Waves In Ferromagnetic Films Research Articles

Resonant and nonlinear phenomena during the propagation of magnetostatic waves in multiferroid, semiconductor and metallized structures based on ferromagnetic films and magnonic crystals

Purpose of this work is to compile an overview of a new and fruitful scientific direction in magnonics, which grew out of the works of Ph.D., Professor Yuri Pavlovich Sharaevsky, and related to the study of resonant and nonlinear phenomena during the propagation of magnetostatic waves in ferromagnetic films, ferromagnetic films with periodic inhomogeneities (magnonic crystals), coupled (layered and lateral) ferromagnetic structures, as well as ferromagnetic structures with layers of a different physical nature (semiconductor, ferroelectric, piezoelectric, normal metal layers). Methods. Experimental and theoretical methods have been used to study spin-wave excitations in a wide class of structures with ferromagnetic layers. In particular, experimental radiophysical methods of microwave measurements and optical methods of Mandelstam-Brillouin spectroscopy. For the construction of theoretical models, the following methods are used: the method of coupled waves, the method of crosslinking magnetic permeability at the boundaries of layers, the method of transmission matrices, long-wave approximation. Results. The presented results are of general scientific importance for understanding the basic laws of the joint influence of coupling, periodicity and interactions of different physical nature (the influence on the magnetostatic wave of deformation in periodic structures with piezoelectric, electromagnetic wave in structures with ferroelectric, electric current in structures with semiconductor, spin current in structures with normal metal). In applied terms, the identified effects open up wide opportunities for creation of new devices of spin-wave electronics with the possibility of dynamic control of characteristics when changing the electric and magnetic fields, as well as the power of the input signal. Conclusions. The review of the most interesting results obtained by the authors together with Yuri Pavlovich and which are an ideological continuation of the foundations laid by him is given.

Reflecting upon some electromagnetic waves in a ferromagnetic film via a variable-coefficient modified Kadomtsev-Petviashvili system

Kadomtsev-Petviashvili-type models are employed in magneto-optics, ferromagnetism, plasma physics, fluid mechanics, etc. For a variable-coefficient modified Kadomtsev-Petviashvili system modelling the electromagnetic waves in an isotropic charge-free infinite ferromagnetic thin film, exciting the magnetization and with the potential application in magneto-optic recording, we symbolically compute out two sets of the similarity reductions, each of which can be from that system to a known ordinary differential equation. Both sets rely on the constant/variable coefficients for that system.

Certain electromagnetic waves in a ferromagnetic film

Electromagnetic-wave/ferromagnetic-material investigations with magneto-optics are carried out in magneto-optic recording, computer data-storage, waveguides, etc. In this paper, we investigate a variable-coefficient modified Kadomtsev–Petviashvili system for certain electromagnetic waves in an isotropic charge-free infinite ferromagnetic thin film with the potential application in magneto-optic recording. With respect to the electromagnetic waves in the ferromagnetic film, symbolic computation helps us work out (1) two sets of the variable-coefficient-dependent auto-Bäcklund transformations via the generalized Laurent series, along with some solitonic features, (2) one set of the variable-coefficient-dependent bilinear forms and (3) two sets of the variable-coefficient-dependent N-solitonic solutions with N being a positive integer. We note that the electromagnetic field can excite the magnetization of a ferromagnetic medium in the form of solitons with the applications in magneto-optic recording. Relevant constraints on the variable coefficients are presented. We hope that the results could help the studies on magneto-optic recording, computer data-storage and waveguides.

Chiral Magnonics: Reprogrammable Nanoscale Spin Wave Networks Based on Chiral Domain Walls.

SummarySpin waves offer promising perspectives as information carriers for future computational architectures beyond conventional complementary metal-oxide-semiconductor (CMOS) technology, owing to their benefits for device minimizations and low-ohmic losses. Although plenty of magnonic devices have been proposed previously, scalable nanoscale networks based on spin waves are still missing. Here, we demonstrate a reprogrammable two-dimensional spin wave network by combining the chiral exchange spin waves and chiral domain walls. The spin-wave network can be extended to two dimensions and offers unprecedented control of exchange spin waves. Each cell in the network can excite, transmit, and detect spin waves independently in the chiral domain wall, and spin-wave logics are also demonstrated. Our results open up perspectives for integrating spin waves into future logic and computing circuits and networks.

Chiral excitation of spin waves in ferromagnetic films by magnetic nanowire gratings

We theoretically investigate the interlayer dipolar and exchange couplings for an array of metallic magnetic nanowires grown on top of an extended ultrathin yttrium iron garnet film. The calculated interlayer dipolar coupling agrees with observed anticrossings [Chen \emph{et al.}, Phys. Rev. Lett. \textbf{120}, 217202 (2018)], concluding that the interlayer exchange coupling is suppressed by a spacer layer between the nanowires and film. The Kittel mode in the nanowire array couples chirally to spin waves in the film, even though Damon-Eshbach surface modes do not exist. The chirality is suppressed when the interlayer exchange coupling becomes strong.

Probing the Dzyaloshinskii-Moriya Interaction via the Propagation of Spin Waves in Ferromagnetic Thin Films

The Dzyaloshinskii-Moriya interaction (DMI) has attracted considerable recent attention owing to the intriguing physics behind and the fundamental role it played in stabilizing magnetic solitons, such as magnetic skyrmions and chiral domain walls. A number of experimental efforts have been devoted to probe the DMI, among which the most popular method is the Brillouin light scattering spectroscopy (BLS) to measure the frequency difference of spin waves with opposite wave vectors $\pm\mathbf{k}$ perpendicular to the in-plane magnetization $\mathbf{m}$. Such a technique, however, is not applicable for the cases of $\mathbf{k}\parallel\mathbf{m}$, since the spin-wave reciprocity is recovered then. For a narrow magnetic strip, it is also difficult to measure the DMI strength using BLS because of the spatial resolution limit of lights. To fill these gaps, we propose to probe the DMI via the propagation of spin waves in ferromagnetic films. We show that the DMI can cause the non-collinearity of the group velocities of spin waves with $\pm\mathbf{k}\parallel\mathbf{m}$. In heterogeneous magnetic thin films with different DMIs, negative refractions of spin waves emerge at the interface under proper conditions. These findings enable us to quantify the DMI strength by measuring the angle between the two spin-wave beams with $\pm\mathbf{k}\parallel\mathbf{m}$ in homogeneous film and by measuring the incident and negative refraction angles in heterogeneous films. For a narrow magnetic strip, we propose a nonlocal scheme to determine the DMI strength via nonlinear three-magnon processes. We implement theoretical calculations and micromagnetic simulations to verify our ideas. The results presented here are helpful for future measurement of the DMI and for designing novel spin-wave spintronic devices.

Anomalous Doppler effect observed during propagation of magnetostatic waves in ferromagnetic films and ferrite-dielectric-metal structures

The anomalous Doppler effect observed during propagation of magnetostatic backward volume waves in a free ferromagnetic film and magnetostatic surface waves in a ferrite-dielectric-metal structure is investigated. The effect is theoretically substantiated, and plots of Doppler frequency shift are constructed. The anomalous Doppler effect is qualitatively analyzed with the use of equifrequency curves.

Magnetostatic spin waves in two-dimensional periodic structures (magnetophoton crystals)

Series of experiments are carried out to study the propagation of magnetostatic spin waves in ferromagnetic films containing 2D periodic structures formed by etched apertures. For spin waves, such films are analogous to photon crystals (namely, magnetophoton or magnon crystals). The spectra of waves transmitted through the structure display features associated with a change in the spin homogeneity due to etching or radiation loss, as well as with Bragg reflection effect or the emergence of forbidden gaps in the spectrum of propagating waves.

Effect of magnetocrystalline anisotropy on the temperature characteristics of magnetostatic waves in ferromagnetic films

The temperature dependence of the eigenfrequencies of magnetization oscillation in a single-crystal film is shown to depend strongly on the temperature dependence of the magnetocrystalline anisotropy field. The conditions are considered under which the temperature coefficient of the ferromagnetic resonance frequency in a film with cubic anisotropy changes sign as the orientation of the magnetization vector is changed from the 〈111〉 to the 〈100〉 direction. The spectrum of surface magnetostatic waves is investigated experimentally in 〈110〉-oriented yttrium iron garnet films. It is established that, due to magnetic anisotropy of the ferrite, the temperature dependence of the long-wavelength limit of the frequency spectrum becomes nonmonotonic when a film of this material is magnetized along the 〈100〉 axis.

Microscopic theory of dipole-exchange spin waves in ferromagnetic films: Linear and nonlinear processes

The linear and nonlinear processes in ferromagnetic films at low temperatures $(T\ensuremath{\ll}{T}_{c})$ are studied in a microscopic theory. Both the long-range magnetic dipole-dipole and the Heisenberg exchange interactions to nearest and next-nearest neighbors are included. The results obtained for the linearized spin-wave spectrum are compared with previous macroscopic theories. For ultrathin films (or for large wave vectors) the microscopic theory provides important corrections. The nonlinear dynamics of the spin waves are studied through a finite-temperature perturbation theory based on Feynman diagrams. We obtain explicit results for the energy shift and damping (or reciprocal lifetime) of the dipole-exchange spin waves due to all possible three-magnon and four-magnon processes involving combinations of the surface and quantized bulk spin waves at low temperatures. To investigate different dipole interaction strengths (relative to the exchange) numerical results are presented using parameters for Fe, EuO, and ${\mathrm{GdCl}}_{3}.$

Exchange-dominated surface spin waves in ferromagnetic and antiferromagnetic films

Theoretical results are presented for the localized surface spin waves in thin magnetic films in the exchange-dominated regime. The method is based on a spin-wave operator and Green-function technique that utilizes special properties of tridiagonal and pentadiagonal matrices, and two applications are described here. One is to study the effects of finite film thickness in coupling the modes localized near the two surfaces of an antiferromagnet with a simple cubic structure for the magnetic ions, and numerical examples are given for ultrathin films. The second application is to consider the surface spin waves in ferromagnetic films with body-centered cubic structure and (111) surfaces. Its relevance to recent experimental data for localized modes in epitaxial W/Ni/W films is discussed.

Induced modulation instability of spin waves in ferromagnetic films

Induced modulation instability of backward volume spin waves in ferromagnetic films is investigated. It is found that the nonlinearity of the spin system of a ferromagnetic sample can greatly enrich the spectrum by excitation of spin waves at close frequencies and, in consequence, result in the appearance of a sequence of soliton-like pulses.

Spin-wave interactions in ultrathin ferromagnetic films: the dipole-exchange regime

A perturbation formalism is employed to study nonlinear processes for the interactions between the discrete spin waves in ferromagnetic films, taking account of both dipole–dipole and exchange coupling. By contrast with previous macroscopic theories of spin-wave interactions the dipolar terms are treated within a Hamiltonian method to obtain results applicable to ultrathin films. The roles of three-magnon and four-magnon processes in the spin-wave energy shift and damping are evaluated and numerical applications to EuO are discussed.

Observation of self-generation of dark envelope solitons for spin waves in ferromagnetic films

We have performed experiments in which self-generation of dark envelope solitons for spin waves at microwave frequencies were obtained. Stable self-generation of dark solitons was observed in a ring consisting of tangentially magnetized yttrium iron garnet film and a microwave signal amplifier.

Effect of third-order dispersion on nonlinear magnetostatic spin waves in ferromagnetic films

The effect of high-order dispersion on nonlinear magnetostatic spin waves has been investigated, theoretically, for ferromagnetic films that have metal plates near both surfaces of the film. The conditions under which third-order dispersion has to be considered are thoroughly analyzed and some numerical calculations concerning the propagation of short microwave pulses in ferromagnetic films are presented.

Observation of cross-phase induced modulation instability of travelling magnetostatic waves in ferromagnetic films

Modulation instability, induced by the simultaneous propagation of two magnetostatic spin waves in ferromagnetic films, has been experimentally observed for the first time. The effect is caused by cross-phase modulation and the spectra of transmitted waves contains sidebands, symmetrically positioned either side of the carrier frequency. They appear as the wave power reaches a threshold value, and disappear when only one wave is present. This is the signature of cross-phase modulation. The dependence of the modulation frequency upon the wave power and frequency is reported and a theoretical explanation of the observed phenomenon, using nonlinear Schrd̈dinger coupled equations, is presented.

Interaction of guided optical wave with nonlinear magnetostatic forward volume waves in ferromagnetic films

Magneto-optic interactions between guided optical waves and nonlinear magnetostatic forward volume waves are studied. For the discussed configuration, when the rf input power reaches 33 dBm and the frequency is lower than 4.2 GHz, the power level of the magnetostatic forward volume wave exceeds the power threshold of the four-magnon process, and the nonlinear magneto-optic dynamic characteristics due to the magnetostatic forward volume wave instability are predicted. The theoretical pattern is supported by experimental results on the magneto-optic mode conversion.

Parametric and modulation instabilities of magnetostatic surface spin waves in ferromagnetic films

First-order parametric instability, modulation instability and second-order instability processes for magnetostatic surface waves propagating in a pure yttrium iron garnet film are investigated in accordance with the relationship between the magnetostatic wave frequency and the internal magnetic field. The transitions from the second-order parametric instability, via the modulation instability, to the first-order parametric instability (when the magnetic field is 720 Oe and the carrier frequency varies from 3.87 to 4.39 GHz), and the transitions from the first-order parametric instability to the second-order parametric instability via the modulation instability (when the carrier frequency is 3.5 GHz and the magnetic field varies from 427 to 647 Oe) are experimentally observed and explained. Dispersion characteristics of the magnetostatic surface waves are modified by introduction of a metallic ground plane in order that the Lighthill criterion, as one of the prerequisites for onset of the modulation instability, is fulfilled in a limited frequency range. Characteristics of magnetostatic surface wave modulation instability are studied by solving the nonlinear Schrödinger equation. Dependencies of the modulation frequency induced by the modulation instability on the carrier frequency and the magnetic field are found to be consistent with experimental data.

Nonlinear self-channeling and beam shaping of magnetostatic waves in ferromagnetic films.

Nonlinear self-channeling and beam shaping of magnetostatic waves in ferromagnetic films.

Excitation of magnetostatic waves in ferromagnetic films by various sources

A general theory of the interaction of magnetostatic waves in ferromagnetic films with various microwave sources is represented. A rigorous analysis based on the initial formulation of the eigenvalue problem and the use of a complete functional basis is realized. The excitation equations for interactions of magnetostatic waves with the rf external electric and magnetic fields, electric current, and magnetic charges are obtained. © 1996 John Wiley & Sons, Inc.