Two-magnon Scattering Research Articles

A comprehensive study of ferromagnetic resonance and structural properties of iron-rich nickel ferrite (NixFe3−xO4, x≤1) films grown by chemical vapor deposition

We report a detailed study of the structural and ferromagnetic resonance properties of spinel nickel ferrite (NFO) films, grown on (100)-oriented cubic MgAl2O4 substrates by direct liquid injection chemical vapor deposition (DLI-CVD) technique. Three different compositions of NFO films (NixFe3−xO4 where x=1, 0.8, 0.6) deposited at optimized growth temperature of 600°C are characterized using X-Ray Diffraction (XRD), Scanning Electron Microscopy (SEM), Vibrating Sample Magnetometry (VSM), and broadband ferromagnetic resonance (FMR) techniques. XRD confirms the growth of epitaxial, single crystalline NixFe3−xO4 films. The out-of-plane lattice constant (c) obtained for Ni0.8Fe2.2O4 film is slightly higher than the bulk value (0.833nm), indicating only partial strain relaxation whereas for the other two compositions (x=1 and x=0.6) films exhibit complete relaxation. The in-plane and out-of-plane FMR linewidths measurements at 10GHz give the lowest values of 458Oe and 98Oe, respectively, for Ni0.8Fe2.2O4 film as compared to the other two compositions. A comprehensive frequency (5–40GHz) and temperature (10–300K) dependent FMR study of the Ni0.8Fe2.2O4 sample for both in-lane and out-of-plane configurations reveals two magnon scattering (TMS) as the dominant in-plane relaxation mechanism. It is observed that the TMS contribution to the FMR linewidth scales with the saturation magnetization Ms. In-plane angle-dependent FMR measurements performed on the same sample show that the ferromagnetic resonance field (Hres) and the FMR linewidth (ΔH) have a four-fold symmetry that is consistent with the crystal symmetry of the spinel. SEM measurements show formation of pyramid-like microstructures at the surface of the Ni0.8Fe2.2O4 sample, which can explain the observed four-fold symmetry of the FMR linewidth.

Broad-Band FMR Linewidth of Co2MnSi Thin Films with Low Damping Factor: The Role of Two-Magnon Scattering**Supported by the National Basic Research Program of China under Grant No 2015CB921502, the National Natural Science Foundation of China under Grant Nos 11474184 and 11174183, the Program for New Century Excellent Talents of China under Grant No NCET-10-0541, the Scientific Research Foundation for Returned

The low Gilbert damping factor, which is usually measured by ferromagnetic resonance, is crucial in spintronic applications. Two-magnon scattering occurs when the orthogonality of the ferromagnetic resonance mode and other degenerate spin wave modes was broken by magnetic anisotropy, voids, second phase, surface defects, etc., which is important in analysis of ferromagnetic resonance linewidth. Direct fitting to linewidth with Gilbert damping is advisable only when the measured linewidth is a linear function of measuring frequency in a broad band measurement. We observe the nonlinear ferromagnetic resonance linewidth of Co2MnSi thin films with respect to measuring frequency in broad band measurement. Experimental data could be well fitted with the model including two-magnon scattering with no fixed parameters. The fitting results show that two-magnon scattering results in the nonlinear linewidth behavior, and the Gilbert damping factor is much smaller than reported ones, indicating that our Co2MnSi films are more suitable for the applications of spin transfer torque.

The contributions of intrinsic damping and two magnon scattering on the ferromagnetic resonance linewidth in [Fe65Co35/SiO2]n multilayer films

In order to investigate microwave damping mechanisms of ferromagnetic films with a structure of [ferromagnetic (FM)/non-magnetic insulator (NMI)]n, a serial of [Fe65Co35/SiO2]n multilayer films was prepared by a magnetron sputtering method on the glass substrate. As-prepared films show excellent soft magnetic properties with tiny coercivities along the easy and hard axis respectively, and remarkable in-plane unixial anisotropies were observed too. The microwave properties were characterized by the ferromagnetic resonance (FMR) and a broadband permeameter. The corresponding theoretical fitting was conducted based on the Landau–Lifshitz–Gilbert (LLG) and two magnon scattering (TMS) theory. Fitting results show the TMS linewidth has a value of 36 times bigger than Landau–Lifshitz intrinsic linewidth, which gives a quantitative and explicit physical picture of microwave damping mechanisms in [Fe65Co35/SiO2]n multilayer films and may be important for the understanding of damping in [FM/NMI]n multilayer films.

Ferromagnetic resonance linewidth mechanisms in polycrystalline ferrites: Role of grain-to-grain and grain-boundary two-magnon scattering processes

The frequency dependence of the ferromagnetic resonance linewidth $\ensuremath{\Delta}H$ in polycrystalline hot isostatically pressed pure and Ca-Ge substituted yttrium iron garnet (YIG) spheres was measured between 1.95 and 6 GHz and analyzed. The linewidths for these ultradense ferrite materials are in the 5--40 and 5--25 Oe ranges for the pure and the substituted YIG samples, respectively. The $\ensuremath{\Delta}H$ vs frequency data show especially sharp Buffler peaks due to the band-edge crossover effect that is the signature for grain-to-grain (GG) two-magnon scattering (TMS) [C. R. Buffler, J. Appl. Phys. 30, S172 (1959)]. Both the GG and recent grain-boundary (GB) TMS models were used to obtain quantitative fits to the data. The fits demonstrate the expected GG TMS contribution to the linewidth for frequencies above the Buffler peak. They also reveal two unexpected results: (1) a dominant GB TMS role for frequencies below the Buffler peak where the GG TMS linewidth contribution is essentially zero and (2) a significant GB TMS role for frequencies above the peak where the linewidth has generally been associated with GG processes only. In the high-frequency regime, the GB scattering term appears to explain about half of the overall linewidth.

Microwave damping in polycrystalline Fe-Ti-N films: Physical mechanisms and correlations with composition and structure

Ferromagnetic resonance (FMR) derivative linewidths were measured from $3\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}12\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ on $50\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ thick sputtered polycrystalline Fe-Ti-N films with $3\phantom{\rule{0.3em}{0ex}}\mathrm{at.}\phantom{\rule{0.2em}{0ex}}%$ titanium and a nitrogen content $({x}_{N})$ from $1.9\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}12.7\phantom{\rule{0.3em}{0ex}}\mathrm{at.}\phantom{\rule{0.2em}{0ex}}%$. The measurements were made with both stripline and waveguide FMR spectrometers. Linewidths were generally lowest at ${x}_{N}=7\phantom{\rule{0.3em}{0ex}}\mathrm{at.}\phantom{\rule{0.2em}{0ex}}%$, with derivative linewidth $(\ensuremath{\Delta}H)$ values in the $15--25\phantom{\rule{0.3em}{0ex}}\mathrm{Oe}$ range and a nominally linear increase with frequency $(f)$. This minimum linewidth composition is connected with the bcc to bct structural transition in the Fe-Ti-N system. Linewidths increased at both larger and smaller ${x}_{N}$ values and were accompanied by the development of a more rounded frequency profile that is indicative of two-magnon scattering. All of the $\ensuremath{\Delta}H$ vs $f$ data could be fitted successfully with a constant inhomogeneity broadening linewidth of $8--11\phantom{\rule{0.3em}{0ex}}\mathrm{Oe}$, a two-magnon scattering (TMS) linewidth from the random grain-to-grain fluctuations in the effective anisotropy field directions for the polycrystal, and a magnon-electron (m-e) intrinsic relaxation term modeled through Gilbert damping with a single $\ensuremath{\alpha}$ value of 0.003. The actual fits were done through the convolution of a Gaussian linewidth for the inhomogeneity term and a Lorentzian linewidth for the TMS and m-e terms. The fitted anisotropy field parameters from the TMS analysis ranged between 398 and $883\phantom{\rule{0.3em}{0ex}}\mathrm{Oe}$, with the minimum also at the bcc to bct structural transition at ${x}_{N}=7\phantom{\rule{0.3em}{0ex}}\mathrm{at.}\phantom{\rule{0.2em}{0ex}}%$.

Time Resolved Magnetization Dynamics of Ultrathin Fe(001) Films: Spin-Pumping and Two-Magnon Scattering

The time-resolved magnetic response of ultrathin epitaxial Fe(001) films grown on GaAs(001) and covered by Au, Pd, and Cr capping layers was investigated by time and spatially resolved Kerr effect measurements. The magnetization was excited by an in-plane magnetic field pulse using the transient internal field generated at a Schottky barrier while the wavelength of the excitation (resonant mode) was roughly 4 microm. Each of the three cap layers affected the spin relaxation in a unique way. Au cap layers resulted in the bulk Gilbert damping of the Fe film. Pd cap layers caused an additional Gilbert damping due to spin-pump or spin-sink effects. Cr cap layers lead to a strong extrinsic damping which can be described by two-magnon scattering. In this case the strength of the extrinsic damping can be controlled by a field induced shift of the spin wave manifold with respect to the excited k vector.

Two-Magnon Scattering Amplitudes for a Pit of Arbitrary Shape in a Ferromagnet

The calculation by Sparks, Loudon, and Kittel of the amplitudes $F(\mathrm{k})$ in the two-magnon scattering $\mathcal{H}=\ensuremath{\Sigma}[F(\mathrm{k}){b}_{\mathrm{k}}{{b}_{0}}^{\ifmmode\dagger\else\textdagger\fi{}}+\mathrm{H}.\mathrm{c}.]$ induced by a spherical pit in an infinite ferromagnetic crystal is extended to pits of arbitrary shape. By expressing the energy in terms of the interaction of magnetostatic charges, two terms of different types are identified. One, which is linear in pit distribution, is solved exactly and explicitly for any collection of pits of arbitrary shape and size. The second, which is nonlinear in pit distribution, is solved explicitly only for a general ellipsoidal pit. The approach presented here can also be used to solve the problem of scattering from modes other than the uniform precession.

Two-Magnon Scattering of Neutrons

We report the experimental observation of the inelastic scattering of slow neutrons by two-magnon processes and present theoretical calculations which account for the shape and wave-vector dependence of the spectrum.

Two-Magnon Scattering Amplitudes for Pits of Arbitrary Shape

The quantum mechanical technique of Sparks, Loudon, and Kittel for determining the two-magnon scattering amplitudes F(k, k′) in H = ΣF (k, k′) bk+bk′ induced by a spherical pit in an infinite crystal, is extended to pits of arbitrary shape. By expressing the energy in terms of a charge-charge interaction rather than as a field-moment interaction, the selection of relevant terms and the inherent symmetries are much clearer. Two terms which are linear in pit distribution can be solved exactly and explicitly for any collection of pits of arbitrary shapes and sizes. For scattering from the uniform precession the result is F(0,k)=(2πMγℏ/V)[ ∫ VPexp(ik·r)dτ](3 cos2θk−1),and reduces to the Sparks et al. result for a single sphere. The integral has a simple interpretation in terms of Huygens wavelets from each missing spin which interfere according to the phase exp(ik·r). A third term which is not linear in pit distribution can be solved explicitly only for a general ellipsoidal pit. It reduces to a constant addition of between −2 and +1 to the 3 cos2Θk−1 factor. For a spherical pit it vanishes. An explicit solution for scattering from modes other than the uniform precession can also be obtained.