Surface Spin-wave Modes Research Articles

Out-of-plane Ferromagnetic Resonance and Surface Spin Wave Modes in Ni80Fe20 Film on Ripple-Patterned Sapphire Substrate

The study of surface magnetic anisotropy of magnetic films is beneficial to understanding the behaviors of films at high frequencies and further promoting their high-frequency magnetic applications. We investigated the out-of-plane ferromagnetic resonance (FMR) and surface spin wave modes in 40-nm Ni80Fe20 (NiFe) films deposited on ripple-patterned sapphire substrate with periodicity and a flat sapphire substrate by broad-band FMR technique. When measuring the FMR of the film on ripple-patterned substrate, the in-plane angle (\U0001d711 H of the external applied magnetic field was along the direction of the ripples (\U0001d711 H = 90°) and perpendicular to the ripple direction (\U0001d711 H = 0°) respectively. The spin-wave resonance spectra consisting of up to two surface spin wave (SSW) modes were observed as the external magnetic field polar angle θH varied from “in-plane configuration” (θH = 90° ) to “out-of-plane configuration” (θH = 0°). As the decrease of θH , the two surface spin excitations disappeared in sequence and further only FMR mode was observed in the region θH which was smaller than the “critical angle” θc . The θc of \U0001d711 H = 90° is found to be different from that for \U0001d711 H = 0°. The dependences of field shift vs. out-of-plane angles θH for each SSW mode were analyzed by the surface inhomogeneity model. From the model, the surface anisotropy constants Ks of films were obtained. The results show that the values of surface anisotropy constants for the two SSW modes are different. Compared with the film sputtered on flat sapphire substrate, after introducing ripple-patterned substrate, the variation of Ks is only on the order of 0.01 erg/cm2 for the film of this thickness.

Imaging of caustic-like spin wave beams using optical heterodyne detection

We investigated caustic-like spin wave beams radiated from a narrow waveguide to a continuous film using a Permalloy. For this purpose, we developed a spatially resolved optical heterodyne detection of propagating spin waves by using the polar Kerr effect, which allows the measurement of the intensity and the phase information of the spin waves. We characterized magnetostatic surface spin wave modes in one-dimensional (1D) propagation and caustic-like spin wave beams in two-dimensional (2D) propagation as a function of excitation frequency. The fast Fourier transformations of the real space images reconstruct 1D and 2D spin wave dispersion, which agree with the theoretical calculations.

Surface anisotropy and spin wave resonance in submicron amorphous wires

Abstract The influence of surface magnetic anisotropy on ferromagnetic resonance (FMR) in submicron wires is investigated both theoretically and experimentally. An analytical formula for resonance fields of radial spin waves in a long axially magnetized circular cylinder is obtained. Three types of surface anisotropy with the easy direction along one of the cylindrical coordinates are considered. For sufficiently strong surface anisotropy with hard direction parallel to the cylinder axis the surface spin wave mode is observed. The theoretical results are verified by FMR measurements at six microwave frequencies from 9 to 69 GHz on glass-covered amorphous FeCrSiB wires with diameters from 541 to 1032 nm. From the bulk spin wave resonances the exchange stiffness constant about 6.5 10−7 erg/cm is obtained. The frequency dependence of the surface mode resonance field indicates that a perpendicular surface anisotropy with anisotropy constant Ks = 6.2 erg/cm2 is present at the metal/glass interface.

Control of Spin-Wave Propagation using Magnetisation Gradients

We report that in an in-plane magnetised magnetic film the in-plane direction of a propagating spin wave can be changed by up to 90 degrees using an externally induced magnetic gradient field. We have achieved this result using a reconfigurable, laser-induced magnetisation gradient created in a conversion area, in which the backward volume and surface spin-wave modes coexist at the same frequency. Shape and orientation of the gradient control the conversion efficiency. Experimental data and numerical calculations agree very well. Our findings open the way to magnonic circuits with in-plane steering of the spin-wave modes.

Theory of spin and lattice wave dynamics excited by focused laser pulses

We develop a theory of spin wave dynamics excited by ultrafast focused laser pulses in a magnetic film. We take into account both the volume and surface spin wave modes in the presence of applied, dipolar and magnetic anisotropy fields and include the dependence on laser spot exposure size and magnetic damping. We show that the sound waves generated by local heating by an ultrafast focused laser pulse can excite a wide spectrum of spin waves (on top of a dominant magnon–phonon contribution). Good agreement with recent experiments supports the validity of the model.

Magnonic band structure in a Co/Pd stripe domain system investigated by Brillouin light scattering and micromagnetic simulations

By combining Brillouin light scattering and micromagnetic simulations, we studied the spin-wave (SW) dynamics of a Co/Pd thin film multilayer, which features a stripe domain structure at remanence. The periodic up and down domains are separated by corkscrew type domain walls. The existence of these domains causes a scattering of the otherwise bulk and surface SW modes, which form mode families, similar to a one-dimensional magnonic crystal. The dispersion relation and mode profiles of SWs are measured for the transferred wave vector parallel and perpendicular to the domain axis.

Magnetization dynamics in magnonic structures with different geometries: interfaces, notches and waveguides

The discovery of ultrafast magnetization dynamics 20 years ago has led to a broad variety of experimental techniques to explore phenomena in magnetic materials with high temporal resolution. In the current article we present a study dealing with broadband excitation of spin-wave packets at different magnonic crystal continuous magnetic film interfaces. Similar to protected conducting states on the surfaces of topological band insulators, these interfaces exhibit surface spin-wave modes that propagate out of the crystal into the continuous film. The propagation distance depends on the direction of the applied magnetic field as well as the surface geometry of the crystal.

Theoretical methods for understanding advanced magnetic materials: The case of frustrated thin films

Materials science has been intensively developed during the last 30 years. This is due, on the one hand, to an increasing demand of new materials for new applications and, on the other hand, to technological progress which allows for the synthesis of materials of desired characteristics and to investigate their properties with sophisticated experimental apparatus. Among these advanced materials, magnetic materials at nanometric scale such as ultra thin films or ultra fine aggregates are no doubt among the most important for electronic devices.In this review, we show advanced theoretical methods and solved examples that help understand microscopic mechanisms leading to experimental observations in magnetic thin films. Attention is paid to the case of magnetically frustrated systems in which two or more magnetic interactions are present and competing. The interplay between spin frustration and surface effects is the origin of spectacular phenomena which often occur at boundaries of phases with different symmetries: reentrance, disorder lines, coexistence of order and disorder at equilibrium. These phenomena are shown and explained using of some exact methods, the Green's function and Monte Carlo simulation. We show in particular how to calculate surface spin-wave modes, surface magnetization, surface reorientation transition and spin transport.

On the Existence Conditions of Surface Spin Wave Modes in (Ga,Mn)As Thin Films

Spin-wave resonance is a newly emerged method for studying surface magnetic anisotropy and surface spinwave modes in (Ga,Mn)As thin films. The existence of surface spin-wave modes in (Ga,Mn)As thin films has recently been reported in the literature; surface spin-wave modes have been observed in the in-plane configuration (with variable azimuth angle φM between the in-plane magnetization of the film and the surface [100] crystal axis), in the azimuth angle range between two in-plane critical angles φc1 and φc2. We show here that cubic surface anisotropy is an essential factor determining the existence conditions of the above-mentioned surface spin-wave modes: conditions favorable for the occurrence of surface spin-wave modes in a (Ga,Mn)As thin film in the inplane configuration are fulfilled for those azimuth orientations of the magnetization of the sample that lie around the hard axes of cubic magnetic anisotropy. This implies that a hard cubic anisotropy axis can be regarded in (Ga,Mn)As thin films as an easy axis for surface spin pinning.

Interface Magnetic Properties in Piezoelectric/Ferromagnetic AlN/FeNi Heterostructures

The spin wave resonance technique was utilized to investigate the interface magnetic properties in AlN/FeNi heterostructures. Obtained surface spin wave (SSW) mode becomes the uniform mode at a critical angle as applied field rotating to the normal direction. Beyond this angle SSW transforms into the uniform mode and the higher-order spin wave modes are also shown. The surface anisotropy caused by the interface pinning between AlN and FeNi resulted in an additional in-plane biaxial anisotropy, which was confirmed by the in-plane angular dependence of remanence measurement. The observed four-fold anisotropy may have potential application in magnetoelectric coupling based information devices.

Ferrimagnetic resonance and magnetoelastic excitations in magnetoelectric hexaferrites

Static field properties of magnetoelectric hexaferrites have been explored extensively in the past five years. In this paper, dynamic properties of magnetoelectric hexaferrites are being explored. In particular, effects of the linear magnetoelectric coupling $(\ensuremath{\alpha})$ on ferrimagnetic resonance (FMR) and magnetoelastic excitations are being investigated. A magnetoelastic free energy which includes Landau-Lifshitz mathematical description of a spin spiral configuration is proposed to calculate FMR and magnetoelastic excitations in magnetoelectric hexaferrites. It is predicted that the ordinary uniform precession FMR mode contains resonance frequency shifts that are proportional to magnetoelectric static and dynamic fields. The calculated FMR fields are in agreement with experiments. Furthermore, it is predicted at low frequencies (approximately megahertz ranges), near zero magnetic field FMR frequencies, there is an extra uniform precession FMR mode besides the ordinary FMR mode which can only be accounted by dynamic magnetoelectric fields. Whereas the FMR frequency shifts in the ordinary FMR mode due to the $\ensuremath{\alpha}$ coupling scale as $\ensuremath{\alpha}$, the shifts in the new discovered FMR mode scale as ${\ensuremath{\alpha}}^{2}$. Also, magnetoelastic dispersions were calculated, and it is predicted that the effect of the $\ensuremath{\alpha}$ coupling are the following: (1) The strength of admixture of modes and splitting in energy between spin waves and transverse acoustic waves is proportional to $\ensuremath{\alpha}$. (2) The degeneracy of the two transverse acoustic wave modes is lifted even for relatively low values of $\ensuremath{\alpha}$. Interestingly, at low frequencies near zero field FMR frequencies, the surface spin wave mode branch flip-flops with the volume spin wave branch whereby one branch assumes real values of the propagation constant and the other purely imaginary upon the application of a static electric field.

Spin pumping and the inverse spin-hall effect via magnetostatic surface spin-wave modes in Yttrium-Iron garnet/platinum bilayers

Spin pumping at a boundary between a yttriumiron garnet (YIG) film and a thin platinum (Pt) layer is studied under conditions in which a magnetostatic surface spin wave (MSSW, or DamonEshbach mode) is excited in YIG by a narrow strip-line antenna. It is shown that the voltage created by the inverse spin-Hall effect (ISHE) in Pt is strongly dependent on the wavevector of the excited MSSW. For YIG film thicknesses of 41 and 0.9m, the maximum ISHE voltage corresponds to the maximum of efficiently excited MSSW wavevectors and does not coincide with the maximum of absorbed microwave power. For a thinner (0.175m) YIG film, the maximum of the ISHE voltage moves closer to the ferromagnetic resonance and almost coincides with the region of the maximum microwave absorption. We show that the effect is related to the change in the thickness profile and the wavenumber spectrum of the excited MSSW taking place when the YIG film thickness is increased.

Surface modes with biquadratic coupling and uniaxial anisotropy in semi-infinite Heisenberg antiferromagnet

We address the role and the influence of both biquadratic exchange and uniaxial anisotropy in the study of bulk and surface magnetic excitations for a two-sublattices semi-infinite Heisenberg antiferromagnet. The calculations apply to combined effect and are based on a matching technique within the framework of both non-interacting spin-wave theory and random phase approximation. Emphasis has been laid upon the advantage of handling bulk and surface spin precessional fields, characterized by their symmetry in particular. Analytic expressions for the bulk and surface equations of motion are also derived which enables us to analyze qualitatively the nature of the modes by observing the response of the energy branches to the variation of both biquadratic exchange and single-ion anisotropy field as well as exchange parameters occurring on the surface. Two numerical applications of the theoretical formalism developed in this work are described. First concerns the situation when the free surface model is assumed. The second application considers the existence of surface perturbations and treats the effects of the presence of biquadratic exchange term on the bulk and surface spin-wave spectra showing two kinds of surface propagating modes which depend on the presence or not of the uniaxial anisotropy contribution and also on the variations of the bulk–surface exchange parameters. A significant conclusion which this work reached relates to the checking of the results obtained in the literature by using our own theoretical formalism. We show that this formalism is very well adapted to calculations of localized bulk and surface spin-wave modes associated with the simultaneous presence of biquadratic exchange and uniaxial anisotropy. Also, the results obtained for the bulk spin fluctuations field as well as for the magnetic surface waves, are found to be in qualitative agreement with those obtained in the literature. The analytic formulation presented in this work provides an accurate and practical scheme for calculating the surface spin dynamics under the influence of surface exchange parameters, biquadratic coupling and uniaxial anisotropy terms.

Dipolar surface pinning and spin-wave modes vs. lateral surface dimensions in thin films

In rod samples of circular cross-section (magnetized along rod’s axis) the character of spatial non-homogeneity of the demagnetization field strongly depends on the aspect ratio (the diameter to length ratio) of the rod. When the aspect ratio is large the sample can be regarded as a thin film of finite lateral dimensions. We show the spatial profile of the demagnetization field in a thin film evolves towards a nearly uniform distribution as the lateral dimensions of the film increase. Therefore, the Surface Inhomogeneity (SI) model, in which the value of surface anisotropy (responsible for surface dipole pinning) is assumed to depend on the lateral dimensions of the surface, can be used for description of magnetic excitations in thin films. Derived in this study, a formula for the dipolar surface anisotropy energy (including its dependence on the lateral dimensions) indicates the dipolar surface anisotropy is caused by interactions, which bind a surface dipole with all the dipoles in the adjacent subsurface layer. Summing up the energy contributions due to these interactions leads to a surprising result: the dipolar surface energy is found to grow as the surface lateral dimensions decrease and in the nanometer range of the aspect ratio this energy increases even by as much as an order of magnitude.

Ferromagnetic resonance studies of surface and bulk spin-wave modes in a CoFe∕PtMn∕CoFe multilayer film

We studied exchange-dominated surface and bulk spin-wave modes in a single period of CoFe∕PtMn∕CoFe trilayer film grown on a seed layer of Ru with CoFe film compositions being Co-16at.%Fe. The thickness of the ferromagnetic CoFe layers is ∼400Å and that of the antiferromagnetic layer is 120Å. Multimode spin-wave spectra were observed using the ferromagnetic resonance technique, as the sample plane was rotated with respect to the direction of the magnetic field. The effective magnetic anisotropy parameters and the g factor of the magnetic film were calculated from the field corresponding to the main (strongest) resonance peak at different angles. In addition, we identified a high-order standing spin wave in our spectra and found a “critical angle” in the multilayer sample. As H is significantly rotated away from the normal, there is a critical orientation where only a single acoustic spin-wave mode can be observed. We included an effective surface anisotropy field to describe our results. From the surface anisotropy, we are able to analyze the spin-wave resonance spectra in terms of the dynamic surface spin pinning. This allows us to determine the exchange interaction stiffness in the CoFe layers, J∼2.7meV.

Angular dependence of spin-wave resonances and surface spin pinning in ferromagnetic (Ga,Mn) As films

We present a study of exchange-dominated surface and bulk spin-wave modes in (Ga,Mn)As films grown by molecular beam epitaxy. Multimode spin-wave spectra were observed using the ferromagnetic resonance technique, as the direction of the magnetic field $\mathbf{H}$ was varied within the plane of the layer, as well as relative to the plane. The field corresponding to the main (strongest) resonance peak at each angle is used to calculate bulk magnetic anisotropy parameters and the $g$ factor of the magnetic films. The dependence of spin-wave (SW) modes on the orientation of $\mathbf{H}$ is analyzed in terms of two fundamental models: the surface inhomogeneity model and the volume inhomogeneity model. Typically, when $\mathbf{H}$ is normal or near normal to the sample plane (i.e., $\mathbf{H}\ensuremath{\Vert}[001]$), a spectrum consisting of a series of well-resolved SW modes is observed. However, as $\mathbf{H}$ is rotated significantly away from the normal, at some orientation, a ``critical angle'' is found, at which only the single uniform mode is observed. As $\mathbf{H}$ is rotated further and approaches the in-plane direction (such as the [110] direction), a multiple-mode spectrum reemerges, ascribed in part to the appearance of a surface spin excitation due to unpinned surface spins. The analysis of spin-wave resonance spectra in terms of the dynamic surface spin pinning (derived from the surface anisotropy) allows us to determine the value of the exchange stiffness constant $D$.

Magnetic properties of polycrystalline [formula omitted] alloys

We have investigated the magnetic properties of the Heusler phase Co 2 Cr 1 - x Fe x Al in the composition regime ( x = 0.3 - 0.5 ) in the disordered B2 phase. Both bulk and surface static and dynamic magnetic aspects were addressed by employing alternating gradient magnetometry (AGM), magneto-optical Kerr effect (MOKE) and Brillouin light scattering (BLS). All samples show ferromagnetic hysteresis loops and a tendency of increasing saturation magnetization M s with the iron content. With BLS the behavior of bulk spin waves and the Damon Eshbach (DE) surface spin wave mode have been studied. The spectra are typical for opaque bulk ferromagnetic samples with strong exchange. The measured spin wave frequencies as a function of magnetic field are in good agreement with the calculated values. Saturation magnetization and gyromagnetic ratio g have been determined from the field-dependent peak positions of the bulk and the DE modes. The g -factor extracted from the DE mode shows a clear tendency of increase with increasing Fe-content. However, we could not find any peculiarities of the alloy with x = 0.4 , which had been proposed as a Heusler phase on the basis of electronic structure calculations [T. Block, C. Felser, G. Jakob, J. Ensling, B. Mühling, P. Gütlich, R.J. Cava, J. Solid State Chem. 176 (2003) 646].

Linear deformation effect on the SWR acoustic mode in La0.67Ca0.33MnO3 manganite film

AbstractIn this work, the influence of linear deformation on the magnetic resonance spectrum including the surface spin wave mode in La0.67Ca0.33MnO3 manganite film grown on LiNbO3 substrate has been investigated using a microwave technique. The parameters of the spectrum are established to depend strongly on strains in the film that influence both the profile of the magnetic resonance spectrum and the mode position and intensity. The magnetostriction constants of both the bulk film and surface mode were first determined using the shift of resonance fields as a function of mechanical stress. The tensile strain is shown to favor excitation of the surface spin‐wave mode, and its influence is stronger on the film surface layer. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Structure-induced magnetic anisotropy in the Fe(110)∕Mo(110)∕Al2O3(112¯0) system

Fe(110) films were epitaxially grown on sapphire substrates using a Mo(110) buffer layer in an ultrahigh-vacuum molecular-beam epitaxy system. The magnetic properties were examined ex situ by Brillouin light scattering and superconducting quantum interference device magnetometry. To determine the magnetic anisotropy constants the frequency of the Damon-Eshbach [J. Phys. Chem. Solids 19, 308 (1961)] surface spin-wave mode was measured as a function of the in-plane angle between the external magnetic field and the Fe[001] crystal axis. The angle-dependent frequency was fitted by a spin-wave model. We found that the easy axis of the cubic magnetocrystalline anisotropy K1 and an additional uniaxial in-plane anisotropy K‖(2) are aligned parallel to the in-plane Fe[001] axis for Fe-layer thicknesses from 0.8to37nm, with K1 increasing and K‖(2) decreasing with increasing Fe thickness. Possible origins of the observed uniaxial anisotropy are discussed.

Brillouin light scattering study of magnetic dots

Brillouin light scattering investigation of the thermally activated spin-waves in micrometer-size permalloy square dots shows evidence of a frequency discretization of the surface spin-wave mode which is due to the lateral confinement of the magnetic excitations. The observed frequencies are compared to those derived from the analytical expression in a continuous layer assuming that the finite size of the dots is responsible of the quantization of the wave vectors and of the lowering of the internal magnetic field.