Spin Wave Interference Research Articles

Experimental prototype of a spin-wave majority gate

Featuring low heat dissipation, devices based on spin-wave logic gates promise to comply with increasing future requirements in information processing. In this work, we present the experimental realization of a majority gate based on the interference of spin waves in an Yttrium-Iron-Garnet-based waveguiding structure. This logic device features a three-input combiner with the logic information encoded in a phase of 0 or π of the input spin waves. We show that the phase of the output signal represents the majority of the three phase states of the spin waves in the three inputs. A switching time of about 10 ns in the prototype device provides evidence for the ability of sub-nanosecond data processing in future down-scaled devices.

Non-volatile spin wave majority gate at the nanoscale

A spin wave majority fork-like structure with feature size of 40 nm, is presented and investigated, through micromagnetic simulations. The structure consists of three merging out-of-plane magnetization spin wave buses and four magneto-electric cells serving as three inputs and an output. The information of the logic signals is encoded in the phase of the transmitted spin waves and subsequently stored as direction of magnetization of the magneto-electric cells upon detection. The minimum dimensions of the structure that produce an operational majority gate are identified. For all input combinations, the detection scheme employed manages to capture the majority phase result of the spin wave interference and ignore all reflection effects induced by the geometry of the structure.

Spin wave interference in YIG cross junction

This work is aimed at studying the interference between backward volume magnetostatic spin waves and magnetostatic surface spin waves in a magnetic cross junction. These two types of magnetostatic waves possess different dispersion with zero frequency overlap in infinite magnetic films. However, the interference may be observed in finite structures due to the effect magnetic shape anisotropy. We report experimental data on spin wave interference in a micrometer size Y3Fe2(FeO4)3 cross junction. There are four micro antennas fabricated at the edges of the cross arms. Two of these antennas located on the orthogonal arms are used for spin wave generation, and the other two antennas are used for the inductive voltage detection. The phase difference between the input signals is controlled by the phase shifter. Prominent spin wave interference is observed at the selected combination of operational frequency and bias magnetic field. The maximum On/Off ratio exceeds 30dB at room temperature. The obtained results are important for a variety of magnetic devices based on spin wave interference.

Magnonic interferometric switch for multi-valued logic circuits

We investigated a possible use of the magnonic interferometric switches in multi-valued logic circuits. The switch is a three-terminal device consisting of two spin channels where input, control, and output signals are spin waves. Signal modulation is achieved via the interference between the source and gate spin waves. We report experimental data on a micrometer scale prototype based on the Y3Fe2(FeO4)3 structure. The output characteristics are measured at different angles of the bias magnetic field. The On/Off ratio of the prototype exceeds 13 dB at room temperature. Experimental data are complemented by the theoretical analysis and the results of micro magnetic simulations showing spin wave propagation in a micrometer size magnetic junction. We also present the results of numerical modeling illustrating the operation of a nanometer-size switch consisting of just 20 spins in the source-drain channel. The utilization of spin wave interference as a switching mechanism makes it possible to build nanometer-scale logic gates, and minimize energy per operation, which is limited only by the noise margin. The utilization of phase in addition to amplitude for information encoding offers an innovative route towards multi-state logic circuits. We describe possible implementation of the three-value logic circuits based on the magnonic interferometric switches. The advantages and shortcomings inherent in interferometric switches are also discussed.

Ultrafast annular-magnetic-field-driven vortex-core reversals

By micromagnetic numerical simulations, we investigate the dynamics of vortex-core reversal in a soft magnetic nanodisk under the excitation of annular, perpendicular, resonant magnetic fields. The non-fundamental radial modes of the nanodisk are characterized into alternating radial-phase-regions for which two adjacent regions across a node point are in antiphase. We show that radial spin-waves excited by fields applied in the in-phase regions are in phase, and therefore generate strong magnetization oscillations resulting from constructive spin-wave interference. Such annular magnetic fields can substantially speed up the vortex-core reversal and lower the threshold field amplitude in comparison with the global field. Our work provides an efficient mechanism for spin-wave excitation and ultrafast vortex-core switching.

Prime factorization using magnonic holographic devices

Determining the prime factors of a given number N is a problem that requires super-polynomial time for conventional digital computers. A polynomial-time algorithm was invented by Shor for quantum computers. In this paper, we present experimental data that demonstrate prime factorization using spin-wave interference but without quantum entanglement. Prime factorization includes three major steps. First, a general-type computer calculates the sequence of numbers mkmod(N), where N is the number to be factorized, m is a randomly chosen positive integer, and k = 1, 2, 3, 4, 5, 6…. Next, the period of the calculated sequence r is determined by exploiting spin-wave interference. Finally, the general-type computer determines the primes based on the obtained r. The experiment for period finding was conducted on a six-terminal Y3Fe2(FeO4)3 device. We chose number 15 for testing and determined its primes using a sequence of measurements. The obtained experimental data for a micrometer-sized prototype aimed to demonstrate the benefits of using spin-wave devices to solve complex computational problems. Scalability is one of the major strengths inherent in this type of wave-based device, which may provide a route to nanometer-sized logic circuits. We discuss the physical and technological limitations of this approach, which define the maximum size of N and the computational speed. Although this classical approach cannot compete with the quantum algorithm in terms of efficiency, magnonic holographic devices can potentially be used as complementary logic units aimed at speeding up prime factorization for classical computers.

Phase stability of magnonic logic operation in microfabricated metallic wires

We measured magnon densities during spin-wave interference using microfocused Brillouin light scattering spectroscopy. Spatial mapping of the magnon density revealed that the spin-wave interference is confined in the central region of the microwire and indicated the contribution of higher-order transverse quantized modes than those reported to date. A micromagnetic simulation revealed transverse 100 nm interference patterns, which affect the signal-to-noise ratio of magnonic logic operation. These results will provide a way to design integrated magnonic devices such as all-magnon transistors.

Parallel Read-Out and Database Search With Magnonic Holographic Memory

In this paper, we present the most recent results on the development of magnonic holographic memory (MHM). MHM is a type of holographic device, which uses spin waves for data transfer and processing. The most appealing properties of MHM include parallel read-out and database search. We present experimental data showing parallel read-out of four magnetic memory states. In this experiment, the internal magnetic state is recognized by the level of the output inductive voltage produced by the spin-wave interference. We also present the experimental data showing database search in the MHM. In this experiment, the search for the maximum output is accomplished by utilizing spin-wave superposition. The experiments were carried out for six- and eight-terminal yttrium iron garnet-based prototypes. Potentially, magnonic holographic devices can be implemented as complementary memory/logic units to digital processors. Physical limitations and technological constraints of the spin-wave approach are also discussed.

Magnonic Holographic Read-Only Memory

In this work, we consider the possibility of building magnonic holographic read-only memory (MH-ROM) devices exploiting spin-wave interference for readout. MH-ROM consists of a grid of magnetic waveguides connected via cross junctions. Some of the cross junctions have a hole in the center of junctions, whereas others do not. The presence/absence of the hole is assigned to the memory states 0 and 1, respectively. We present experimental data showing spin-wave propagation modification in the Permalloy cross junction due to the presence of the hole. The results show prominent spin-wave modulation which is applicable for application in MH-ROM. Similar to the optical compact-disk ROM (CD-ROM), the internal memory states can be recognized via spin-wave interference. The advantages of using of spin waves instead of optical beams are scalability and compatibility with conventional electronic devices. The memory density scales inversely proportional to the operational wavelength. According to the estimates, the memory density of MH-ROM can be 1 Tb/cm 2 at wavelength λ = 100 nm. We discuss the physical limitations and physical constrains associated with the spin-wave interference. The development of MH-ROMs opens a new horizon for building scalable holographic devices compatible with conventional electronic devices.

Spin phase protection in interference of electron spin waves in lightly hydrogenated graphene

Here, we have realized the extremely light hydrogenation of a graphene surface on SiO2 by precisely controlling the amount of electron beam (EB) irradiation to a specific EB resist including hydrogen atoms, treated on graphene.

Magnonic Holographic Memory: From Proposal to Device

In this paper, we present recent developments in magnonic holographic memory devices exploiting spin waves for information transfer. The devices comprise a magnetic matrix and spin wave-generating/detecting elements placed on the edges of the waveguides. The matrix consists of a grid of magnetic waveguides connected via cross junctions. Magnetic memory elements are incorporated within the junction, while the read-in and read-out are accomplished by the spin waves propagating through the waveguides. We present the experimental data on spin-wave propagation through NiFe and yttrium iron garnet Y3Fe2(FeO4)3 (YIG) magnetic crosses. The obtained experimental data show prominent spin-wave signal modulation (up to 20 dB for NiFe and 35 dB for YIG) by the external magnetic field, where both the strength and the direction of the magnetic field define the transport between the cross arms. We also present the experimental data showing parallel read-out of two magnetic memory elements via spin-wave interference. The recognition between the four possible memory states is achieved via proper adjustment of the phases of the interfering spin waves. All experiments are done at room temperature. Magnonic holographic devices aim to combine the advantages of magnetic data storage with wave-based information transfer. We present estimates on the spin-wave holographic devices performance, including power consumption and functional throughput. According to the estimates, the magnonic holographic devices may provide data processing rates higher than $1\times 10^{18}$ b/cm2/s while consuming 0.15 mW. Technological challenges and fundamental physical limits of this approach are also discussed.

Realization of a micrometre-scale spin-wave interferometer.

The recent development of spin dynamics opens perspectives for various applications based on spin waves, including logic devices. The first important step in the realization of spin-wave-based logics is the manipulation of spin-wave interference. Here, we present the experimental realization of a micrometre-scale spin-wave interferometer consisting of two parallel spin-wave waveguides. The spin waves propagate through the waveguides and the superposition or interference of the electrical signals corresponding to the spin waves is measured. A direct current flowing through a metal wire underneath one of the spin-wave waveguides affects the propagation properties of the corresponding spin wave. The signal of constructive or destructive interference depends on the magnitude and direction of the applied direct current. Thus, the present work demonstrates a unique manipulation of spin-wave interference.

Pattern recognition with magnonic holographic memory device

In this work, we present experimental data demonstrating the possibility of using magnonic holographic devices for pattern recognition. The prototype eight-terminal device consists of a magnetic matrix with micro-antennas placed on the periphery of the matrix to excite and detect spin waves. The principle of operation is based on the effect of spin wave interference, which is similar to the operation of optical holographic devices. Input information is encoded in the phases of the spin waves generated on the edges of the magnonic matrix, while the output corresponds to the amplitude of the inductive voltage produced by the interfering spin waves on the other side of the matrix. The level of the output voltage depends on the combination of the input phases as well as on the internal structure of the magnonic matrix. Experimental data collected for several magnonic matrixes show the unique output signatures in which maxima and minima correspond to specific input phase patterns. Potentially, magnonic holographic devices may provide a higher storage density compare to optical counterparts due to a shorter wavelength and compatibility with conventional electronic devices. The challenges and shortcoming of the magnonic holographic devices are also discussed.

Cross Junction Spin Wave Logic Architecture

Backward volume magnetostatic spin wave interference in ferromagnetic cross is explored. Spin waves are excited at the two input arms of the cross, interference signal amplitude, and phase are detected in the other two, output arms of the cross. Spin wave scattering defines the out of phase interference in the output arms of the cross: the constructive (destructive) interference is observed at different input wave phase shifts in different output arms of the cross. Numeric simulations are in a good agreement with experiment. Based on the observed interference, we propose the cross junction spin wave logic device that operates as an OR or NOR logic gates. Spin wave phase represents the logic information. Destructive and constructive interference in the cross center determines the phase of the device output.

Non-equilibrium study of spin wave interference in systems with both Rashba and Dresselhaus (001) spin-orbit coupling

We study the electron spin transport in two dimensional electron gas (2DEG) system with both Rashba and Dresselhaus (001) spin-orbital coupling (SOC). We assume spatial behavior of spin precession in the non-equilibrium transport regime, and study also quantum interference induced by non-Abelian spin-orbit gauge field. The method we adopt in this article is the non-equilibrium Green's function within a tight binding framework. We consider one ferromagnetic lead which injects spin polarized electron to a system with equal strength of Rashba and Dresselhaus (001) SOC, and we observe the persistent spin helix property. We also consider two ferromagnetic leads injecting spin polarized electrons into a pure Dresselhaus SOC system, and we observe the resultant spin wave interference pattern.

Magnonic Holographic Memory

Holography is a technique based on the wave nature of light which allows us to utilize wave interference between the object beam and the coherent background. Holography is usually associated with images being made from light, however, this is only a narrow field of holography. The first holograms were designed for use with electron microscopes and it was not until a decade later with the advent of the laser that optical holographic images were popularized. Multiple other fields have had major contributions made by using wave interference to produce holograms, including acoustic holograms used in seismic applications, and microwave holography used in radar systems. Holography has been also recognized as a future data storing technology with unprecedented data storage capacity and ability to write and read a large number of data in a highly parallel manner. Here, we present a magnonic holographic memory device exploiting spin wave interference.

Current-induced modification of spin wave mode interference

We have studied the effect of adiabatic spin-transfer torque on mode interference of spin waves. The mode interference generates amplitude-localized spots at special positions which do not move with time. When applying current, the wavevector of spin wave is modified, resulting in current-dependent displacement of amplitude-localized spots. This current-dependent change in the mode interference may allow to probe current-induced spin wave Doppler shift in space-domain. In favorable situations, it can be used to estimate the intrinsic properties of magnetic materials such as spin polarization.

Azimuthal spin-wave modes in rolled-up permalloy microtubes: Tuneable mode frequency, mode patterns, and mode splitting

We investigated rolled-up permalloy microtubes using microwave absorption spectroscopy. The resonance frequencies of the tubes are tuneable by the external magnetic field. Up to four resonant azimuthal modes have been found and were attributed to constructive spin-wave interference in axial and perpendicular magnetization geometry. We show that the degeneracy of the mode can be lifted by applying a magnetic field in specified directions. The resonances of the system are described analytically. Thereby, an effective layer thickness and a demagnetization field are used to account for the multilayer structure and the curved surface, respectively. This modeling approach is supported by micromagnetic simulations.

Spin-wave interference in microscopic permalloy tubes

We present permalloy coated needles which act as spin-wave resonators. The permalloy coated needles were investigated using microwave absorption spectroscopy. Thereby, we found up to three resonant modes which correspond to constructively interfering azimuthal spin waves. The resonant modes are well reproduced in calculations based on an analytical model for the spin-wave dispersion employing periodic boundary conditions. The dependence of the resonance frequencies on the needles' radii and the external magnetic field is demonstrated experimentally.

Magnonic holographic devices for special type data processing

In this work, we consider the possibility of building magnetic analog logic devices utilizing spin wave interference for special task data processing. As an example, we consider a multi-terminal magnonic matrix switch comprising multiferroic elements and a two-dimensional grid of magnetic waveguides connected via four-terminal cross-junctions. The multiferroic elements are placed on the periphery of the switch and used as input/output ports for signal conversion among the electric and magnetic domains. Data processing is accomplished via the use of spin wave interference within the magnonic matrix. We present the results of numerical modeling illustrating device operation for pattern matching, finding the period of the data string, and image processing. We also present the results of numerical modeling showing the device capabilities as a magnetic holographic memory. Magnonic holographic devices are of great potential to complement the conventional general-type processors in special task data processing and may provide a new direction for functional throughput enhancement. According to estimates, magnonic holographic devices can provide up to 1 Tb/cm2 data storage density and data processing rate exceeding 1018 bits/s/cm2. The physical limitations and practical challenges of the proposed approach are discussed.