Nonlinearity of magnetoacoustic excitations in planar structures

This paper reports on the results of experimental investigations into the threshold power of the onset of nonlinearity of magnetoacoustic vibrations in planar structures (such as a ferrite film-dielectric substrate structure) in the range of phase matching of the higher bulk magnetostatic and acoustic modes. Under the experimental conditions, the wavelength of the higher bulk magnetostatic modes is of the order of 1 μm and shorter. On this basis, the energy of these vibrations with respect to the origin of the magnetostatic wave spectrum is determined by the energy of the inhomogeneous exchange interaction. The standing magnetoacoustic waves are examined in conventional yttrium iron garnet films with free surface spins in which, under standard conditions, only dipole magnetostatic vibrations are excited in planar resonators. Consideration is given to the threshold power of the onset of precession instability of the dipole exchange acoustic modes which, as was shown earlier by the authors, are excited in the range of the phase matching of the exchange and acoustic modes. A comparative analysis is performed for the threshold powers of dipole magnetostatic, exchange acoustic, and dipole exchange acoustic modes. It is demonstrated that the threshold power of the instability of magnetostatic modes decreases significantly when the natural frequencies of the dipole modes coincide with those of the exchange acoustic modes. __________ Translated from Fizika Tverdogo Tela, Vol. 44, No. 7, 2002, pp. 1285–1289. Original Russian Text Copyright ? 2002 by Bugaev, Gorsky.     

Magnetostatic volume waves in exchange-coupled ferrite films

The influence of exchange coupling of layers on the propagation of magnetostatic dipole volume waves in normally and tangentially magnetized two-layer epitaxial ferrite structures is investigated. It is shown that the indicated influence is manifested in the form of dynamic spin pinning effects on the interlayer boundary and formation of a common dipole-exchange wave spectrum for the entire structure. In this case, at the synchronism frequencies of the dipole and exchange waves the losses of the dipole waves grow and anomalous segments appear in the dispersion. In films magnetized in the “hard” direction relative to the axis of normal uniaxial surface anisotropy the magnetostatic dipole volume waves can interact resonantly with the surface spin waves supported by the boundaries with pinned spins. Zh. Tekh. Fiz. 68, 97–110 (July 1998)     

Magnetoelastic Waves in Submicron Yttrium–Iron Garnet Films Manufactured by Means of Ion-Beam Sputtering onto Gadolinium–Gallium Garnet Substrates

A series of equidistant oscillations have been revealed in the transmission spectrum and dispersion law of Damon–Eshbach surface magnetostatic waves (SMSWs) propagating in submicron (200-nm) yttrium–iron garnet (YIG) films manufactured by means of ion-beam sputtering onto gadolinium–gallium garnet (GGG) substrates. These oscillations correspond to the excitation of magnetoelastic waves in the YIG–GGG structure at frequencies of resonant interaction between the surface magnetostatic waves and the elastic shear modes of the wave-guiding YIG–GGG structure. The obtained results show that the studied YIG films are characterized by an efficient magnetoelastic coupling between their spin and elastic subsystems and the matching of acoustic impedances at the YIG–GGG interface, thus providing the possibility to consider the ion-beam sputtering of YIG films onto GGG substrates as a promising technology for the creation of magnonic and straintronic devices.     

Spin wave dispersion of FeBO3 at small wavevectors

Brillouin scattering from thermally excited magnons and ferromagnetic resonance are used to determine the spin wave dispersion of the low-frequency spin wave branch in FeBO₃, a transparent weak ferromagnet. In addition to the dominant exchange and Zeeman contributions, the investigation takes into account magnetic dipole and magnetoelastic interactions. Due to the antisymmetric exchange enhancement the material exhibits a broad spin wave band and a large gap energy at small magnetic fields. Competing directional dependences of the dipole and the exchange energy produce a degeneracy of spin waves with a certain magnitude of the wavevector propagating in different directions. The gap energy is shown to be due to magnetoelastic coupling, whereas the contribution of the anisotropy in the easy plane is negligible atT=300 K.     

Localized spin modes on the insulating antiferromagnetic stepped surface model

We present a numerical method to calculate the spin fluctuation dynamics on a stepped surface. The model discussed here consists of an extended antiferromagnetic surface step at the surface boundary of an insulating antiferromagnetic substrate. The stepped surface is formed by two straight steps dropped randomly and the spins moments of the steps and the substrate are considered as local with no electronic effects. The full magnetic problem arising from the absence of translational symmetry due to the presence of a magnetic surface and steps is considered and studied. The calculations concern in particular the energies of localized spin-wave modes near the surface steps and employ the matching procedure in the random-phase approximation and mean field approximation. Only the nearest-neighbor exchange interactions are considered between the spins in the model. The analytical formalism presented here is adapted from an earlier work on the vibrational spectra of two isolated steps, a structure that can be considered as a low dimensional system and solved for the three dimensional evanescent crystal spin field in the bulk and the surface domains around the steps. This spin field arises from the breakdown of the magnetic translation symmetry of the system. The results are used to calculate the spin mode energies associated with the steps and surface terraces. We show the presence of localized acoustic and optical spin wave modes propagating along the surface and the steps as well as the interface surface-steps, their fields are also described as evanescent in the plane normal to the surface step layers and depend on the nature of the exchange interaction near the steps.Received: 9 March 2004, Published online: 30 September 2004PACS: 75.70.Ak Magnetic properties of monolayers and thin films - 75.50.Ee Antiferromagnetics - 75.30.Ds Spin waves - 76.70.Hb Optically detected magnetic resonance (ODMR)     

Specific features of magnetoacoustic waves in Fe<Subscript>3</Subscript>BO<Subscript>6</Subscript>

The specific features of magnetoacoustic waves propagating in an orthorhombic antiferromagnet with weak ferromagnetism, namely, the Fe₃BO₆ orthoborate, are investigated experimentally in the vicinity of the spontaneous, first-order orientational phase transition. It is revealed that, at the phase transition point, the amplitude of active acoustic waves interacting with spin waves increases significantly. A phenomenological theory of magnetoelastic waves in orthoferrites is proposed. This theory allows for an intermediate domain structure existing in the range of a first-order orientational phase transition and offers a satisfactory explanation of the experimentally observed anomaly in the amplitude of active acoustic waves.     

The peculiarities of coupled electromagnetic and magnetoelastic waves in antiferromagnets

A spectrum of coupled electromagnetic, spin and elastic waves in a two-sublattice antiferromagnet with weak ferromagnetism is theoretically investigated. The influence of the g-factor anisotropy and the transverse and longitudinal relaxation in magnetic subsystem on the spectrum of coupled waves is considered. The most changes of dispersion laws occurred in long-wavelength approximation and near the spin reorientation point, then the vectors of ferromagnetism and antiferromagnetism reoriented onto another crystallographic axis. It is shown that the magnetoelastic, the Dzyaloshinsky and the dipole interactions, the anisotropy of g-factor, the external magnetic field and the longitudinal susceptibility determine the activation of quasiferromagnetic waves. The dispersion laws of quasielectromagnetic and quasielastic waves can change from linear dependence to square. At large damping in magnetic subsystem, one from these modes can become the pure relaxation one.     

Magnon–Phonon Interaction in the Transition Layer of an Epitaxial YIG Film

Physics of the Solid State - It is shown that the effects of collinear magnetoelastic interaction of exchange spin waves (ESW) and acoustic waves (AW) arise in the transition layer of an epitaxial...     

Absence of a spontaneous long-range order in a mixed spin-(1/2, 3/2) Ising model on a decorated square lattice due to anomalous spin frustration driven by a magnetoelastic coupling

The mixed spin-(1/2, 3/2) Ising model on a decorated square lattice, which takes into account lattice vibrations of the spin-3/2 decorating magnetic ions at a quantum-mechanical level under the assumption of a perfect lattice rigidity of the spin-1/2 nodal magnetic ions, is examined via an exact mapping correspondence with the effective spin-1/2 Ising model on a square lattice. Although the considered magnetic structure is in principle unfrustrated due to bipartite nature of a decorated square lattice, the model under investigation may display anomalous spin frustration driven by a magnetoelastic coupling. It turns out that the magnetoelastic coupling is a primary cause for existence of the frustrated antiferromagnetic phases, which exhibit a peculiar coexistence of antiferromagnetic long-range order of the nodal spins with a partial disorder of the decorating spins with possible reentrant critical behavior. Under certain conditions, the anomalous spin frustration caused by the magnetoelastic coupling is responsible for unprecedented absence of spontaneous long-range order in the mixed-spin Ising model composed from half-odd-integer spins only.     

Effects of spin-wave energy degeneracy induced by in-plane wave propagation in ferromagnetic thin films

This work presents an investigation of the collapse effect predicted to occur in the spin-wave band structure of magnetic cubic thin films. The system under consideration is described by the Heisenberg model with exchange interactions between the nearest (NN) and next-nearest neighbors (NNN) taken into account. In the collapse effect, which occurs for some specific directions of in-plane propagation of spin waves, the effective coupling between spins in adjacent layers vanishes dynamically and each mode becomes confined to a single atomic plane; this means that all the bulk modes and, independently, all the surface modes become energetically degenerate. This effect of ‘directional collapse’ can only occur when the exchange interactions between NN or NNN include bonds oblique with respect to the direction of in-plane propagation.     

Microscopic imaging of Fe magnetic domains exchange coupled with those in a NiO(001) surface

We revealed the micromagnetic structure of an Fe thin film exchange interacting with the spins of a fully compensated (001) surface of antiferromagnetic NiO. The interface exchange interaction causes the Fe domains to follow the NiO domains. The Fe spin polarization is in plane and the spin polarization in each domain is roughly perpendicular to an easy-spin axis of the NiO. These results agree with numerically calculated spin directions. Our numerical results also show that the NiO spins at the interface cant from the easy-spin axis towards the Fe spin because of exchange coupling.     

Electromagnetic-wave reflectivity of the surface of a cubic-ferrite plate

The electromagnetic-wave reflectivity of the surface of an insulating cubic-ferromagnet (ferrite) plate is calculated analytically and numerically with allowance for spin-wave damping. The frequency and magnetic-field dependences of the reflectivity are found at the orientational phase transition point and in the vicinity of this point for various values of the plate thickness. It is shown that the reflectivity exhibits anomalous behavior when the dynamic magnetic permeability becomes equal to the dielectric constant, as well as when dimensional resonances occur for electromagnetic or acoustic waves or ferromagnetic resonance takes place. At frequencies below the magnetoelastic gap in the quasi-spin-wave spectrum, the reflectivity may have anomalously low (down to zero) or anomalously high (up to unity) values. Such frequencies can lie in the microwave region.     

Elastic properties of magnetic materials

This review discusses the theoretical aspects of magnetoelastic coupling with emphasis on the magnetic perturbation of elastic properties. The basic theory of magnetostriction is set out with application to ferromagnets, ferrimagnets and antiferromagnets, and is followed by a discussion of the physical origin of the magnetoelastic coupling coefficients in both localized and itinerant magnetic systems. Magnetic contributions to elastic compliance are then discussed and sound velocity anomalies near magnetic phase transitions investigated, including the cooperative Jahn-Teller limit for which the acoustic mode itself drives a structural transition even when magnetic ordering does not occur. The review concludes with discussion of magnetoelastic (or mixed magnon-phonon) waves in low temperature magnetically ordered phases and with a study of local striction phenomena in magnetically dilute materials. The latter leads to a recognition of internal rearrangement modes which may also be present in concentrated magnetic systems, and which may or may not couple significantly to bulk homogenous strain.     

Rotationally invariant theory of magnetoacoustic wave attenuation in cubic ferromagnets

Rotationally invariant theory is used to study the effect of magnetization relaxation on the spectrum of magnetoacoustic waves propagating in a cubic ferromagnet with an induced uniaxial anisotropy along the [011] direction. It is found that the inclusion of rotationally invariant terms leads to certain contributions to the propagation velocity and rate of attenuation of magnetoelastic waves, thus increasing the degree of anisotropy of these characteristics. Among different types of coupled waves, only quasi-sound modes exhibit a relaxation nature in the region of magnetic phase stability loss. The introduction of dissipation and rotational invariance affects the acoustic birefringence, while the latter gives rise to an additional term in the expression for the phase shift.     

Calculations of localized modes on surface and impurity layer embedded in a semi-infinite Heisenberg ferromagnet

We investigate the magnetic excitations for the magnetic problem arising from the absence of magnetic translation symmetry in one dimension due to the presence of an impurity layer embedded within a semi-infinite ferromagnet. A Heisenberg model is employed to investigate the possibility that localized modes can occur with an impurity layer implanted within a semi-infinite ferromagnet. No electronic effects are considered. The theoretical approach employs the matching procedure in the mean field approximation and determines the propagating and evanescent spin amplitude fields including the contribution due to an applied field. The results are used to calculate the energies of localized modes associated with the impurity layer and with the surface. Numerical examples of the modes are given and they are found to exhibit various effects due to the interplay between the impurity layer and surface modes. It is shown that more localized modes can occur and the modification of the spin wave spectra can be signaled by the appearance of surface and impurity modes, besides the bulk excitations. Also, the bulk spin fluctuations field, the spin waves localized on the surface as well as on impurity layer depend are shown to depend on the nature of the exchange coupling between spin sites, the values of spin sites and the position of the impurity layer from the surface.     

Total reflection of ultrasound from a ferromagnetic plate with surface pinning of the spins

Using the effective transfer matrix for coupled elastic and spin waves, formulas are derived for the amplitudes of reflection and transmission of right-hand polarized elastic waves incident, in a direction along the normal, on a transversely magnetized ferromagnetic film with homogeneous conditions for pinning of the spins on the surfaces of the film. It is shown that a series of lines with reflectance maxima appears, to the extent of the magnetoelastic coupling, near the magnetoacoustic resonance. The shapes of the spectral line contours and the effect of the thickness of the film and damping are analyzed. The possibility of a similar effect in other polariton systems is discussed.     

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.     

圆柱状铁磁体中的偶极-交换自旋波

对于轴向磁化的圆柱状铁磁体,同时考虑偶极作用和交换作用,得到了偶极-交换自旋波的本征方程,给出了频谱的数值结果。当自旋波波矢β较小,即偶极能起主要作用时,相当于静磁模的结果,β较大,即交换能起主要作用时,过渡到宏观自旋波交换模理论的结果。     

Magnetoelastic waves in ferromagnet plates and films

The explosive development of investigations of magnetization waves in ferrite layers (plates and films) that occurred in recent years resulted in significant deepening and expansion of our conceptions of the effects of the interaction between such magnetization waves and elastic waves. The possibility of synchronization and hybridization of magnetization waves and elastic waves was shown in theory and experimentally for phase velocities of these waves in the direction of propagation along the ferrite layer exceeding the sound speed in the ferrite by one to two orders. At such phase velocities the inhomogeneous exchange energy often turns out to be insubstantial for magnetization wave propagation, and only the dipole energy is substantial. Therefore, we speak substantially about a new kind of magnetoelastic waves, the result of hybridization of pure magnetodipole and elastic waves. Such waves have been designated fast magnetoelastic waves. A brief survey of the theoretical, experimental, and applied investigations of fast magnetoelastic waves is contained in this paper. In the section Theory we present and discuss the fundamental equations, boundary conditions, and approximations necessary for the computation of fast magnetoelastic wave properties and the effects accompanying their propagation. The results of such computations currently known are presented. In the section Experiments we describe the fundamental requirements imposed on the specimens and the measurement methodology to detect and investigate the properties of fast magnetoelastic waves. Results of measurements executed at the present time as well as the prospects for further development in this direction are discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 6–23, November, 1988.     

Spin-wave modes in a compressible Heisenberg chain of classical spins

The spin dynamics of a compressible chain of classical spins is studied by means of a four pole approximation for the spin relaxation function. The frequency moments are calculated with the help of a computer. The general qualitative influence of the coupling to the phonons on the dynamic structure factor is discussed. Quantitative results for frequency shift, line width and the condition for the observability of spin waves are obtained. Especially the latter is quite different from the result for the rigid Heisenberg chain. The coupling to the phonon degrees of freedom does not lead to additional resonances in the spin spectrum.Aspirant van het Belgisch Nationaal Fonds voor Wetenschappelijk Onderzoek