Spin-wave Beams Research Articles

Nonreciprocal spin-wave beam transport in a metallized T-shaped magnonic junction

Nonreciprocal spin-wave beam transport in a metallized T-shaped magnonic junction

Lateral semiconductor magnonics: an array of GaAs stripes atop the YIG layer

In this work, we demonstrate the numerical and experimental research of the spin-wave transport in a structure composed of a gallium arsenide (GaAs) stripe lattice interfaced to an yttrium iron garnet layer. We show that this structure can be considered as an array of an infinite number of laterally coupled ferrite-semiconductor waveguides. We show that the surface wave properties for colinear propagation along the semiconductor stripes are similar to the waves in magnetic films with partial metallization. In addition, the properties of these surface waves depend on the electron concentration of the GaAs and thus may be tuned. With regard to the wave propagation at a certain angle to the GaAs stripe lattice, the Bragg resonance forms and the corresponding band gap depend on the angle between the wave to the stripes and on the GaAs electron density. The Brillouin light scattering technique was used to experimentally observe the spin-wave beam transformation, and microwave measurements support the numerical data and reveal the mechanism of the dip formation and widening of the frequency range in the spin-wave transmission. The proposed structure could be used as a reconfigurable metasurface and magnonic beam separation unit.

Magnonic notch filter based on spin wave caustic beams

Here, we study a magnonic crystal made of low-damping yttrium iron garnet that utilizes pseudo-caustic spin wave beams generated from subwavelength square well features arranged in a two-dimensional array. The lattice symmetry and the angle between the caustic beam propagation direction and the applied magnetic field were tailored to optimize the interaction of spin waves with the engineered defects. A prominent, narrow 3 MHz feature with large rejection efficiency is observed in the spin wave transmission spectrum that could be useful as a narrowband notch filter, and time- and space-resolved Brillouin light scattering (BLS) measurements suggest that both caustic interference and edge effects may contribute to this notch feature. Furthermore, the BLS measurements show that caustics are generated efficiently at the laser ablated wells, and by tuning the frequency by 30 MHz, the caustic beam angles and, hence, the details of how the spin wave caustics hit the ablated wells change sufficiently to add and remove caustic beams, which can be used to create additional device functionality. The generation and conversion of caustic beams show promise for applications that require directional energy transport and for magnonic devices.

Propagation of spin waves in a lattice of laterally and vertically coupled YIG microwaveguides by changing the magnetization angle in linear and nonlinear modes

Purpose. Investigation of the joint manifestation of the effects of anisotropic signal propagation, coupling, and nonlinear power dependence of the medium parameters in a lattice of laterally and vertically coupled spin-wave (SW) microwaveguides. Consideration of the case of the influence of the rotation of the magnetization angle and the change of the lateral gap between microwaveguides located on the same substrate on the transverse profile of the spin-wave beam and the spatial localization of the SW amplitude. Methods. The method of micromagnetic modeling based on the numerical solution of the Landau–Lifshitz–Hilbert equation shows the possibility of controlling the direction of propagation of SW in an ensemble of laterally and vertically coupled iron yttrium garnet (YIG) microwaveguides by changing the magnetization angle. By the method of numerical integration of the system of coupled discrete nonlinear Schrodinger equations, the possibility of changing the transverse profile of the spin-wave beam by changing the level of the initial signal amplitude is shown. Results. The spatial distributions of the components of the dynamic magnetization of the SW excited in two microwaveguides located on the same substrate obtained in micromagnetic simulations indicate a change in the character of localization of the SW power in the output sections of the microwaveguides. At variation of the lattice magnetization angle, a shift of the threshold power value is observed, at which a characteristic curbing of the transverse width of the spin-wave beam in the nonlinear mode appears. Conclusion. When excitation of surface magnetostatic SW in a lattice of laterally and vertically coupled microwaveguides, a transformation of the transverse profile of the wave is observed at a deviation of the magnetization angle of the structure by 15º , which is manifested in the change of the SW length and its localization in each of the microwaveguides. The combined effects of dipole coupling, gyrotropy, and nonlinearity of the medium make it possible to control the value of the threshold power of the SW, at which the mode of diffractionless propagation of the spin-wave beam is realized in a single layer of the structure.

Magnon-Optic Effects with Spin-Wave Leaky Modes: Tunable Goos-Hänchen Shift and Wood's Anomaly.

We demonstrate numerically how a spin wave (SW) beam obliquely incident on the edge of a thin film placed below a ferromagnetic stripe can excite leaky SWs guided along the stripe. During propagation, leaky waves emit energy back into the layer in the form of plane waves and several laterally shifted parallel SW beams. This resonance excitation, combined with interference effects of the reflected and re-emitted waves, results in the magnonic Wood's anomaly and a significant increase of the Goos-Hänchen shift magnitude. This yields a unique platform to control SW reflection and transdimensional magnonic router that can transfer SWs from a 2D platform into a 1D guided mode.

Caustic spin wave beams in soft thin films: Properties and classification

In the context of wave propagation, caustics are usually defined as the envelope of a finite-extent wavefront; folds and cusps in a caustic result in enhanced wave amplitudes. Here, we tackle a related phenomenon, namely, the existence of well-defined beams originating solely from the geometric properties of the corresponding dispersion relation. This directional emission, termed caustic beam, is enabled by a stationary group velocity direction, and has been observed first in the case of phonons. We propose an overview of this ``focusing'' effect in the context of spin waves excited in soft, thin ferromagnetic films. Based on an analytical dispersion relation, we provide tools for a systematic survey of caustic spin wave beams. Our theoretical approach is validated by time-resolved microscopy experiments using the magneto-optical Kerr effect. Then, we identify two cases of particular interest both from fundamental and applicative perspectives. Indeed, both of them enable broadband excitations (in terms of wave vectors) to result in narrow-band beams of low divergence.

High wave vector non-reciprocal spin wave beams

We report unidirectional transmission of micron-wide spin waves beams in a 55 nm thin YIG. We downscaled a chiral coupling technique implementing Ni80Fe20 nanowires arrays with different widths and lattice spacing to study the non-reciprocal transmission of exchange spin waves down to λ ≈ 80 nm. A full spin wave spectroscopy analysis of these high wavevector coupled-modes shows some difficulties to characterize their propagation properties, due to both the non-monotonous field dependence of the coupling efficiency, and also the inhomogeneous stray field from the nanowires.

Experimental methods for the study of spin waves

Purpose of this paper is to give an overview of various experimental methods for investigation of spin waves characteristics. Methods. The paper presents a description of a number of experimental techniques, such as the probing method, the phase shift method, the method of measure of equiphase dependences, the method of intersecting wave beams, and the use of Fourier analysis of the complex transfer coefficient of spin waves to determine their spatial spectrum. The conditions for using the listed methods and the characteristics of spin waves that one can measure by means of these methods are discussed in detail. Results. The paper presents a number of fundamental results that have been obtained on the basis of described methods. For example, the probing method was successfully used to visualize the amplitude and phase distribution of spin waves in the ferrite film plane and, in particular, it was used to experimentally confirm the previously predicted appearance of super-directed propagation of surface and backward volume spin wave beams. The phase-shift measurement method made it possible to measure the dispersion dependence of spin waves in ferrite structures such as ferrite – metal and ferrite – dielectric – metal, where measurements cannot be made by the probing method. The method of measuring equiphase dependences of spin waves made it possible, in particular, to measure for the first time with great accuracy the value of an external magnetic field magnetizing an yttrium iron garnet film to saturation in various crystallographic directions. The method of intersecting wave beams has made it possible to clarify the mechanism of parametric instability of surface spin waves. Fourier analysis of the complex transfer coefficient of spin waves allowed to determine the spatial spectrum of these waves; in particular, dispersion dependences of higher modes of the backward volume spin wave were first measured using this method. Conclusion. The methods described in this paper may continue to be successfully used for investigations of spin waves characteristics in various magnon crystals, ferrite structures and meta-structures.

All-magnonic Stern–Gerlach effect in antiferromagnets

The Stern–Gerlach (SG) effect is well known as the spin-dependent splitting of a beam of atoms carrying magnetic moments by a magnetic-field gradient, leading to the concept of electron spin. Antiferromagnets can accommodate two magnon modes with opposite spin polarizations, which is equivalent to the spin property of electrons. Here, we propose an all-magnonic SG effect in an antiferromagnetic magnonic system, where a linearly polarized spin-wave beam is deflected by a straight Dzyaloshinskii–Moriya interaction (DMI) interface into two opposite polarized spin-wave beams propagating in two discrete directions. Moreover, we observe bi-focusing of antiferromagnetic spin waves induced by a curved DMI interface, which can also spatially separate thermal magnons with opposite polarizations. Our findings provide a unique perspective to understand the rich phenomena associated with antiferromagnetic magnon spin and would be helpful for polarization-dependent application of antiferromagnetic spintronic devices.

Inelastic Spin-Wave Beam Scattering by Edge-Localized Spin Waves in a Ferromagnetic Thin Film

Spin waves are promising chargeless information carriers for the future, energetically efficient beyond CMOS systems. Among many advantages are the ease of achieving nonlinearity, the variety of possible interactions, and excitation types. Although the rapidly developing magnonic research has already yielded impressive realizations, multimode nonlinear effects, particularly with propagating waves and their nanoscale realizations, are still an open research problem. We theoretically study the dynamic interactions of spin waves confined to the edge of a thin ferromagnetic film with the spin-wave beam incident at this edge. We find inelastically scattered spin-wave beams at frequencies increased and decreased by the frequency of the edge spin-wave relative to the specularly reflected beam. We observe a strong dependence of the angular shift of the inelastic scattered spin-wave beam on the edge-mode frequency, which allows us to propose a magnonic demultiplexing of the signal encoded in spin waves propagating along the edge. Since dynamic magnetostatic interactions, which are ubiquitous in the spin-wave dynamics, are decisive in this process, this indicates the possibility of implementing the presented effects in other configurations and their use in magnonic systems.

Magnonic Metamaterials for Spin-Wave Control with Inhomogeneous Dzyaloshinskii-Moriya Interactions.

A magnonic metamaterial in the presence of spatially modulated Dzyaloshinskii–Moriya interaction is theoretically proposed and demonstrated by micromagnetic simulations. By analogy to the fields of photonics, we first establish magnonic Snell’s law for spin waves passing through an interface between two media with different dispersion relations due to different Dzyaloshinskii–Moriya interactions. Based on magnonic Snell’s law, we find that spin waves can experience total internal reflection. The critical angle of total internal reflection is strongly dependent on the sign and strength of Dzyaloshinskii–Moriya interaction. Furthermore, spin-wave beam fiber and spin-wave lens are designed by utilizing the artificial magnonic metamaterials with inhomogeneous Dzyaloshinskii–Moriya interactions. Our findings open up a rich field of spin waves manipulation for prospective applications in magnonics.

Collimated Bidirectional Propagating Spin Wave Generated by a Nonlocal Spin-Current Nano-oscillator

Pure spin currents, generated by nonlocal spin injection and spin-orbit effects, have been widely used to control magnetization reversal and dynamics by current without charge transfer and its side effects in the device's actual working region. Here we experimentally demonstrate that a single coherent spin-wave mode can be excited by the pure spin current in a nonlocal spin-injection spin-valve device. The microwave spectra show that the observed spin-wave frequency is higher than the ferromagnetic resonance frequency, and almost does not change with the excitation current at moderate magnetic fields, indicating that the observed dynamical mode is a linear propagating spin-wave mode. Furthermore, micromagnetic simulations based on our device geometry generally reproduce the experimentally observed field-dependent and current-dependent oscillation characteristics, and provide us with the additional spatial information that the spin-wave mode exhibits collimated and bidirectional propagation paths in the direction perpendicular to the applied magnetic field. Our simulation results also show that the current-local Oersted field in our nonlocal device is much smaller than in conventional nanocontact magnetic oscillators, and has a minimal impact on the spin-wave dynamics. A near-symmetrically-collimated and bidirectional propagating spin-wave beam with magnetic field--controllable beam direction and current-independent frequency, achieved in our demonstrated nonlocal spin-current nano-oscillator, can be used as a local spin-wave source for magnonic logic devices and can be used to build daisy-chaining oscillatory neural networks with mutual synchronization.

Building Blocks for Magnon Optics: Emission and Conversion of Short Spin Waves.

Magnons have proven to be a promising candidate for low-power wave-based computing. The ability to encode information not only in amplitude but also in phase allows for increased data transmission rates. However, efficiently exciting nanoscale spin waves for a functional device requires sophisticated lithography techniques and therefore, remains a challenge. Here, we report on a method to measure the full spin wave isofrequency contour for a given frequency and field. A single antidot within a continuous thin film excites wave vectors along all directions within a single excitation geometry. Varying structural parameters or introducing Dzyaloshinskii–Moriya interaction allows the manipulation and control of the isofrequency contour, which is desirable for the fabrication of future magnonic devices. Additionally, the same antidot structure is utilized as a multipurpose spin wave device. Depending on its position with respect to the microstrip antenna, it can either be an emitter for short spin waves or a directional converter for incoming plane waves. Using simulations we show that such a converter structure is capable of generating a coherent spin wave beam. By introducing a short wavelength spin wave beam into existing magnonic gate logic, it is conceivable to reduce the size of devices to the micrometer scale. This method gives access to short wavelength spin waves to a broad range of magnonic devices without the need for refined sample preparation techniques. The presented toolbox for spin wave manipulation, emission, and conversion is a crucial step for spin wave optics and gate logic.

Propagation of spin waves through a Néel domain wall

Spin waves have the potential to be used as a next-generation platform for data transfer and processing as they can reach wavelengths in the nanometer range and frequencies in the terahertz range. To realize a spin-wave device, it is essential to be able to manipulate the amplitude as well as the phase of spin waves. Several theoretical and recent experimental works have also shown that the spin-wave phase can be manipulated by the transmission through a domain wall (DW). Here, we study propagation of spin waves through a DW by means of micro-focused Brillouin light scattering microscopy (μBLS). The 2D spin-wave intensity maps reveal that spin-wave transmission through a Néel DW is influenced by a topologically enforced circular Bloch line in the DW center and that the propagation regime depends on the spin-wave frequency. In the first regime, two spin-wave beams propagating around the circular Bloch line are formed, whereas in the second regime, spin waves propagate in a single central beam through the circular Bloch line. Phase-resolved μBLS measurements reveal a phase shift upon transmission through the domain wall for both regimes. Micromagnetic modeling of the transmitted spin waves unveils a distortion of their phase fronts, which needs to be taken into account when interpreting the measurements and designing potential devices. Moreover, we show that, by means of micromagnetic simulations, an external magnetic field can be used to move the circular Bloch line within the DW and to manipulate spin-wave propagation.

Optical elements for anisotropic spin-wave propagation

We perform micromagnetic simulations to investigate the propagation of spin-wave beams through spin-wave optical elements. Despite spin-wave propagation in magnetic media being strongly anisotropic, we use axicons to excite spin-wave Bessel–Gaussian beams and gradient-index lenses to focus spin waves in analogy to conventional optics with light in isotropic media. Moreover, we demonstrate spin-wave Fourier optics using gradient-index lenses. Our results are valid for all three possible external magnetic field orientations and thus contribute to the growing field of spin-wave optics.

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.

Magnetic Skyrmion Tubes as Nonplanar Magnonic Waveguides

Various latest experiments have proven the theoretical prediction that domain walls in planar magnetic structures can channel spin waves as outstanding magnonic waveguides, establishing a superb platform for building magnonic devices. Recently, three-dimensional nanomagnetism has been boosted up and become a significant branch of magnetism, because three-dimensional magnetic structures expose a lot of emerging physics hidden behind planar ones and will inevitably provide broader room for device engineering. Skyrmions and antiSkyrmions, as natural three-dimensional magnetic configurations, are not considered yet in the context of spin-wave channeling and steering. Here, we show that skyrmion tubes can act as nonplanar magnonic waveguides if excited suitably. An isolated skyrmion tube in a magnetic nanoprism induces spatially separate internal and edge channels of spin waves; the internal channel has a narrower energy gap, compared to the edge channel, and accordingly can transmit signals at lower frequencies. Additionally, we verify that those spin-wave beams along magnetic nanoprism are restricted to the regions of potential wells. Transmission of spin-wave signals in such waveguides results from the coherent propagation of locally driven eigenmodes of skyrmions, i.e., the breathing and rotational modes. Finally, we find that spin waves along the internal channels are less susceptible to magnetic field than those along the edge channels. Our work will open a new arena for spin-wave manipulation and help bridge skyrmionics and magnonics.

Sub-micrometer near-field focusing of spin waves in ultrathin YIG films

We experimentally demonstrate tight focusing of a spin wave beam excited in extended nanometer-thick films of yttrium iron garnet by a simple microscopic antenna functioning as a single-slit near-field lens. We show that the focal distance and the minimum transverse width of the focal spot can be controlled in a broad range by varying the frequency/wavelength of spin waves and the antenna geometry. The experimental data are in good agreement with the results of numerical simulations. Our findings provide a simple solution for the implementation of magnonic nanodevices requiring a local concentration of the spin-wave energy.

Optically Inspired Nanomagnonics with Nonreciprocal Spin Waves in Synthetic Antiferromagnets.

Integrated optically inspired wave-based processing is envisioned to outperform digital architectures in specific tasks, such as image processing and speech recognition. In this view, spin waves represent a promising route due to their nanoscale wavelength in the gigahertz frequency range and rich phenomenology. Here, a versatile, optically inspired platform using spin waves is realized, demonstrating the wavefront engineering, focusing, and robust interference of spin waves with nanoscale wavelength. In particular, magnonic nanoantennas based on tailored spin textures are used for launching spatially shaped coherent wavefronts, diffraction-limited spin-wave beams, and generating robust multi-beam interference patterns, which spatially extend for several times the spin-wave wavelength. Furthermore, it is shown that intriguing features, such as resilience to back reflection, naturally arise from the spin-wave nonreciprocity in synthetic antiferromagnets, preserving the high quality of the interference patterns from spurious counterpropagating modes. This work represents a fundamental step toward the realization of nanoscale optically inspired devices based on spin waves.

Goos-Hänchen effect of spin waves at heterochiral interfaces

We theoretically investigate the Goos-H\"{a}nchen (GH) effect of spin-wave beams reflected from the interface between two ferromagnetic films with different Dzyaloshinskii-Moriya interactions (DMIs). The formula of the GH shift as functions of the incident angle and material parameters is derived analytically. We show that the GH effect occurs only when spin waves are totally reflected at the interface and vanishes otherwise. We further explore the GH shift of spin waves by narrow DMI strips of different widths. It is found that the induced shift is independent of the strip width down to $10$ nm, offering a novel approach to measure the DMI strength of ultra-narrow magnetic strips which is out the scope of current technology. Full micromagnetic simulations compare well with our theoretical findings. Strong distortion of edge magnetizations for narrower strips however generates a width dependence of the GH shift. The results presented in this work are helpful for understanding the GH effect in chiral magnets and for quantifying the DMI parameter in magnetic strips of sub-$50$ nm scales.