Spin-wave Transmission Research Articles

Nanomagnonic devices based on the spin-transfer torque.

Magnonics is based on signal transmission and processing by spin waves (or their quanta, called magnons) propagating in a magnetic medium. In the same way as nanoplasmonics makes use of metallic nanostructures to confine and guide optical-frequency plasmon-polaritons, nanomagnonics uses nanoscale magnetic waveguides to control the propagation of spin waves. Recent advances in the physics of nanomagnetism, such as the discovery of spin-transfer torque, have created possibilities for nanomagnonics. In particular, it was recently demonstrated that nanocontact spin-torque devices can radiate spin waves, serving as local nanoscale sources of signals for magnonic applications. However, the integration of spin-torque sources with nanoscale magnetic waveguides, which is necessary for the implementation of integrated spin-torque magnonic circuits, has not been achieved to date. Here, we suggest and experimentally demonstrate a new approach to this integration, utilizing dipolar field-induced magnonic nanowaveguides. The waveguides exhibit good spectral matching with spin-torque nano-oscillators and enable efficient directional transmission of spin waves. Our results provide a practical route for the implementation of integrated magnonic circuits utilizing spin transfer.

Ballistic transport of spin waves incident from cobalt leads across cobalt–gadolinium alloy nanojunctions

Calculations are presented for the scattering and ballistic transport of spin waves (SW) incident from cobalt leads, on ultrathin ferrimagnetic cobalt–gadolinium ‥Co][Co(1−c)Gd(c)]ℓ[Co‥ nanojunction systems. The nanojunction [Co(1−c)Gd(c)]ℓ itself is a randomly disordered alloy of thickness ℓ hcp lattice planes between matching hcp planes of the Co leads, at known stable concentrations c≤0.5 for this alloy system. To compute the spin dynamics, and the SW scattering and ballistic transport, this alloy nanojunction is modeled in the virtual crystal approximation (VCA), valid in particular at the length scale of the nanojunction for submicroscopic SW wavelengths. The phase field matching theory (PFMT) is applied to compute the localized and resonant magnons on the nanojunction. These magnons, characteristic of the embedded nanostructure, propagate in its symmetry plane with spin precession amplitudes that decay or match the spin wave states in the semi-infinite leads. The eigenvectors of these magnon modes are calculated for certain cases to illustrate the spin precession configurations on the nanojunction. The VCA-PFMT approach is also used to calculate the reflection and transmission spectra for the spin waves incident from the Co leads on the nanojunction. The results demonstrate resonance assisted maxima for the ballistic SW transmission spectra due to interactions between the incident spin waves and the nanojunction magnon modes. These properties are general for variable nanojunction thicknesses and alloy stable concentrations c≤0.5. In particular, the positions of the resonance assisted maxima of spin wave transmission can be modified with nanojunction thickness and alloy concentration.

Magnons in one-dimensional k-component Fibonacci structures

We have studied the magnon transmission through of one-dimensional magnonic k-component Fibonacci structures, where k different materials are arranged in accordance with the following substitution rule: Sn(k)=Sn−1(k)Sn−k(k) (n≥k=0,1,2,…), where Sn(k) is the nth stage of the sequence. The calculations were carried out in exchange dominated regime within the framework of the Heisenberg model and taking into account the RPA approximation. We have considered multilayers composed of simple cubic spin-S Heisenberg ferromagnets, and, by using the powerful transfer-matrix method, the spin wave transmission is obtained. It is demonstrated that the transmission coefficient has a rich and interesting magnonic pass- and stop-bands structures, which depends on the frequency of magnons and the k values.

Magnonic band gaps in waveguides with a periodic variation of the saturation magnetization

We present a micromagnetic analysis of spin-wave propagation in a magnonic crystal realized as a permalloy spin-wave waveguide with a spatial periodical variation of its saturation magnetization. Frequency band gaps were clearly observed in the spin-wave transmission spectra, and their origin is traced back to an overlap of individual band gaps of the fundamental and higher-order spin-wave width modes. The control of the depth, width, and position in frequency and space of the rejection band gaps by the width areas with a reduced magnetization and by the modulation level is discussed in this study.

Nanostripe of subwavelength width as a switchable semitransparent mirror for spin waves in a magnonic crystal

Spin wave transmission experiments are performed on a one-dimensional magnonic crystal (MC) where an injection pad for domain walls reverses the magnetization $M$ of selected nanostripes independently from the otherwise saturated MC. The MC consists of a periodic array of 255-nm-wide permalloy nanostripes with an edge-to-edge separation of 45 nm. In the experiment and simulations, we find that a single nanostripe with antiparallel $M$ performing opposite spin precession reduces significantly the transmission of long-wavelength spin waves. Our findings allow for the implementation and current-controlled operation of magnonic devices such as spin-wave-based logic on the nanoscale.

A micro-structured ion-implanted magnonic crystal

We investigate spin-wave propagation in a microstructured magnonic-crystal waveguide fabricated by localized ion implantation. The irradiation caused a periodic variation in the saturation magnetization along the waveguide. As a consequence, the spin-wave transmission spectrum exhibits a set of frequency bands, where spin-wave propagation is suppressed. A weak modification of the saturation magnetization by 7% is sufficient to decrease the spin-wave transmission in the band gaps by a factor of 10. These results evidence the applicability of localized ion implantation for the fabrication of efficient micron- and nano-sized magnonic crystals for magnon spintronic applications.

Perfect transmission of spin waves in a one-dimensional magnonic quasicrystal

Abstract Existence of the perfect transmission resonances of spin waves in a one-dimensional Thue–Morse magnonic quasicrystal is proposed. We find that occurrence of the perfect transmission just corresponds to the repeated bandedges in the bandedge map. Frequencies at the perfect transmissions for system with arbitrary generation order can be predicted by the bandedge map of the second and third order systems using two iterative schemes. These results show that density of the perfect transmission resonance increases exponentially for increasing the order of the system. However, the perfect transmissions are kept for higher order systems even if the peaks become denser.

Edge-state-dependent tunneling of dipole-exchange spin waves in submicrometer magnetic strips with an air gap

We have investigated the tunneling of dipole-exchange spin waves across an air gap in submicrometer-sized permalloy magnetic strips by means of micromagnetic simulations. The magnetizations beside the gap could form three distinct end-domain states with various strengths of dipolar coupling. Spin-wave tunneling through the gap at individual end-domain states is studied. It is found that the tunneling behavior is strongly dependent on these domain states. Nonmonotonic decay of transmission of spin waves with the increase of the gap width is observed. The underlying mechanism for these behaviors is proposed. The tunneling characteristics of the dipole-exchange spin waves differ essentially from those of the magnetostatic ones reported previously.

Dissipative Soliton Oscillator With a Nonlinear Spin Wave Transmission Line and a Signal-to-Noise Enhancer in the Feedback Loop

This study reports on a dissipative soliton oscillator utilizing two nonlinear magnetostatic spin wave (MSW) devices in a feedback loop. Both nonlinear MSW devices [a spin wave transmission line (TL) and a signal-to-noise enhancer (SNE)] operate in the frequency band where three-wave parametric processes are allowed. Self-generation of a complex-modulated MW signal is caused by nonlinearity of the spin wave TL. The SNE carries out a passive locking of the spin wave self-modulation frequencies and forms the dissipative soliton trains. It is shown, that electronic control of a repetition interval and pulse ratio of dissipative solitons is realized by the change of a klystron beam current.

Magnonic Spin-Transfer Torque and Domain Wall Propagation

Magnonic spin-transfer torque (STT) is introduced. In comparison with electronic STT, magnonic STT is more efficient in driving domain wall (DW) propagation along a magnetic nanowire because of the total spin wave transmission through a DW. Furthermore, the energy consumption is more than millions times lower than that by electronic STT when the magnonic STT is used to drive a DW to propagate at a practically useful speed.

Passage of two-frequency signals in the Bragg resonance band of a one-dimensional magnon crystal

Passage of a two-frequency signal with high and low power levels through a spin-wave transmission line with a one-dimensional periodic microstructure formed on the surface of a ferromagnetic film is experimentally studied. Experiments are carried out under the condition of three-wave parametric instability of spin waves. It is shown that, near the central frequency of the first Bragg resonance at certain power levels of the large and small signals, the nonlinear spin-wave transmission line can operate as either a power limiter or a signal-to-noise enhancer.

Enhanced Transmission through Squeezed Modes in a Self-Cladding Magnonic Waveguide

We study spin-wave propagation in 360-nm wide Ni(80)Fe(20) nanowires using all-electrical spin-wave spectroscopy. Creating a zigzag-like magnetization state, we find enhanced spin-wave transmission compared to the states of more homogeneous magnetization. Micromagnetic simulations show that the spin waves propagate in narrow channels, which in particular, are remotely positioned from the edges. The internal channels reflect field-controlled self-cladding. Interestingly, rotation of the magnetic field at a specific value is found to vary the propagation velocity without changing the eigenfrequency. This opens the perspective of the velocity modulation transistor following a concept known from semiconductor electronics.

Enhanced functionality in magnonics by domain walls and inhomogeneous spin configurations

This paper discusses nanomagnetic structures enabling the manipulation of propagating spin waves. We address in particular how domain walls, or more generally speaking inhomogeneous spin configurations, enhance the control of spin-wave transmission and thereby the functionality of magnonic devices. Three different microscopic mechanisms are outlined, considering an interference device, a spin-wave bus and a magnonic crystal. Inhomogeneous spin configurations are argued to shift the spin-wave phase, guide spin waves in nanochannels and allow for reprogrammable spin-wave band structures in periodic nanostructures, respectively. Such devices and functionalities are relevant for further developments in magnonics.

Unattenuated conical spin wave in spiral magnet: The role of Dzyaloshinskii-Moriya interaction

A direct inter-conversion between conduction electron spin-current and spin wave spin-current has been experimentally realized in Pt/Y3Fe5O12 and Pt/Y3Fe5O12/Pt heterostructures [Y. Kajiwara et al., Nature 464, 262 (2010)]. We investigate the dynamics of this inter-conversion in an in-plane spiral magnet with the nearest-neighboring interaction and Dzyaloshinskii-Moriya interaction, using the modified Landau-Lifshitz-Gilbert equation. The calculations indicate that an unattenuated conical spin wave in the spiral magnet can be excited by a spin-torque representing a conduction-electron spin-current. The substantial role of the Dzyaloshinskii-Moriya interaction in stabilizing such unattentuated spin wave transmission is revealed. In addition, the influences of the spin-torque term and damping coefficient on the stability of the spin wave transmission are discussed.

Employing magnonic crystals to dictate the characteristics of auto-oscillatory spin-wave systems

Spin-wave active rings–positive-feedback systems incorporating spin-wave waveguides–provide important insight into fundamental magnetics, enable experimental investigations into nonlinear wave phenomena, and potentially find application in microwave electronics. Such rings break into spontaneous, monomode oscillation at a certain threshold value of feedback gain. In general, the wavenumber of this initially excited, threshold mode is impossible to predict precisely. Here we discuss how, by exploiting resonant spin-wave reflections from a magnonic crystal, an active ring system having a threshold mode with a well-defined and precisely predictable wavenumber may be realized. Our work suggests that study and development of active ring systems incorporating magnonic crystals may deliver useful insight into spin-wave transmission in structured magnetic films as well as devices with technological applicability.

Spin information transfer and transport in hybrid spinmechatronic structures

Spin waves have long been recognized as potential signal carriers in spintronic devices. However, practical development of spin wave based information platforms is its infancy. To date, work in this area has focused on one-dimensional topologies based on purely magnetic thin-film transmission systems, typically exploiting interference phenomena to perform logical operations. In this paper, we describe an alternative approach in which spinmechatronic structures combining spin-wave transmission systems with magnetically loaded micro- and nano-mechanical elements provide spin-information processing functionality.

Formation of narrow spin-wave transmission bands in lateral magnetic superlattices

It is shown theoretically that an alternating magnetic field applied locally to a stripe periodic heterostructure with different saturation magnetizations, ${M}_{1}$ and ${M}_{2}$, excites dipolar spin waves, which are able to propagate along the periodicity direction within a narrow frequency band $(\ensuremath{\Delta}\ensuremath{\omega}/\ensuremath{\omega}<5\mathrm{%})$ in the absence of Bragg scattering. A mechanism is found for trapping the out-of-band modes inside a potential well whose formation is mediated by spin pinning at the ${M}_{1}/{M}_{2}$ interfaces.

Magnonic crystal based forced dominant wavenumber selection in a spin-wave active ring

Spontaneous excitation of the dominant mode in a spin-wave active ring—a self-exciting positive-feedback system incorporating a spin-wave transmission structure—occurs at a certain threshold value of external gain. In general, the wavenumber of the dominant mode is extremely sensitive to the properties and environment of the spin-wave transmission medium, and is almost impossible to predict. In this letter, we report on a backward volume magnetostatic spin-wave active ring system incorporating a magnonic crystal. When mode enhancement conditions—readily predicted by a theoretical model—are satisfied, the ring geometry permits highly robust and consistent forced dominant wavenumber selection.

Formation of nonlinear magnetization oscillations by spin waves transmission through the boundary of two uniaxial ferromagnets

In this paper, the possibility of nonlinear spin wave formation at transmission of a bulk spin wave through the boundary of two ferromagnets with uniaxial magnetic anisotropy in the external magnetic field was shown at the certain conditions. The bulk spin waves with different values of precession angles of magnetizations can propagate in the second ferromagnet so both linear and nonlinear states can be excited. Also, expressions for coefficients of reflection and transmission of spin waves were obtained depending on value of a precession angle of magnetization in the second ferromagnet.

Nanostructured Magnonic Crystals with Size-Tunable Bandgaps

Just as a photonic crystal is a periodic composite composed of materials with different dielectric constants, its lesser known magnetic analogue, the magnonic crystal can be considered as a periodic composite comprising different magnetic materials. Magnonic crystals are excellent candidates for the fabrication of nanoscale microwave devices, as the wavelengths of magnons in magnonic crystals are orders of magnitude shorter than those of photons, of the same frequency, in photonic crystals. Using advanced electron beam lithographic techniques, we have fabricated a series of novel bicomponent magnonic crystals which exhibit well-defined frequency bandgaps. They are in the form of laterally patterned periodic arrays of alternating cobalt and permalloy stripes of various widths ranging from 150 to 500 nm. Investigations by Brillouin light scattering and computer modeling show that the dispersion spectrum of these crystals is strongly dependent on their structural dimensions. For instance, their first frequency bandgap is found to vary over a wide range of 1.4-2.6 gigahertz. Such a functionality permits the tailoring of the bandgap structure which controls the transmission of information-carrying spin waves in devices based on these crystals. Additionally, it is observed that the bandgap width decreases with increasing permalloy stripe width, but increases with increasing cobalt stripe width, and that the bandgap center frequency is more dependent on the stripe width of permalloy than that of cobalt. This information would be of value in the design of magnonic crystals for potential applications in the emerging field of magnonics.