Standing Spin Wave Resonances Research Articles

Spin current and spin waves at a platinum/yttrium iron garnet interface: impact of microwave power and temperature

The spectra of ferromagnetic resonance and spin current of the heterostructure consisting of an epitaxial film of yttrium iron garnet Y3Fe5O12 (YIG) grown on a gallium gadolinium garnet (Gd3Ga5O12) substrate and with 10 nm thick platinum (Pt) film on top were studied at frequencies f = 2–18 GHz under applied power in the range of 20 μW–50 mW as well as temperatures T = 77–300 K. The standing spin-wave resonances (SWRs) with both magnetostatic backward volume spin waves and magnetostatic surface spin waves (MSSWs) were detected. The SWR evolution was investigated with change of microwave power. Due to generation of spin current perpendicular to the Pt/YIG interface and the inverse spin Hall effect the charge current on the Pt film was registered and analyzed. The SWR resulted in deviations of spin current spectral lines from a Lorentz line form, indicating that at high microwave power the main contribution is made by MSSW. As the temperature decreases, the amplitude of the spin current decreases, although the width of the spectral line remains the same while the magnetization increases at lower temperatures. A decrease in spin Hall angle with cooling may explain this behavior of the spin current at low temperatures.

Thickness dependence of dynamic magnetic properties of soft (FeCo)-Si alloy thin films

${\mathrm{Fe}}_{69}{\mathrm{Co}}_{26}{\mathrm{Si}}_{5}$ alloy thin films of various thicknesses were deposited on MgO(100) single crystal substrates by magnetron sputtering at $230{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$ substrate temperature. The thickness dependence of the dynamic magnetic properties was investigated using broadband ferromagnetic resonance (FMR). The x-ray diffraction results indicate that all films are of the bcc structure with an in-plane epitaxial alignment of ${[100]}_{\mathrm{FeCoSi}}//{[110]}_{\mathrm{MgO}}$. The exchange constant was determined from the field shift between the uniform precession FMR mode and the first order perpendicular standing spin wave resonance mode in the FMR spectra. The effective damping parameter decreases dramatically with increasing film thickness up to 16 nm due to the decrease of the spin pumping contribution and then remains relatively constant as the film thickness increases. In-plane angle dependent FMR measurements reveal that the in-plane anisotropy of these films is dominated by a fourfold magnetic anisotropy, which increases sharply with increasing film thickness up to 16 nm and then shows a slightly decreasing trend as the film thickness increases. In-plane angular dependence of the FMR linewidth shows a strong two-magnon scattering contribution.

Wave-Number-Dependent Gilbert Damping in Metallic Ferromagnets.

A wave-number-dependent dissipative term to magnetization dynamics, mirroring the conservative term associated with exchange, has been proposed recently for ferromagnetic metals. We present measurements of wave-number-(k-)dependent Gilbert damping in three metallic ferromagnets, NiFe, Co, and CoFeB, using perpendicular spin wave resonance up to 26GHz. In the thinnest films accessible, where classical eddy-current damping is negligible, size effects of Gilbert damping for the lowest and first excited modes support the existence of a k^{2} term. The new term is clearly separable from interfacial damping typically attributed to spin pumping. Higher-order modes in thicker films do not show evidence of enhanced damping, attributed to a complicating role of conductivity and inhomogeneous broadening. Our extracted magnitude of the k^{2} term, Δα_{kE}^{*}=Δα_{0}^{*}+A_{k}^{*}k^{2}, where A_{k}^{*}=0.08-0.1 nm^{2} in the three materials, is an order of magnitude lower than that identified in prior experiments on patterned elements.

Interferometric properties of standing spin waves and the application to a phase comparator

We numerically studied the material and structural parameter dependence of interferometric properties of the standing spin wave resonance (SSWR) by micromagnetic simulations and demonstrate the feasibility of practical application to an integrated phase comparator. The micromagnetic configuration of the synthesized SSWR emitted from the two microwave currents flowing through the parallel strip lines depends on the phase difference Δϕ between them. Resultantly, the Δϕ is converted to the related output voltage with an overlaid phase detector, inductively coupled to the magnetic strip. Among the investigated various material systems, low damping (α ∼ 0.001) metallic ferromagnets are found to exhibit superior device performance due to the reduced viscous dissipation.

Standing spin-wave mode structure and linewidth in partially disordered hexagonal arrays of perpendicularly magnetized sub-micron Permalloy discs

Standing spin wave mode frequencies and linewidths in partially disordered perpendicular magnetized arrays of sub-micron Permalloy discs are measured using broadband ferromagnetic resonance and compared to analytical results from a single, isolated disc. The measured mode structure qualitatively reproduces the structure expected from the theory. Fitted demagnetizing parameters decrease with increasing array disorder. The frequency difference between the first and second radial modes is found to be higher in the measured array systems than predicted by theory for an isolated disc. The relative frequencies between successive spin wave modes are unaffected by reduction of the long-range ordering of discs in the array. An increase in standing spin wave resonance linewidth at low applied magnetic fields is observed and grows more severe with increased array disorder.

Waveguide-based ferromagnetic resonance measurements of metallic ferromagnetic films in transmission and reflection

In this work, we have studied the ferromagnetic and standing spin wave resonance response of in-plane magnetized exchange-coupled bi-layer ferromagnetic metallic films placed in a section of a rectangular waveguide. The measurements have been performed in transmission and reflection of electromagnetic waves in the 8–12 GHz frequency range. The 30 to 70 nm-thick Co-permalloy films on silicon substrates tightly fitted the cross-section of the waveguide. It was found that the responses of the films in transmission and reflection were very different. In transmission, the response of the fundamental mode dominates, but in reflection, the first (anti-symmetric) standing spin wave mode demonstrates the largest variation in amplitude with respect to the off-resonance regime. The results we obtain are in agreement with recently developed theory which demonstrates the high relevance of strong microwave screening (or shielding) by eddy currents in the film for the formation of the observed response.

Transmission of microwaves through exchange-coupled bi-layer magnetic films in ferromagnetic and standing spin wave resonances

In this work, we have studied theoretically the transmission and reflection of electromagnetic waves in the microwave frequency range through the in-plane magnetized exchange-coupled bi-layer ferromagnetic metallic films. It was found that responses of the films in transmission and reflection are very different. In transmission, the response of the fundamental mode dominates, but in reflection, the first exchange mode demonstrates the largest variation in amplitude with respect to the off-resonance regime. The theory also predicts an interesting regime of low-loss transmission associated with the resonance excitation of the first (anti-symmetric) exchange standing spin wave mode. In this regime, the transmission through the sample increases instead of decreasing for this mode.

Ferromagnetic resonance in submicron amorphous wires

Ferromagnetic resonance in glass-coated amorphous wires with the diameter of metallic core varying from 25 μm to 133 nm is investigated. The microwave frequencies of 49.1 and 69.7 GHz are used and static magnetic field is applied either parallel or perpendicular to the long wire axis. In agreement with theoretical predictions the resonance curves of submicron wires substantially differ from the curves of the bulk wires. Depending on the symmetry and intensity of microwave electric and magnetic fields in the sample vicinity the circumferential and/or dipolar resonance modes can be excited. In bulk wires the resonance fields of the two modes coincide. In submicron wires, however, their resonance fields differ, indicating the metallic character of the circumferential mode and the insulator character of the dipolar mode. In wires with diameters 717 and 869 nm radial standing spin wave resonances are observed in parallel field configuration. The experimental results for the parallel field configuration can be well explained by the rigorous theoretical model. From the fit of experimental data the exchange stiffness constant A = 8.2 10−12 J/m and perpendicular surface anisotropy constant Ks = 6 × 10−4 J/m2 are obtained. The resonance curves measured in the transversal field configuration can be well explained in the frame of the skin effect and quasistatic approximations for the bulk and submicron wires, respectively. In submicron wires, however, an additional resonance of unknown origin is observed at higher magnetic fields.

Ferromagnetic Resonance Investigation of Macroscopic Arrays of Magnetic Nanoelements Fabricated Using Polysterene Nanosphere Lithographic Mask Technique

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A dense plane periodical array of cylindrical magnetic nanodots has been fabricated using a lithographic mask formed by self-organization of polystyrene nanospheres. In this paper, we study collective static and dynamic magnetic behavior of this array. We find that this technique produces samples with reasonably small dispersion of magnetic parameters of individual dots. This is evidenced by magnetometry and well-resolved discrete frequencies of standing spin waves measured with cavity and coplanar-waveguide ferromagnetic resonance. The standing spin wave resonances could be reliably observed in a large range of frequencies (4–15 GHz). However the measured linewidth of resonances is about ten times larger than for unpatterned Permalloy. This may be due to some variation in shape and magnetic parameters from dot to dot resulting in inhomogeneous broadening of the resonance lines. </para>

Theory of spin waves in ultrathin ferromagnetic films: The case of Co on Cu(100)

We present theoretical studies of the nature of spin waves in ultrathin ferromagnetic Co films deposited on the Cu(100) surface. Motivation for the calculations are the recent experimental SPEELS data reported by Vollmer et al. Our calculations employ a realistic electronic structure for both the Co film and the semi-infinite Cu substrate, modeled through use of an empirical tight binding model with ferromagnetism in the Co film driven by intra-atomic Coulomb interactions within the Co $3d$ shell. Mean field theory describes the ground state, and we use the Random Phase Approximation to generate spin wave spectra. We obtain an excellent quantitative account of the value of the exchange stiffness reported in previous Brillouin lights scattering studies of epitaxially deposited Co films on Cu(100). As in the SPEELS experiment, we find a single very broad feature dominates the spin wave spectral density throughout much of the surface Brillouin zone, in contrast to the sequence of sharp standing spin wave resonances which result from generation of spin wave spectra via adiabatic approaches. Landau damping absent from such treatments influence the calculated spectra qualitatively, as in our earlier theoretical studies of related systems. It is the case, however, that the spin waves reported in the SPEELS experiments are very considerably softer than those generated by our theory.

Ferromagnetic resonance study on magnetic homogeneity in spin-sprayed NiZn ferrite films highly permeable at gigahertz frequencies

Ferromagnetic resonance (FMR), including standing spin-wave resonance (SWR) modes, were measured in NiZn ferrite films, which have high permeability even up to the gigahertz range. They were prepared from an aqueous solution by spin spray ferrite plating at 90/spl deg/C. The perpendicular field FMR spectra exhibited SWR modes whose line separation had linear dependence on spin wave number, deviating from the quadratic behavior. This indicated that the films have inhomogeneous distribution of magnetization perpendicular to film plane, and have different magnetic surface anisotropies between the inner and outer surfaces of the respective films. The in-plane field FMR spectra revealed no SWR mode. A possible model is proposed to explain the features not only of the FMR spectra, but also of the initial permeability spectra measured on the films.

Ferromagnetic resonance in epitaxial FePd thin films with perpendicular anisotropy

Ferromagnetic resonance (FMR) investigations on epitaxial partially ordered FePd thin films with a perpendicular magnetic anisotropy (PMA) are presented. The measurements have been performed over a wide frequency range (6–18 GHz) in the monodomain state. Besides the determination of magnetic parameters (anisotropy constants, gyromagnetic ratio), two main results emerge: (i) the occurrence of well-resolved perpendicular standing spin–wave resonances which depart from the n 2-law, (ii) the perpendicular uniform resonance linewidth was found to be independent of frequency over the (6–18 GHz) range. These results are discussed in terms of weak volume inhomogeneities (anisotropy, defects) induced by the film growth process.

Spin-wave resonance in high-conductivity films: The Fe-Co alloy system.

A detailed standing spin-wave resonance (SSWR) study in the frequency range 17-69 GHz in normal and parallel configurations is presented for ${\mathrm{Fe}}_{x}{\mathrm{Co}}_{1\ensuremath{-}x}$ alloy films. The implications of the use of different approximate theoretical descriptions for the line positions, widths, and intensities are investigated and compared to the complete theory which includes the coupling of the spin waves to electromagnetic waves by means of the high conductivity of the material. For $x=0.55$, the exchange parameter $A$ is determined to be 2.7 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}6}$ erg/cm, i.e., significantly higher than for pure Fe (2.0 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}6}$ erg/cm). In contrast, the $g$ factor and the damping constant $\ensuremath{\lambda}$ are almost the same for $x=0.55 \mathrm{and} 1$. The problem of interpretation of the surface anisotropy parameter ${K}_{s}$ obtained by different experimental methods on different film thicknesses is discussed.

Surface impedance of SSWR in thin metallic films for parallel configuration

AbstractSSWR (standing spin‐wave resonance) spectra for parallel configuration were calculated analytically for the case of metallic thin films, including surface anisotropy (of equal value at both surfaces). Landau‐Lifshits damping, and electrical conductivity effects. The analytical formulae for the surface impedance and for the microwave magnetic fields propagating in the film are derived, symmetrical and antisymmetrical cases of spin‐wave mode excitation are treated following Wolf's method.

Standing spin wave resonances in manganite films

We present first measurements of the spin wave stiffness in the giant magnetoresistance material La 0.67Ba 0.33MnO 3 by observation of standing spin wave resonances in about 100 nm thick films.

Ferromagnetic resonance investigations of spin waves in Fe-Ni multilayers

The standing spin-wave resonance (SSWR) at 9.2 GHz has been investigated in a multilayer structure composed of alternating layers of Ni and Fe for the as-prepared sample and at different annealing temperatures between 420 and 570 K. Changes of the resonance field and of the intensity of spin-wave modes with annealing temperature indicate the excitation of a surface mode in the as-prepared sample. Heating of the multilayer above 520 K leads to a spin-wave spectrum which exhibits a behavior corresponding to an alloy with comparable chemical composition. The SSWR fields show a quadratic dependence of the wave number of the spin waves at all annealing temperatures but a drastic change of surface spin pinning with increasing temperature.

Analysis of the boundary problem of SSWR in asymmetric isotropic insulator films

The influence of various combinations of the uniaxial surface anisotropy constantsKs1 andKs2 on the angular dependence of the standing spin-wave resonance (SSWR) spectrum is studied for an isotropic insulator film with asymmetrically pinned spins. It is shown that the (Ks1,Ks2)-plane can be divided into zones in which the angular dependence of the SSWR spectrum has different characteristic features. These features are studied in detail.

Angular Dependence of Spin‐Wave Resonance in Thin Films with Asymmetrical Boundary Conditions. Analytical Treatment

AbstractThe boundary problem is solved for an isotropic homogeneous infinite insulator film with spins pinned asymmetrically by a uniaxial surface anisotropy. An arbitrarily oriented external magnetic field is assumed. Formally a simple condition for the values of the resonant wave‐vector k1 is obtained. The analytical expressions for the standing spin‐wave resonance (SSWR) mode linewidths and intensities are derived and discussed. The second part of the paper is devoted to the SSWR in thin metallic films with thicknesses 2d ≪ δ (the skin depth). The influence of conductivity on the mode positions, linewidths, and intensities is investigated analytically with the help of the spin‐wave approximation.

Magnetostatic forward volume wave - spin wave conversion by etched gratings in LPE-YIG

Experiments in the 3 GHz region are reported normal incidence of magnetostatic forward volume waves (MSFVW) on etched groove arrays. Significant mode conversion to standing spin wave resonances (SSWR) along the axis normal to the films has been observed and correlated to the SSWR spectrum. A criterion is derived which allows design of etched groove arrays with optimum bandwidth including the effects of the SSWR mode conversion. Suitable pass-band characteristics can be achieved by choice of etch groove depth.

Temperature dependence of standing spin wave resonance in ferromagnetic thin films

Temperature dependence of standing spin wave resonance in ferromagnetic thin films