiment.

Critical spin dynamics in EuO

Mode-mode coupling equations have been solved for the decay rates of the hydrodynamic spin fluctuations in the vicinity of the critical point in EuO. Dipolar effects are included. With no adjustable parameters calculated values of the spin-wave linewidth and the paramagnetic spin diffusion constant are in reasonable agreement with available experimental data for vertical-bar 1 - T/T/subc/ vertical-bar approximately-greater-than 0.05. (AIP)

Scattering of spin waves by pores in ferrimagnetic materials

The differential cross section of the 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 $\frac{1}{k}$ 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. The present theory indicates that the spin-wave linewidth is a function of the number of pores and their radii. Agreement between the formula and the experimental results is good except in the region very near $k\ensuremath{\approx}0$.