Article

# Nonreciprocity engineering in magnetostatic spin waves

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## Abstract

Magnetostatic surface spin waves (MSSW) excited from a coplanar waveguide antenna travel in different directions with different amplitudes. This effect, called nonreciprocity of MSSW, has been investigated by micromagnetic simulations. The ratio of amplitude of two counter propagating spin waves, the nonreciprocity parameter {\kappa}, is obtained for different ferromagnetic materials, such as NiFe (Py), CoFeAl, yttrium iron garnet (YIG), and GaMnAs. A device schematic has been proposed in which {\kappa} can be tuned to a large value by varying simple geometrical parameters of the device.

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... Thus, spin wave nonreciprocity can provide additional degrees of freedom for the control of signal propagation 13-17 . Spin wave nonreciprocity has large potential for applications in switches and logic devices due to selectively unidirectional spin wave propagation 12,18 , while in devices that require bidirectional signal propagation, the spin wave intensity should be the same in both directions 19 . ...
... The intensity difference is likely due to asymmetric field application, induced by the antenna, which is also www.nature.com/scientificreports/ observed in other studies 15,16,19 . Thus, the characteristics in sample B cannot be utilized for the control of asymmetric spin wave excitation and propagation, as reported in previous research 16 . ...
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Asymmetric spin wave excitation and propagation are key properties to develop spin-based electronics, such as magnetic memory, spin information and logic devices. To date, such nonreciprocal effects cannot be manipulated in a system because of the geometrical magnetic configuration, while large values of asymmetry ratio are achieved. In this study, we suggest a new magnetic system with two blocks, in which the asymmetric intensity ratio can be changed between 0.276 and 1.43 by adjusting the excitation frequency between 7.8 GHz and 9.4 GHz. Because the two blocks have different widths, they have their own spin wave excitation frequency ranges. Indeed, the spin wave intensities in the two blocks, detected by the Brillouin light scattering spectrum, were observed to be frequency-dependent, yielding tuneable asymmetry ratio. Thus, this study provides a new path to enhance the application of spin waves in spin-based electronics.
... We applied the total non-reflection effect on only a few of antidots in a plane YIG film to create a strong SW beam. To switch the direction of the beam we used the effect of non-reciprocal excitation of the surface spin waves by the microstrip antenna 18,41 . Moreover, we demonstrate by the micromagnetic simulations (MS) and iso-frequency curve method that the formation of a strong SW beam results from the refraction of SWs near the antidots in an area in which the internal magnetic field is reduced by the demagnetizing field. ...
... This component oscillates in antiphase on the two sides of the antenna, and is responsible for the changing of the SW propagation direction on reversal of the magnetic field 43 . The difference of SW intensities between SWs emitted on opposite sides of the microstripe obtained in MS is similar to the measured values, and reach 10, according with the literature data 41,44 . The result of simulations, a high-intensity narrow SWs beam propagating along the line of antidots, with an amplitude much larger than that of the incident plane SW is visible in Fig. 6(a). ...
Article
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The application of spin waves in communication with information encoded in amplitude and phase could replace or enhance existing microelectronic and microwave devices with significantly decreased energy consumption. Spin waves (SW) are usually transported in a magnetic material shaped to act as a waveguide. However, the implementation of SW transport and switching in plane homogeneous magnetic films and running as a narrow beam with a small divergence angle still present a challenge. We propose a realization of a strong SW switchers based on a patterned yttrium iron garnet (YIG) film that could serve as a magnonic fundamental building block. Our concept relies on the creation of a narrow beam of relatively short-wavelength SW by effect of a total non-reflection, found to be tied to refraction on the decreasing internal magnetic field, near a line of antidots at YIG. Nonreciprocal SW excitation by a microstrip antenna is used for controlling the direction of the signal flow. We demonstrate unique features of the propagation of microwave-excited SW beams, provide insight into their physics and discuss their potential applications in high-frequency devices.
... Due to the existence of the Au ground layer, the MSSW at the top surface is different from the one propagating along the bottom surface, leading to the nonreciprocal effect. The measure of this nonreciprocity is characterized by the ratio of the amplitude and the phase difference between the two counterpropagating MSSWs [30], [38] NR − Amplitude = 20 log 10 ...
... It is worth mentioning that without placing a neighbor metallic layer, the origin of the nonreciprocity of the MSSW stems from either the constructive or destructive interference between the in-and out-plane components of the RF signals. In this case, the magnitude of the counterpropagating MSSWs is different, while the phase is preserved [38]. This is different from our results: by placing a metallic layer underneath the NiFe film, both the magnitude and the phase are changed. ...
Article
Nonreciprocal spin wave propagation, induced by placing a neighboring metallic nonmagnetic layer, has been studied in metallic ferromagnetic thin films. The structure consists of a set of coupled microstrip transmission lines acting as antennas placed over a thin Ni₈₀Fe₂₀ layer. Nonreciprocal propagation of magnetostatic surface waves (MSSWs) has been observed. The nonreciprocal effect is evaluated by the amplitude ratio and the phase difference of the MSSWs traveling in opposite directions. By investigating the correlation between the device structure and the nonreciprocal effects, a maximum of -26.0 dB of the amplitude ratio and -180.0° phase difference were obtained. These results can be applied to optimize the nonreciprocal device.
... The specific property of the nonreciprocity might be a benefit for the enhancement of logic circuits based on magnetic waveguide. Therefore, the characterization and tuning of the nonreciprocity in magnonics has been intensively investigated (20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31), including the relation between the nonreciprocity and spin pumping (32) or Dzyaloshinskii-Moriya interaction (33,34). The nonreciprocity, due to its intrinsic characteristic in the magnetostatic surface wave (MSSW) mode (35), together with Joule-heat-free transport in GHz-frequencies (30) and compatibility with the spin Hall current system (36,37) makes spin wave one of the promising candidates for future data carriers. ...
... In order to confirm the spin pumping effect, we have performed the ferromagnetic resonance (FMR) measurements with the same devices of the spin pumping measurements. Taking the spin pumping effect into account, the presence of Ta layer enhances the damping parameter of Py above the intrinsic value (45,46), It must be noted that our observations are different from the earlier reports on spin wave nonreciprocity studied only in the MSSW mode (22,23,26,28). In order to compare our results with the MSSW mode, we have also measured the nonreciprocity value with sweeping in-plane magnetic field, Hy. ...
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Spin waves are propagating disturbances in the magnetization of magnetic materials. One of their interesting properties is nonreciprocity, exhibiting that their amplitude depends on the magnetization direction. Nonreciprocity in spin waves is of great interest in both fundamental science and applications because it offers an extra knob to control the flow of waves for the technological fields of logics and switch applications. We show a high nonreciprocity in spin waves from Ta/Py bilayer systems with out-of-plane magnetic fields. The nonreciprocity depends on the thickness of Ta underlayer, which is found to induce an interfacial anisotropy. The origin of observed high nonreciprocity is twofold: different polarities of the in-plane magnetization due to different angles of canted out-of-plane anisotropy and the spin pumping effect at the Ta/Py interface. Our findings provide an opportunity to engineer highly efficient, nonreciprocal spin wave–based applications, such as nonreciprocal microwave devices, magnonic logic gates, and information transports.
... The dispersion relation and excitation of spin waves mainly depend on the direction of spin wave propagation with respect to the magnetization direction. Most of the magnetic materials used in spin wave studies have an in-planeoriented magnetic easy axis, for instance, magnetostatic spin waves (MSSW) in Permalloy (NiFe), CoFeAl ferromagnetic thin films [15], dipole-exchange spin waves in Fe-N thin films [16], and spin wave resonance investigation in half metallic ferromagnets [17]. The studies on characterization of spin wave propagation in nanometer-thick YIG thin films which have in-plane anisotropy (IPA) were carried out in [18,19]. ...
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Magnetic insulating materials with perpendicular magnetic anisotropy bring an innovation to the existing spin-related technologies and magnonic applications. Yttrium iron garnet (YIG) stands out among other ferrimagnetic insulators due to its remarkable and unique properties. In this work, we represent perpendicular magnetic anisotropy (PMA) in relatively thick YIG films between 40 nm and 120 nm grown on Si (100) substrates. The strain at the interface of the Si substrate / YIG film promoted by the lattice mismatch resulted in a magnetic easy axis along the film normal. Excitation of standing spin wave modes within the films through ferromagnetic resonance was studied. Based on the ferromagnetic spectra, multiple spin wave modes were obtained in all films up to 120 nm. Spin wave modes along the lateral of the film originate from inhomogeneous confined magnetic regions on the film surface. Exchange stiffness constant of YIG films was estimated between 1.02×10⁻⁹ and 5.12 ×10⁻⁹ Oe.cm². We anticipate that these findings will bring up investment in advanced magnonics, insulator spintronics, and quantum information processing applications.
... On the other hand, the localized source of MW magnetic fields in a wide FM sam- ple and overall geometry of the PE experiment suggests non- locality of magnetization precession and the possibility for excitation of magnetostatic surface wave (MSSW). [57][58][59][60][61] In thin film geometry, the MSSW propagates with the wave vector ~ k aligned in-plane and perpendicular to the applied magnetic field, i.e., along the longest dimension of the FM sample in PE geometry. To capture the MSSW activity, we perform dynamic micromagnetic simulations employing a 2D 1 Â 1000 Â 12 mesh with 7 Â 0.05 Â 0.055 lm cells, fol- lowing Ref. 59. ...
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In this work, we propose and explore a sensitive technique for investigation of ferromagnetic resonance and corresponding magnetic properties of individual micro-scaled and/or weak ferromagnetic samples. The technique is based on coupling the investigated sample to a high-Q transmission line superconducting resonator, where the response of the sample is studied at eigen frequencies of the resonator. The high quality factor of the resonator enables sensitive detection of weak absorption losses at multiple frequencies of the ferromagnetic resonance. Studying the microwave response of individual micro-scaled permalloy rectangles, we have confirmed the superiority of fluxometric demagnetizing factor over the commonly accepted magnetometric one and have depicted the demagnetization of the sample, as well as magnetostatic standing wave resonance.
... Another key requirement for logic implementation is non-reciprocity, ie., controlling the direction of signal flow such that the output gets affected by the input and not the reverse. Recently, the non-reciprocal behavior of magnetostatic surface spin waves has been investigated for logic applications 24,25 . The origin of the non-reciprocity was the interference of the spin waves produced by two different components (in-plane and out-of-plane) of the magnetic field due to a current flowing through the waveguide. ...
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It is fortunate that the garnet films that support magnetostatic wave propagation are also transparent to infrared light in the range of wavelengths between 1 and 5 μm. This includes wavelengths of 1.3 μm and 1.5 μm, which are of particular interest for optical fiber communications systems. Since a single film can be used simultaneously as a waveguide for optical and magnetostatic modes, interactions between these modes can be exploited for devices such as microwave spectrum analyzers, optical frequency shifters, tunable optical filters, and optical beam deflectors.
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The characteristic modes of a thin slab magnetized in its plane are obtained in the magnetostatic limit,and the mode spectrum and configuration are discussed. The wavelength dependence of magnetostatic modedensity is determined and utilized to establish a connection to the modes obtained in the spin-wave approximation.In this geometry the modes lying above the spin-wave band are surface waves, decaying toward theinterior of the slab, while volume modes occur in the same frequency range as the long-wavelength limit ofthe spin-wave band of an infinite medium. The mode density exhibits poles at the upper and lower frequencylimits of the surface mode spectrum. The surface modes become statistically less important at shorter wavelengthsbecause the ratio of surface mode density to volume mode density varies approximately as 1/∣k∣.
Article
This book is designed to give the student a fundamental, in-depth understanding of all the essential features of the magnetic recording process for both high density disk and tape recording. The book provides a thorough grounding in four basic areas of magnetic recording: structure and fields of heads and media, the replay process, the recording process, and medium noise analysis. Besides the fundamental issues, key systems questions of nonlinearities, overwrite, side track phenomena, error rate estimates as well as comparisons of MR and inductive heads will be discussed. The student will be able to use the information presented to design and analyze key experiments for head and medium evaluation as well as for overall system performance decisions. A parallel treatment of time and frequency response will enable the student to evaluate signal processing schemes. The book is intended either for senior-year undergraduates or first-year graduates. It assumes that the reader has had basic introductory electrical engineering or physics courses such as electricity and magnetism and applied mathematics.
Article
This paper describes a systematic study of ferromagnetic resonance (FMR) carried out on a series of specimens of the ferromagnetic semiconductor Ga1-xMnxAs in thin film form. The GaMnAs layers were grown by low-temperature molecular beam epitaxy either on GaAs or on GaInAs buffers, the two buffers being used to obtain different strain conditions within the ferromagnetic layer. Our aim has been to map out the dependence of the FMR position on temperature and on the angle between the applied magnetic field and crystallographic axes of the sample. The analysis of the FMR data allowed us to obtain the values of the cubic and the uniaxial magnetic anisotropy fields---i.e., those which are associated with the natural (undistorted) zinc blende structure and those arising from of strain.
Article
The authors have investigated the possibility of utilizing spin waves for inter- and intra-chip communications, and as logic elements using both simulations and experimental techniques. Through simulations it has been shown that the decay lengths of magnetostatic spin waves are affected most by the damping parameter, and least by the exchange stiffness constant. The damping and dispersion properties of spin waves limit the attenuation length to several tens of microns. Thus, we have ruled out the possibility of inter-chip communications via spin waves. Experimental techniques for the extraction of the dispersion relationship have also been demonstrated, along with experimental demonstrations of spin wave interference for amplitude modulation. The effectiveness of spin wave modulation through interference, along with the capability of determining the spin wave dispersion relationships electrically during manufacturing and testing phase of chip production may pave the way for using spin waves in analog computing wherein the circuitry required for performing similar functionality becomes prohibitive.
Article
This review is devoted to both the experimental and theoretical aspects of lateral confinement effects observed for spin waves, with the wavevector in the 10 2-10 6 cm -1 range, where the magnetic dipole interaction plays the most important role. The Brillouin light scattering (BLS) technique is a powerful tool for the investigation of these effects. In addition to a high sensitivity, which is characteristic for a standard BLS system, we have extended the method to achieve high lateral spatial (30-50 mum), as well. As temporal (1-2 ns) resolution. This is central for the studies summarized in the review. Two representative experimental situations are reviewed: (1) Spin wave confinement in micron size laterally patterned structures (regular arrays of magnetic dots and wires). We focus on the quantization of spin wave wavevectors due to the lateral boundaries of a dot or a wire, and the influence of the static and dynamic coupling between islands. (2) Spatial, temporal and spatio-temporal confinement of linear and nonlinear spin waves in magnetic ferrite films. The formation, propagation, and collision of envelope solitons and their two-dimensional analogs (spin wave bullets) are analyzed. Both analytical and numerical models for spin waves in quasi-one-dimensional waveguides and in wide films are discussed
Article
Gilbert damping for the epitaxial Co <sub>2</sub> FeAl Heusler alloy films was investigated. Gilbert damping constant for the films was evaluated by analyzing the data of ferromagnetic resonance measured at the frequency of 2–20 GHz. Gilbert damping constant for the film without annealing was rather large, while it decreased remarkably with postannealing. Gilbert damping constant for the film annealed at 600 ° C was ≃0.001 . These behavior of Gilbert damping constant can be well explained by the fact that the density of states calculated from first principles decreases with increasing the degree of B2 order.
Article
GaAs-based diluted magnetic semiconductor, (Ga, Mn)As, with Mn composition x up to 0.07 was prepared by molecular-beam epitaxy on GaAs substrate at temperatures ranging from 160 to 320°C. Clear reflection high-energy electron diffraction oscillations were observed at the initial growth stage, indicating that the growth mode is two-dimensional. The lattice constant of (Ga, Mn)As films determined by X-ray diffraction showed a linear increase with the increase of Mn composition. Well-aligned in-plane ferromagnetic order was observed by magnetization measurements. Magnetotransport measurements also revealed the presence of ferromagnetic order in the (Ga, Mn)As layer. The easy axis of magnetization can be reversed by changing the strain direction in (Ga, Mn)As. superlattice structures with high crystal perfection and good interface quality were also prepared.
Article
Novel material properties can be realized by designing waves' dispersion relations in artificial crystals. The crystal's structural length scales may range from nano- (light) up to centimeters (sound waves). Because of their emergent properties these materials are called metamaterials. Different to photonics, where the dielectric constant dominantly determines the index of refraction, in a ferromagnet the spin-wave index of refraction can be dramatically changed already by the magnetization direction. This allows a different flexibility in realizing dynamic wave guides or spin-wave switches. The present review will give an introduction into the novel functionalities of spin-wave devices, concepts for spin-wave based computing and magnonic crystals. The parameters of the magnetic metamaterials are adjusted to the spin-wave k-vector such that the magnonic band structure is designed. However, already the elementary building block of an antidot lattice, the singular hole, owns a strongly varying internal potential determined by its magnetic dipole field and a localization of spin-wave modes. Photo-magnonics reveal a way to investigate the control over the interplay between localization and delocalization of the spin-wave modes using femtosecond lasers, which is a major focus of this review. We will discuss the crucial parameters to realize free Bloch states and how, by contrast, a controlled localization might allow to gradually turn on and manipulate spin-wave interactions in spin-wave based devices in the future.
Article
We report a time-resolved propagating spin wave spectroscopy for Fe19Ni81 film. We show that the amplitude of the spin-wave packet depends on the direction of magnetization and that its phase can be controlled by the polarity of pulsed magnetic field for the excitation. The nonreciprocal emission of spin-wave packet can be utilized for the binary spin-wave input into the spin-wave logic circuit.
Article
The energy bandgap of an insulator is large enough to prevent electron excitation and electrical conduction. But in addition to charge, an electron also has spin, and the collective motion of spin can propagate-and so transfer a signal-in some insulators. This motion is called a spin wave and is usually excited using magnetic fields. Here we show that a spin wave in an insulator can be generated and detected using spin-Hall effects, which enable the direct conversion of an electric signal into a spin wave, and its subsequent transmission through (and recovery from) an insulator over macroscopic distances. First, we show evidence for the transfer of spin angular momentum between an insulator magnet Y(3)Fe(5)O(12) and a platinum film. This transfer allows direct conversion of an electric current in the platinum film to a spin wave in the Y(3)Fe(5)O(12) via spin-Hall effects. Second, making use of the transfer in a Pt/Y(3)Fe(5)O(12)/Pt system, we demonstrate that an electric current in one metal film induces voltage in the other, far distant, metal film. Specifically, the applied electric current is converted into spin angular momentum owing to the spin-Hall effect in the first platinum film; the angular momentum is then carried by a spin wave in the insulating Y(3)Fe(5)O(12) layer; at the distant platinum film, the spin angular momentum of the spin wave is converted back to an electric voltage. This effect can be switched on and off using a magnetic field. Weak spin damping in Y(3)Fe(5)O(12) is responsible for its transparency for the transmission of spin angular momentum. This hybrid electrical transmission method potentially offers a means of innovative signal delivery in electrical circuits and devices.
Article
Ferromagnetism in manganese compound semiconductors not only opens prospects for tailoring magnetic and spin-related phenomena in semiconductors with a precision specific to III-V compounds but also addresses a question about the origin of the magnetic interactions that lead to a Curie temperature (T C) as high as 110 K for a manganese concentration of just 5%. Zener's model of ferromagnetism, originally proposed for transition metals in 1950, can explain T C of Ga1− xMnxAs and that of its II-VI counterpart Zn1− xMnxTe and is used to predict materials with T Cexceeding room temperature, an important step toward semiconductor electronics that use both charge and spin.
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