Time-resolved measurement of propagating spin waves in ferromagnetic thin films

Magnetic Interconnects Based on Composite Multiferroics

The development of magnetic logic devices dictates a need for a novel type of interconnect for magnetic signal transmission. Fast signal damping is one of the problems which drastically differs from conventional electric technology. Here, we describe a magnetic interconnect based on a composite multiferroic comprising piezoelectric and magnetostrictive materials. Internal signal amplification is the main reason for using multiferroic material, where a portion of energy can be transferred from electric to magnetic domains via stress-mediated coupling. The utilization of composite multiferroics consisting of piezoelectric and magnetostrictive materials offers flexibility for the separate adjustment of electric and magnetic characteristics. The structure of the proposed interconnect resembles a parallel plate capacitor filled with a piezoelectric, where one of the plates comprises a magnetoelastic material. An electric field applied across the plates of the capacitor produces stress, which, in turn, affects the magnetic properties of the magnetostrictive material. The charging of the capacitor from one edge results in the charge diffusion accompanied by the magnetization change in the magnetostrictive layer. This enables the amplitude of the magnetic signal to remain constant during the propagation. The operation of the proposed interconnects is illustrated by numerical modeling. The model is based on the Landau-Lifshitz-Gilbert equation with the electric field-dependent anisotropy term included. A variety of magnetic logic devices and architectures can benefit from the proposed interconnects, as they provide reliable and low-energy-consuming data transmission. According to the estimates, the group velocity of magnetic signals may be up to 10⁵ m/s with energy dissipation less than 10^-18 J per bit per 100 nm. The physical limits and practical challenges of the proposed approach are also discussed.

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.

Applications of nanomagnets as dynamical systems: II

In Part I of this topical review, we discussed dynamical phenomena in nanomagnets, focusing primarily on magnetization reversal with an eye to digital applications. In this part, we address mostly wave-like phenomena in nanomagnets, with emphasis on spin waves in myriad nanomagnetic systems and methods of controlling magnetization dynamics in nanomagnet arrays which may have analog applications. We conclude with a discussion of some interesting spintronic phenomena that undergird the rich physics exhibited by nanomagnet assemblies.

Effective phase noise considerations in magnon based parametric excitations

Magnon-phase is an important entity in the parametric processes involving magnons, yet the general qualitative and quantitative consequences of the phase-noise on nonlinear properties remain far from understood. In the current simulation-based theoretical study, we explore the direct impact the phase-noise has on non-linearity. We use analytical techniques usually employed in the study of hydrodynamics to explain the magnon-based nonlinear phenomena. The behavior of the threshold-field and growth rate of the magnons in the presence of Gaussian phase-noise is analytically predicted. These predictions are verified by micromagnetic simulations. Such results are of crucial importance in the design and engineering of both traditional and futuristic devices.

Magnetoelectric Spin Wave Modulator Based On Synthetic Multiferroic Structure

We describe a spin wave modulator - spintronic device aimed to control spin wave propagation by an electric field. The modulator consists of a ferromagnetic film serving as a spin wave bus combined with a synthetic multiferroic comprising piezoelectric and magnetostrictive materials. Its operation is based on the stress-mediated coupling between the piezoelectric and magnetostrictive materials. By applying an electric field to the piezoelectric layer, the stress is produced. In turn, the stress changes the direction of the easy axis in the magnetostrictive layer and affects spin wave transport. We present experimental data on a prototype consisting of a piezoelectric [Pb(Mg_1/3Nb_2/3)O₃]_(1-x) -[PbTiO₃]_x substrate, and 30 nm layer of magnetostrictive Ni film, where the film is attached to a 30 nm thick Ni₈₁Fe₁₉ spin wave bus. We report spin wave signal modulation in Ni₈₁Fe₁₉ layer by an electric field applied across the piezoelectric layer. The switching between the spin wave conducting and non-conducting states is achieved by applying ±0.3 MV/m electric field. We report over 300% modulation depth detected 80 μm away from the excitation port at room temperature. The demonstration of the spin wave modulator provides a new direction for spin-based device development by utilizing an electric field for spin current control.

Current-induced instability of domain walls in cylindrical nanowires

We study the current-driven domain wall (DW) motion in cylindrical nanowires using micromagnetic simulations by implementing the Landau-Lifshitz-Gilbert equation with nonlocal spin-transfer torque in a finite difference micromagnetic package. We find that in the presence of DW, Gaussian wave packets (spin waves) will be generated when the charge current is suddenly applied to the system. This effect is excluded when using the local spin-transfer torque. The existence of spin waves emission indicates that transverse domain walls can not move arbitrarily fast in cylindrical nanowires although they are free from the Walker limit. We establish an upper velocity limit for DW motion by analyzing the stability of Gaussian wave packets using the local spin-transfer torque. Micromagnetic simulations show that the stable region obtained by using nonlocal spin-transfer torque is smaller than that by using its local counterpart. This limitation is essential for multiple DWs since the instability of Gaussian wave packets will break the structure of multiple DWs.

A Magnetometer Based on a Spin Wave Interferometer

We describe a magnetic field sensor based on a spin wave interferometer. Its sensing element consists of a magnetic cross junction with four micro-antennas fabricated at the edges. Two of these antennas are used for spin wave excitation while two other antennas are used for detection of the inductive voltage produced by the interfering spin waves. Two waves propagating in the orthogonal arms of the cross may accumulate significantly different phase shifts depending on the magnitude and direction of the external magnetic field. This phenomenon is utilized for magnetic field sensing. The sensitivity attains its maximum under the destructive interference condition, where a small change in the external magnetic field results in a drastic increase of the inductive voltage, as well as in the change of the output phase. We report experimental data obtained for a micrometer scale Y₃Fe₂(FeO₄)₃ cross structure. The change of the inductive voltage near the destructive interference point exceeds 40 dB per 1 Oe. The phase of the output signal exhibits a π-phase shift within 1 Oe. The data are collected at room temperature. Taking into account the low thermal noise in ferrite structures, we estimate that the maximum sensitivity of the spin wave magnetometer may exceed attotesla.

Nanoscale spectrum analyzer based on spin-wave interference

We present the design of a spin-wave-based microwave signal processing device. The microwave signal is first converted into spin-wave excitations, which propagate in a patterned magnetic thin-film. An interference pattern is formed in the film and its intensity distribution at appropriate read-out locations gives the spectral decomposition of the signal. We use analytic calculations and micromagnetic simulations to verify and to analyze the operation of the device. The results suggest that all performance figures of this magnetoelectric device at room temperature (speed, area, power consumption) may be significantly better than what is achievable in a purely electrical system. We envision that a new class of low-power, high-speed, special-purpose signal processors can be realized by spin-waves.

Spin-wave propagation in cubic anisotropy materials

The information carrier of modern technologies is the electron charge whose transport inevitably generates Joule heating. Spin-waves, the collective precessional motion of electron spins, do not involve moving charges and thus avoid Joule heating [1-3]. In this respect, magnonic devices in which the information is carried by spin-waves attract interest for low-power computing. However implementation of magnonic devices for practical use suffers from low spin-wave signal and on/off ratio. Here we demonstrate that cubic anisotropy materials can enhance spin-wave signals by improving spin-wave amplitude as well as group velocity and attenuation length. Furthermore, cubic anisotropy material shows an enhanced on/off ratio through a laterally localized edge mode, which closely mimics the gate-controlled conducting channel in traditional field-effect transistors. These attractive features of cubic anisotropy materials will invigorate magnonics research towards wave-based functional devices.

Overcoming thermal noise in non-volatile spin wave logic

Spin waves are propagating disturbances in magnetically ordered materials, analogous to lattice waves in solid systems and are often described from a quasiparticle point of view as magnons. The attractive advantages of Joule-heat-free transmission of information, utilization of the phase of the wave as an additional degree of freedom and lower footprint area compared to conventional charge-based devices have made spin waves or magnon spintronics a promising candidate for beyond-CMOS wave-based computation. However, any practical realization of an all-magnon based computing system must undergo the essential steps of a careful selection of materials and demonstrate robustness with respect to thermal noise or variability. Here, we aim at identifying suitable materials and theoretically demonstrate the possibility of achieving error-free clocked non-volatile spin wave logic device, even in the presence of thermal noise and clock jitter or clock skew.

Giant nonreciprocal emission of spin waves in Ta/Py bilayers

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.

Non-volatile Clocked Spin Wave Interconnect for Beyond-CMOS Nanomagnet Pipelines

The possibility of using spin waves for information transmission and processing has been an area of active research due to the unique ability to manipulate the amplitude and phase of the spin waves for building complex logic circuits with less physical resources and low power consumption. Previous proposals on spin wave logic circuits have suggested the idea of utilizing the magneto-electric effect for spin wave amplification and amplitude- or phase-dependent switching of magneto-electric cells. Here, we propose a comprehensive scheme for building a clocked non-volatile spin wave device by introducing a charge-to-spin converter that translates information from electrical domain to spin domain, magneto-electric spin wave repeaters that operate in three different regimes - spin wave transmitter, non-volatile memory and spin wave detector, and a novel clocking scheme that ensures sequential transmission of information and non-reciprocity. The proposed device satisfies the five essential requirements for logic application: nonlinearity, amplification, concatenability, feedback prevention, and complete set of Boolean operations.

Spin excitations in solids from many-body perturbation theory

Collective spin excitations form a fundamental class of excitations in magnetic materials. As their energy reaches down to only a few meV, they are present at all temperatures and substantially influence the properties of magnetic systems. To study the spin excitations in solids from first principles, we have developed a computational scheme based on many-body perturbation theory within the full-potential linearized augmented plane-wave (FLAPW) method. The main quantity of interest is the dynamical transverse spin susceptibility or magnetic response function, from which magnetic excitations, including single-particle spin-flip Stoner excitations and collective spin-wave modes as well as their lifetimes, can be obtained. In order to describe spin waves we include appropriate vertex corrections in the form of a multiple-scattering T matrix, which describes the coupling of electrons and holes with different spins. The electron-hole interaction incorporates the screening of the many-body system within the random-phase approximation. To reduce the numerical cost in evaluating the four-point T matrix, we exploit a transformation to maximally localized Wannier functions that takes advantage of the short spatial range of electronic correlation in the partially filled d or f orbitals of magnetic materials. The theory and the implementation are discussed in detail. In particular, we show how the magnetic response function can be evaluated for arbitrary k points. This enables the calculation of smooth dispersion curves, allowing one to study fine details in the k dependence of the spin-wave spectra. We also demonstrate how spatial and time-reversal symmetry can be exploited to accelerate substantially the computation of the four-point quantities. As an illustration, we present spin-wave spectra and dispersions for the elementary ferromagnet bcc Fe, B2-type tetragonal FeCo, and CrO₂ calculated with our scheme. The results are in good agreement with available experimental data.

Spin wave nonreciprocity for logic device applications

The utilization of spin waves as eigenmodes of the magnetization dynamics for information processing and communication has been widely explored recently due to its high operational speed with low power consumption and possible applications for quantum computations. Previous proposals of spin wave Mach-Zehnder devices were based on the spin wave phase, a delicate entity which can be easily disrupted. Here, we propose a complete logic system based on the spin wave amplitude utilizing the nonreciprocal spin wave behavior excited by microstrip antennas. The experimental data reveal that the nonreciprocity of magnetostatic surface spin wave can be tuned by the bias magnetic field. Furthermore, engineering of the device structure could result in a high nonreciprocity factor for spin wave logic applications.

Time-domain measurement of current-induced spin wave dynamics

The performance of spintronic devices critically depends on three material parameters, namely, the spin polarization in the current (P), the intrinsic Gilbert damping (α), and the coefficient of the nonadiabatic spin transfer torque (β). However, there has been no method to determine these crucial material parameters in a self-contained manner. Here we show that P, α, and β can be simultaneously determined by performing a single series of time-domain measurements of current-induced spin wave dynamics in a ferromagnetic film.

Logic Devices with Spin Wave Buses - an Approach to Scalable Magneto-Electric Circuitry

We analyze spin wave-based logic circuits as a possible route to building reconfigurable magnetic circuits compatible with conventional electron-based devices. A distinctive feature of the spin wave logic circuits is that a bit of information is encoded into the phase of the spin wave. It makes possible to transmit information as a magnetization signal through magnetic waveguides without the use of an electric current. By exploiting sin wave superposition, a set of logic gates such as AND, OR, and Majority gate can be realized in one circuit. We present experimental data illustrating the performance of a three-terminal micrometer scale spin wave-based logic device fabricated on a silicon platform. The device operates in the GHz frequency range and at room temperature. The output power modulation is achieved via the control of the relative phases of two input spin wave signals. The obtained data shows the possibility of using spin waves for achieving logic functionality. The scalability of the spin wave-based logic devices is defined by the wavelength of the spin wave, which depends on the magnetic material and waveguide geometry. Potentially, a multifunctional spin wave logic gate can be scaled down to 0.1μm2. Another potential advantage of the spin wave-based logic circuitry is the ability to implement logic gates with fewer elements as compared to CMOS-based circuits in achieving same functionality. The shortcomings and disadvantages of the spin wave-based devices are also discussed.

Anisotropic propagation and damping of spin waves in a nanopatterned antidot lattice

All-electrical spin-wave spectroscopy, Brillouin light scattering, as well as the magneto-optical Kerr effect are combined to study spin-wave propagation through a magnetic antidot lattice nanopatterned into a Ni(80)Fe(20) thin film. The propagation velocities and, in particular, the relaxation are found to depend characteristically on the applied in-plane magnetic field. We explain the observed anisotropies by magnetic field-controlled spin-wave guiding in a network of interconnected nanowires which takes place over distances of up to 20  μm.

Feasibility study of logic circuits with a spin wave bus

We present a feasibility study of logic circuits utilizing spin waves for information transmission and processing. As an alternative approach to the transistor-based architecture, logic circuits with a spin wave bus do not use charge as an information carrier. In this work we describe the general concept of logic circuits with a spin wave bus and illustrate its performance by numerical simulations based on available experimental data. Theoretical estimates and results of numerical simulations on signal attenuation, signal phase velocity, and the minimum spin wave energy required per bit in the spin bus are obtained. The transport parameters are compared with ones for conventional electronic transmission lines. The spin wave bus is not intended to substitute traditional metal interconnects since it has higher signal attenuation and lower signal propagation speed. The potential value of a spin wave bus is, however, an interface between electronic circuits and integrated spintronics circuits. The logic circuits with a spin wave bus allow us to provide wireless read-in and read-out.

Spin wave dynamics and the determination of intrinsic damping in locally excited Permalloy thin films

Time-resolved scanning Kerr effect microscopy has been used to study magnetization dynamics in Permalloy thin films excited by transient magnetic pulses generated by a micrometer-scale transmission line structure. The results are consistent with magnetostatic spin wave theory and are supported by micromagnetic simulations. Magnetostatic volume and surface spin waves are measured for the same specimen using different bias field orientations and can be accurately calculated by k-space integrations over all excited plane wave components. A single damping constant of Gilbert form is sufficient to describe both scenarios. The nonuniform pulsed field plays a key role in the spin wave dynamics, with its Fourier transform serving as a weighting function for the participating modes. The intrinsic Gilbert damping parameter alpha is most conveniently measured when the spin waves are effectively stationary.