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In this work, we consider a type of magnetic memory where information is encoded into the mutual arrangements of magnets. The device is an active ring circuit comprising magnetic and electronic parts connected in series. The electric part includes a broad-band amplifier, phase shifters, and attenuators. The magnetic part is a mesh of magnonic waveguides with magnets placed on the waveguide junctions. There are amplitude and phase conditions for auto-oscillations to occur in the active ring circuit. The frequency(s) of the auto-oscillation and spin wave propagation route(s) in the magnetic part depends on the mutual arrangement of magnets in the mesh. The propagation route is detected with a set of power sensors. The correlation between circuit parameters and spin wave route is the base of memory operation. The combination of input/output switches connecting electric and magnetic parts, and electric phase shifters constitute the memory address. The output of power sensors is the memory state. We present experimental data on the proof-of-the-concept experiments on the prototype with just three magnets placed on top of a single-crystal yttrium iron garnet Y3Fe2(FeO4)3 (YIG) film. The results demonstrate a robust operation with On/Off ratio for route detection exceeding 35 dB at room temperature. The number of propagation routes scales factorial with the size of the magnetic part. Coding information in propagation routes makes it possible to drastically increase the data storage density compared to conventional memory devices. MCM with just 25 magnets can store as much as 25! (10 Yotta) bits. Physical limits and constraints are also discussed.

Traveling Salesman Problem (TSP) is a decision-making problem that is essential for a number of practical applications. Today, this problem is solved on digital computers exploiting Boolean-type architecture by checking one by one a number of possible routes. In this work, we describe a special type of hardware for the TSP solution. It is a magnonic combinatorial device comprising magnetic and electric parts connected in the active ring circuit. There is a number of possible propagation routes in the magnetic mesh made of phase shifters, frequency filters, and attenuators. The phase shifters mimic cities in TSP while the distance between the cities is encoded in the signal attenuation. The set of frequency filters makes the waves on different frequencies propagate through the different routes. The principle of operation is based on the classical wave superposition. There is a number of waves coming in all possible routes in parallel accumulating different phase shifts and amplitude damping. However, only the wave(s) that accumulates the certain phase shift will be amplified by the electric part. The amplification comes first to the waves that possess the minimum propagation losses. It makes this type of device suitable for TSP solution, where waves are similar to the salesmen traveling in all possible routes at a time. We present the results of numerical modeling illustrating the TSP solutions for four and six cities. Also, we present experimental data for the TSP solution with four cities., Comment: 10 figures, 28 pages, and Supplementary materials

In this work, we present experimental data demonstrating the feasibility of magnetic object location using spin waves. The test structure includes a Y$_3$Fe$_2$(FeO$_4$)$_3$) (YIG) film with four micro-antennas placed on the edges. A constant in-plane bias magnetic field is provided by NdFeB permanent magnet. Two antennas are used for spin wave excitation while the other two are used for the inductive voltage measurement. There are nine selected places for the magnet on the film. The magnet was subsequently placed in all nine positions and spin wave transmission and reflection were measured. The obtained experimental data show the difference in the output signal amplitude depending on the magnet position. All nine locations can be identified by the frequency and the amplitude of the absolute minimum in the output power. All experiments are accomplished at room temperature. Potentially, spin waves can be utilized for remote magnetic bit read-out. The disadvantages and physical constraints of this approach are also discussed.

In this work, we describe a logic device in which an act of computation is associated with finding a path connecting input and output ports. The device is based on an active ring circuit comprising electric and magnetic parts. The electric part includes an amplifier, a phase shifter, and an attenuator. The magnetic part is a multi-port magnetic matrix comprising delay lines and frequency filters. Signals propagating on different paths may accumulate different phase shifts. Auto-oscillations occur in the circuit when the magnetic and electric parts match each other to meet the resonance amplitude and phase conditions. The system naturally searches for a resonance path that depends on the position of the electric phase shifter and amplification level. The path is detected by the set of power sensors. The proposed logic device can be used for solving a variety of computational problems. We present the results of numerical modeling illustrating prime factorization and finding the shortest path connected selected points on the mesh., Comment: 45 pages, 14 figures

In this letter, we present experimental data demonstrating spin wave interference detection using spin Hall effect (ISHE). Two coherent spin waves are excited in a yttrium-iron garnet (YIG) waveguide by continuous microwave signals. The initial phase difference between the spin waves is controlled by the external phase shifter. The ISHE voltage is detected at a distance of 2 mm and 4 mm away from the spin wave generating antennae by an attached Pt layer. Experimental data show ISHE voltage oscillation as a function of the phase difference between the two interfering spin waves. This experiment demonstrates an intriguing possibility of using ISHE in spin wave logic circuit converting spin wave phase into an electric signal

Quantum computing is an emerging field of science which will eventually lead us to new and powerful logic devices with capabilities far beyond the limits of current transistor-based technology. There are certain types of problems which quantum computers can solve fundamentally faster than the tradition digital computers. There are quantum algorithms which require both superposition and entanglement (e.g. Shor algorithm). But neither the Grover algorithm nor the very first quantum algorithm due to Deutsch and Jozsa need entanglement. Is it possible to utilize classical wave superposition to speedup database search? This interesting question was analyzed by S. Lloyd. It was concluded that classical devices that rely on wave interference may provide the same speedup over classical digital devices as quantum devices. There were several experimental works using optical beam superposition for emulating Grover algorithm. It was concluded that the use of classical wave superposition comes with the cost of exponential increase of the resources. Since then, it is widely believed that the use of classical wave superposition for quantum algorithms is inevitably leading to an exponential resources overhead (number of devices, power consumption, precision requirements). In this work, we describe a classical Oracle machine which utilizes classical wave superposition for database search and data processing. We present experimental data on magnetic database search using spin wave superposition. The data show a fundamental speedup over the digital computers without any exponential resource overhead. We argue that in some cases the classical wave-based approach may provide the same speedup in database search as quantum computers.

In this work, we consider the possibility of energy storage enhancement in electric capacitors using the compensational method. The essence of the proposed approach is the use of inductive voltage V_ind to partially compensate the electrostatic voltage q/C produced by the electric charges on the capacitor plates. We hypothesize that it may be possible to increase the amount of charge stored on the plates before the breakdown and increase the energy stored in the capacitor using the compensational inductive voltage. There are several possible scenarios of manipulating the inductive voltage to increase the amount of energy released via the discharge. We also consider several electro-magnetic capacitors for practical utilization. Potentially, the energy per volume stored in a simple parallel plate capacitor may exceed the one of gasoline. The physical limits and technological shortcomings of the proposed approach are also discussed., Comment: 14 pages, 6 figures

The low-frequency amplitude and phase noise spectra of magnetization waves, i.e. magnons, was measured in the yttrium iron garnet (YIG) waveguides. This type of noise, which originates from the fluctuations of the physical properties of the YIG crystals, has to be taken into account in the design of YIG-based RF generators and magnonic devices for data processing, sensing and imaging applications. It was found that the amplitude noise level of magnons depends strongly on the power level, increasing sharply at the on-set of nonlinear dissipation. The noise spectra of both the amplitude and phase noise have the Lorentzian shape with the characteristic frequencies below 100 Hz., Comment: 4 pages, 5 figures

We report results of micro-Brillouin-Mandelstam light scattering spectroscopy of thermal magnons in the two-phase synthetic multiferroic structure consisting of a piezoelectric (PMN-PT) substrate and a Ni thin film with the thickness of 64 nm. The experimental data reveal the first two modes of the perpendicular standing spin waves (PSSW) spatially confined across the Ni thin film. A theoretical analysis of the frequency dependence of the PSSW peaks on the external magnetic field reveals the asymmetric boundary condition, i.e. pinning, for variable magnetization at different surfaces of the Ni thin film. The strain field induced by applying DC voltage to PMN-PT substrate leads to a down shift of PSSW mode frequency owing to the magneto-elastic effect in Ni, and corresponding changes in the spin wave resonance conditions. The observed non-monotonic dependence of the PSSW frequency on DC voltage is related to an abrupt change of the pinning parameter at certain values of the voltage. The obtained results are important for understanding the thermal magnon spectrum in ferromagnetic films and development of the low-power spin-wave devices., Comment: 15 pages, 6 figures

We propose an oscillatory neural network implemented with two-dimensional tantalum disulfide devices operating in the change density wave regime at room temperature. An elementary cell of the network consists of two 1T-TaS2 devices connected in series. Such a cell has constant output and oscillatory states. All cells have the same bias voltage. There is constant current flowing through the cell in the constant output mode. The oscillations occur at a certain bias voltage due to the electrical-field driven metal-to-insulator transition owing to the changes in the charge density wave phase in the 1T-TaS2 channel. Two 1T-TaS2 devices oscillate out-of-phase where one of the devices is in the insulator phase while the other one is in the metallic state. The nearest-neighbor cells are coupled via graphene transistors. The cells are resistively coupled if the graphene transistor is in the On state while they are capacitively coupled if the transistor is in the Off state. The operation of the oscillatory neural network is simulated numerically for the 30x30 node network. The results of our numerical modeling show the formation of artificial vortexes and cellular-automata type data processing. The two-dimensional 1T-TaS2 devices, utilized in the network, offer a unique combination of properties such as scalability, high operational frequency, fast synchronization speed, and radiation hardness, which makes them promising for both consumer electronic and defense applications.

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 several 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 the 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.

We propose and develop a concept of magnonic logic gates enabling reversible computing. The gates consist of passive elements: waveguides, cross-junctions and phase shifters. Logical 0 and 1 are encoded in the relative phase of the propagating spin wave packets (0 or {\pi}). The gates contain several possible trajectories for each packet to propagate from the input to the output. Re-direction of the spin wave packets among the possible trajectories is due to the interference in the magnetic cross-junctions. Two wave packets coming to the cross-junction in-phase propagate through the junction without reflection. Two packets coming out-of-phase to the junction are completely reflected back. The operation of the cross-junction is illustrated by numerical modeling. We estimate the power dissipation in the proposed circuits and the feasibility of cascading such magnetic devices in large circuits. The proposed gates may potentially provide a route to magnetic reversible logic circuitry with power dissipation less than kT per operation.

In this work, we consider the possibility of using synthetic multiferroics comprising piezoelectric and magnetostrictive materials as an interconnect for nano magnetic logic circuits. The proposed interconnect resembles a parallel plate capacitor filled with a piezoelectric, where one of the plates is made of a magnetoelastic material. The operation of the interconnect is based on the effect of stress-mediated anisotropy modulation, where an electric field applied across the piezoelectric material produces stress, which, in turn, affects the anisotropy field in the magnetostrictive material. We present the results of numerical modeling illustrating signal propagation through the interconnect. The model combines electric and magnetic parts, where the electric part describes the distribution of an electric field through the piezoelectric and the magnetic part describes the change of magnetization in the magnetoelastic layer. The model is based on the Landau-Lifshitz-Gilbert equation with the electric field dependent anisotropy term included. The utilization of the electro-magnetic coupling makes it possible to amplify magnetic signal during its propagation via energy conversion from the electric to magnetic domains. Potentially, synthetic multiferroic interconnects can be implemented in a variety of spin-based devices ensuring reliable and low-energy consuming data transmission. According to the estimates, the group velocity of magnetic signals may be up to 100 km/s with energy dissipation less than aJ per bit per 100nm. The fundamental limits and practical shortcoming of the proposed approach are also discussed., Comment: 10 pages, 3 figures, 1 table

Graphene revealed a number of unique properties beneficial for electronics. However, graphene does not have an energy band-gap, which presents a serious hurdle for its applications in digital logic gates. The efforts to induce a band-gap in graphene via quantum confinement or surface functionalization have not resulted in a breakthrough. Here we show that the negative differential resistance experimentally observed in graphene field-effect transistors of "conventional" design allows for construction of viable non-Boolean computational architectures with the gap-less graphene. The negative differential resistance - observed under certain biasing schemes - is an intrinsic property of graphene resulting from its symmetric band structure. Our atomistic modeling shows that the negative differential resistance appears not only in the drift-diffusion regime but also in the ballistic regime at the nanometer-scale - although the physics changes. The obtained results present a conceptual change in graphene research and indicate an alternative route for graphene's applications in information processing., Comment: 15 pages with 5 figures

We describe and analyze magnonic logic circuits enabling parallel data processing on multiple frequencies. The circuits combine bi-stable (digital) input/output elements and an analog core. The data transmission and processing within the analog part is accomplished by the spin waves, where logic 0 and 1 are encoded into the phase of the propagating wave. The latter makes it possible to utilize a number of bit carrying frequencies as independent information channels. The operation of the magnonic logic circuits is illustrated by numerical modeling. We also present the estimates on the potential functional throughput enhancement and compare it with scaled CMOS. The described multi-frequency approach offers a fundamental advantage over the transistor-based circuitry and may provide an extra dimension for the Moor's law continuation. The shortcoming and potentials issues are also discussed.

We propose a concept of magnetic logic circuits engineering, which takes an advantage of magnetization as a computational state variable and exploits spin waves for information transmission. The circuits consist of magneto-electric cells connected via spin wave buses. We present the result of numerical modeling showing the magneto-electric cell switching as a function of the amplitude as well as the phase of the spin wave. The phase-dependent switching makes it possible to engineer logic gates by exploiting spin wave buses as passive logic elements providing a certain phase-shift to the propagating spin waves. We present a library of logic gates consisting of magneto-electric cells and spin wave buses providing 0 or p phase shifts. The utilization of phases in addition to amplitudes is a powerful tool which let us construct logic circuits with a fewer number of elements than required for CMOS technology. As an example, we present the design of the magnonic Full Adder Circuit comprising only 5 magneto-electric cells. The proposed concept may provide a route to more functional wave-based logic circuitry with capabilities far beyond the limits of the traditional transistor-based approach.

We describe and analyze a cellular nonlinear network based on magnetic nanostructures for image processing. The network consists of magneto-electric cells integrated onto a common ferromagnetic film - spin wave bus. The magneto-electric cell is an artificial two-phase multiferroic structure comprising piezoelectric and ferromagnetic materials. A bit of information is assigned to the cell's magnetic polarization, which can be controlled by the applied voltage. The information exchange among the cells is via the spin waves propagating in the spin wave bus. Each cell changes its state as a combined effect of two: the magneto-electric coupling and the interaction with the spin waves. The distinct feature of the network with spin wave bus is the ability to control the inter-cell communication by an external global parameter - magnetic field. The latter makes possible to realize different image processing functions on the same template without rewiring or reconfiguration. We present the results of numerical simulations illustrating image filtering, erosion, dilation, horizontal and vertical line detection, inversion and edge detection accomplished on one template by the proper choice of the strength and direction of the external magnetic field. We also present numerical assets on the major network parameters such as cell density, power dissipation and functional throughput, and compare them with the parameters projected for other nano-architectures such as CMOL-CrossNet, Quantum Dot Cellular Automata, and Quantum Dot Image Processor. Potentially, the utilization of spin waves phenomena at the nanometer scale may provide a route to low-power consuming and functional logic circuits for special task data processing.

We demonstrate a three-terminal spin wave-based device utilizing spin wave interference. The device consists of three coplanar transmission lines inductively coupled to the 100nm thick CoFe film. Two spin wave signals are excited by microwave fields produced by electric current in two sets of lines, and the output signal is detected by the third set. The initial phases of the spin wave signals are controlled by the direction of the current flow in the excitation set of lines. Experimental data show prominent output signal modulation as a function of the relative phase (in-phase and out-of phase) of two input signals. The micrometer scale device operates in the GHz frequency range and at room temperature. Our experimental results show that spin-wave devices exploiting spin wave interference may be scaled to micrometer and nanometer scales for potential logic circuit application.

We propose and analyze a spin wave amplifier aimed to enhance the amplitude of the propagating spin wave via the magnetoelectric effect. The amplifier is a two-layer multiferroic structure, which comprises piezoelectric and ferromagnetic materials. By applying electric field to the piezoelectric layer, the stress is produced. In turn, the stress changes the direction of the easy axis in the ferromagnetic layer and the direction of the anisotropy field. The rotation frequency of the easy axis is the same as the frequency of the spin wave propagating through the ferromagnetic layer. As a result of this two-stage process, the amplitude of the spin wave can be amplified depending on the angle of the easy axis rotation. We present results of numerical simulations illustrating the operation of the proposed amplifier. According to numerical estimates, the amplitude of the spin wave signal can be increased by several orders of magnitude. The energy efficiency of the electric-to-magnetic power conversion is discussed. The proposed amplifier preserves the phase of the initial signal, which is important for application to logic circuits based on spin waves.

We propose and describe a magnetic NanoFabric which provides a route to building reconfigurable spin-based logic circuits compatible with conventional electron-based devices. A distinctive feature of the proposed NanoFabric is that a bit of information is encoded into the phase of the spin wave signal. It makes possible to transmit information without the use of electric current and utilize wave interference for useful logic functionality. The basic elements include voltage-to-spin wave and wave-to-voltage converters, spin waveguides, a modulator, and a magnetoelectric cell. As an example of a magnetoelectric cell, we consider a two-phase piezoelectric-piezomagnetic system, where the spin wave signal modulation is due to the stress-induced anisotropy caused by the applied electric field. The performance of the basic elements is illustrated by experimental data and results of numerical modeling. The combination of the basic elements let us construct magnetic circuits for NOT and Majority logic gates. Logic gates AND, OR, NAND and NOR are shown to be constructed as the combination of NOT and a reconfigurable Majority gates. The examples of computational architectures such as Cellular Automata, Cellular Nonlinear Network and Field Programmable Gate Array are described. The main advantage of the proposed NanoFabric is in the ability to realize logic gates with less number of devices than it required for CMOS-based circuits. Potentially, the area of the elementary reconfigurable Majority gate can be scaled down to 0.1um2. The disadvantages and limitations of the proposed NanoFabric are discussed.

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 spin wave bus do not use charge as an information carrier. In this work we describe the general concept of logic circuits with 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. 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 spin wave bus is, however, an interface between electronic circuits and integrated spintronics circuits. The logic circuits with spin wave bus allow us to provide wireless read-in and read-out.