Stripline ͑SL͒, vector network analyzer ͑VNA͒, and pulsed inductive microwave magnetometer ͑PIMM͒ techniques were used to measure the ferromagnetic resonance ͑FMR͒ linewidth for a series of Permalloy films with thicknesses of 50 and 100 nm. The SL-FMR measurements were made for fixed frequencies from 1.5 to 5.5 GHz. The VNA-FMR and PIMM measurements were made for fixed in-plane fields from 1.6 to 8 kA/ m ͑20-100 Oe͒. The results provide a confirmation, lacking until now, that the linewidths measured by these three methods are consistent and compatible. In the field format, the linewidths are a linear function of frequency, with a slope that corresponds to a nominal Landau-Lifshitz phenomenological damping parameter ␣ value of 0.007 and zero frequency intercepts in the 160-320 A / m ͑2-4 Oe͒ range. In the frequency format, the corresponding linewidth versus frequency response shows a weak upward curvature at the lowest measurement frequencies and a leveling off at high frequencies.
A detailed analysis of the two magnon scattering contribution to the microwave relaxation and ferromagnetic resonance linewidth in isotropic and anisotropic films and disks has been made. The analysis is based on the Sparks, Loudon, and Kittel (SLK) theory for the scattering of uniform mode magnons into degenerate spin wave states for isotropic spherical samples in the presence of magnetic inhomogeneities in the form of spherical voids or pores. The SLK theory has been extended to include: (i) thin film and thick film samples magnetized in an oblique out-of-plane direction; (ii) uniaxially anisotropic materials with either easy-axis or easy-plane anisotropy and an anisotropy axis perpendicular to the disk plane; (iii) a modified density of degenerate states to account for the nonzero relaxation rate of the scattered spin waves; and (iv) two limiting cases of the scattering interaction: (a) the original SLK case where the inhomogeneities are modeled as spherical voids and the coupling to the degenerate spin waves varies with the spin wave propagation direction and (b) an isotropic scattering model where the coupling is independent of the propagation direction. The formulation is valid for thick films for which the discrete nature of the spin wave modes may be neglected. The two magnon linewidth as a function of field orientation is calculated for three classes of material parameters corresponding to yttrium iron garnet and barium M-type and zinc Y-type hexagonal ferrites. The linewidth versus static field angle profiles show characteristic profiles which depend on the crystalline anisotropy, the sample dimensions, the nature of the scattering interaction, the inhomogeneity size, and the inhomogeneity volume fraction. These parameters, as well as the shape and evolution of the spin wave band as a function of the field angle under ferromagnetic resonance conditions, play critical roles in determining the linewidth versus angle profiles.
Dark soiitons of magnetostatic surface waves in magnetic films have been observed for the first time. The experiments were conducted at 5.19 GHz on 7.2 /im single-crystal yttrium iron garnet films. The dark soiitons were excited by 15 ns wide **off" pulses in a high power cw microwave signal applied to the film. The characteristic soliton narrowing effect in the output pulses was observed as the input power was increased above the 0.5-1 W threshold levels. The shape of the ''dark" pulse agrees with the |tanh| functional dependence predicted from theory. Direct measurements of the carrier signal showed a phase shift of close to 180° at the center of the dark soliton, also in agreement with theory.PACS numbers: 75.30.Ds, 76.50.+g, 85.70.Ge Envelope soiitons are nonlinear wave packets which preserve their shape without dispersive spreading. In recent years, soliton excitations have been realized in many physical systems [1-3]. One well-known example is the optical-envelope soliton in optical fiibers [4,5]. Envelope soiitons for spin waves at microwave frequencies have been observed in yttrium iron garnet (YIG) thin films for various magnetic field and propagation combinations, including forward-volume wave [6,7], surface wave [8], and backward-volume wave [9] configurations.The envelope of nonlinear spin wave packets propagating in ferromagnetic thin films has been found to be best described by the nonlinear Schrodinger (NLS) equation [10,11]. It is well known that the NLS equation has two different types of solutions which correspond to bright and dark soiitons, depending on the relative signs of the dispersion coeflficient and the nonlinearity coeflficient in the equation [12,13]. Bright soliton solutions exist when the product of these two coefficients is negative, while dark soliton solutions exist when the product is positive. All of the magnetic experiments to date have been for bright soiitons, that is, for normal propagating wave packets.This Letter reports the first observation of microwave magnetic-envelope dark soiitons and the first experimental verification of the 180° phase shift in the carrier signal at the center of the pulse for any category of NLS dark soliton. The experiments were done at 5.19 GHz on in-plane magnetized single-crystal YIG films. Both the output signal envelope and the actual carrier signal output were measured. For input power levels above a certain threshold in the range of 0.5-1 W, the output signal pulses showed a narrowing which is characteristic of dark soiitons and the carrier showed at 180° phase shift over the central minimum region, also characteristic of dark soiitons. These results are in quantitative agreement with the theoretical dark soliton solutions for the NLS equation [13].The propagating spin waves were excited in the magnetic thin film by applying cw microwave power to a magnetostatic wave (MSW) delay line structure using a microstrip transducer [14]. The width of the dark pulse was controlled by chopping the cw signal with a fast microwave switch. The cw si...
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