Emergence of flat bands and localized spin-wave modes in coupled bilayer magnonic crystals with different periodicities

We measure and simulate micromagnetically a framework based upon a nano-contact spin torque oscillator where two distinct localized evanescent spin-wave modes can be detected. The resulting frequency spectrum is composed by two peaks, corresponding to the excited modes, which lie below the ferromagnetic resonance frequency, and a low-frequency tail, which we attribute to the non-stationary switching between these modes. By using Fourier, wavelet, and Hilbert-Huang transforms, we investigate the properties of these modes in time and spatial domains, together with their spatial distribution. The existence of an additional localized mode (which was neither predicted by theory nor by previous numerical and experimental findings) has to be attributed to the large influence of the current-induced Oersted field strength which, in the present setup, is of the same order of magnitude as the external field. As a further consequence, the excited spin-waves, contrarily to what usually assumed, do not possess cylindrical symmetry: the Oersted field induces these modes to be excited at the two opposite sides of the region beneath the nano-contact.

Summary form only given. In the current work a new class of magnetic materials is described and analyzed. Drawing an analogy with photonic crystals possessing a photonic band, namely the frequency range where the wave propagation if completely forbidden, such magnetic media can be named magnonic crystals. Such crystals represent the magnetic medium in which the magnetic properties are varied periodically. The simplest type of the one-dimensional magnonic crystals is a multilayered periodic structure composed from the magnetic layers with the different magnetization. Spin waves propagation through this structure is prohibited within the restricted bands. It is shown that a localized spin wave mode can exist in a forbidden zone if the periodicity of the system is broken in a particular place. Such magnonic crystals in a microwave frequency range can be a challenge for photonic crystals operating at the visual light frequency band. The analysis of such systems is provided along with theoretical and numerical calculations of forbidden zones and spin wave modes. The dispersion characteristics of spin waves in such magnonic crystals are considered along with reflection and transmission of spin waves through such a structure. In particular, the one-dimensional periodic magnetic structure is considered containing magnetic layers with the same thickness but different magnetisation. The wave spectrum contains forbidden zones and the transmission coefficient from such a structure almost equal to 0, thus the wave totally reflected. Numerical calculations are provided for real multilayered structures. It is further shown that three-dimensional periodic magnetic systems can possess a full magnonic band where spin-wave propagation in a particular frequency band is prohibited in all directions. On the contrary to the photonic crystal bands the magnonic band can be tuned by the variation of the external magnetic field. The propagation of optical radiation in a magnetic waveguides with the periodic domain structures (magneto-photonic crystals) is further investigated. Two types of periodic structures are studied -one- and two-dimensional.

Localized spin-wave modes in a triangular magnetic element studied by micro-focused Brillouin light scattering

We study magnetic dynamics of Ni80Fe20/Pt magnonic crystals made of width periodically varied nanostrips using the spin-torque induced ferromagnetic resonance technique. DC voltage signals are detected when nanostrip magnonic crystals (MCs) are driven resonantly. The DC voltage originates dominantly from the spin rectification effect due to the coupling between the AC electrical current and the oscillated anisotropic magnetoresistance. In addition to uniform magnetization precession across the MC, localized spin wave modes are also observed. Their evolution with the strength and direction of the magnetic field are studied. Micromagnetic simulations are performed to illustrate the experimental results.

Collective and localized modes in 3D magnonic crystals

A semiclassical study of intrinsic localized spin-wave modes in a one-dimensional quantum ferromagnetic XXZ chain in an oblique magnetic field is presented in this paper. We quantize the model Hamiltonian by introducing the Dyson-Maleev transformation, and adopt the coherent state representation as the basic representation of the system. By means of the method of multiple scales combined with a quasidiscreteness approximation, the equation of motion for the coherent-state amplitude can be reduced to the standard nonlinear Schrodinger equation. It is found that, at the center of the Brillouin zone, when θ θc a dark intrinsic localized spin-wave resonance mode can occur above the bottom of the magnon frequency band. In other words, the switch between the bright and dark intrinsic localized spin-wave modes can be controlled via varying the angle of the magnetic field. This result has potential applications in quantum information storage. In addition, we find that, at the boundary of the Brillouin zone, the system can only produce a dark intrinsic localized spin-wave mode, whose eigenfrequency is above the upper of the magnon frequency band.

The localized spin wave modes are studied theoretically for insulating ferromagnet with an antiferromagnetic impurity, on the basis of the Heisenberg model with particular reference to the simple cubic lattice. Besides localized p and d modes, which are of the same type as seen in ferromagnet with a ferromagnetic impurity, we have one or two localized s modes for the present case depending on certain conditions. One of them is an antiferromagnetic mode, which comes out of the bottom of the spin wave band. This has no analogue in ferromagnet with a ferromagnetic impurity. The condition for the appearance of localized s modes, the zero-point contraction of spins, and the frequency shirt of localized modes due to magnetic field and anisotropy energy are studied.

We explore the feasibility of exciting localized spin-wave modes in ferromagnetic nanostructures using surface acoustic waves. The time-resolved Faraday effect is used to probe the magnetization dynamics of an array of nickel nanowires. The optical-pump pulse excites both spin-wave modes of the nanowires and acoustic modes of the substrate and we observe that, when the frequencies of these modes coincide, the amplitude of magnetization dynamics is substantially enhanced due to magnetoelastic coupling between the two. Notably, by tuning the magnitude of an externally applied magnetic field, optically excited surface acoustic waves can selectively excite either the upper or lower branches of a splitting in the nanowire’s spin-wave spectrum, which micromagnetic simulations indicate is caused by localization of spin waves in different parts of the nanowire. Thus, our results indicate the feasibility of using acoustic waves to selectively excite spatially confined spin waves, an approach that may find utility in future magnonic devices where coherent structural deformations could be used as coherent sources of propagating spin waves.

It was shown by micromagnetic simulation that a current-driven in-plane magnetized magnetic nanocontact, besides a quasilinear propagating (``Slonczewski'') spin-wave mode, can also support a nonlinear self-localized spin-wave ``bullet'' mode that exists in a much wider range of bias currents. The frequency of the bullet mode lies below the spectrum of linear propagating spin waves, which makes this mode evanescent and determines its spatial localization. The threshold current for the excitation of the self-localized bullet is substantially lower than for the linear propagating mode, but finite-amplitude initial perturbations of magnetization are necessary to generate a bullet in our numerical simulations, where thermal fluctuations are neglected. Consequently, in these simulations the hysteretic switching between the propagating and localized spin-wave modes is found when the bias current is varied.

Ferromagnetic resonance driven spin pumping, a topic of steadily increasing interest since its emergence over two decades ago, remains one of the most exciting research fields in condensed matter physics. Among the many materials that have been explored for spin pumping, yttrium iron garnet (YIG) is one of the most extensively studied because of its exceptionally low magnetic damping and insulating nature. There is a great amount of literature in the spin pumping and related research fields, too broad for this review to cover. In this Topical Review, we focus on the YIG-based spin pumping results carried out by our groups, including: the mechanism and technical details of our off-axis sputtering technique for the growth of single-crystalline YIG epitaxial films with a high degree ordering, experimental evidence for the high quality of the YIG films, spin pumping results from YIG into various transition metals and their heterostructures, dynamic spin transport in YIG/antiferromagnet hybrid structures, intralayer spin pumping by localized spin wave modes confined by a micromagnetic probe, dynamic spin coupling between YIG and nitrogen-vacancy centers in diamond, parametric spin pumping from high-wavevector spin waves in YIG, and localized spin wave mode behavior in broadly tunable spatially complex magnetic configurations. These results build on the power and versatility of YIG spin pumping to improve our understanding of spin dynamics, spin currents, spin Hall physics, spin–orbit coupling, dynamic magnetic coupling, and the relationship between these phenomena in a broad range of materials, geometries, and settings.

Magnetic states and dynamics of bistable square Fe nanoislands

The spectrum of spin wave excitations on a nanometric two-dimensional periodical array of circular holes in a magnetic film was measured using the Brillouin light scattering technique. Two modes with positive group velocity in the frequency range between 4 and 7GHz were observed. Our calculations show that these correspond to the two lowest modes propagating along the edges of an effective stripe waveguide, perpendicular to the applied field, whose width is equal to the interhole distance. Moreover, a number of higher-frequency modes has been measured and identified as volume excitations of the same effective stripe.

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.

Spin fluctuations dynamics on the insulating antiferromagnetic stepped surface model

The dynamic response of dipole skyrmions in Fe/Gd multilayer films is investigated by ferromagnetic resonance measurements and compared to micromagnetic simulations. We detail thickness and temperature dependent studies of the observed modes as well as the effects of magnetic field history on the resonant spectra. Correlation between the modes and the magnetic phase maps constructed from real-space imaging and scattering patterns allows us to conclude the resonant modes arise from local topological features such as dipole skyrmions but does not depend on the collective response of a closed packed lattice of these chiral textures. Using, micromagnetic modeling, we are able to quantitatively reproduce our experimental observations which suggests the existence of localized spin-wave modes that are dependent on the helicity of the dipole skyrmion. We identify four localized spin wave excitations for the skyrmions that are excited under either in-plane or out-of-plane r.f. fields. Lastly we show that dipole skyrmions and non-chiral bubble domains exhibit qualitatively different localized spin wave modes.