Combinatorial memory is a class of memory in which information is encoded in the set of paths through a structured mesh. In this work, we introduce a systematic encoding framework, referred to as the Color-Rule-Function (CRF) approach, for representing information in combinatorial memory. The method consists of four key steps: selecting a sequence of paths in the mesh, assigning values (e.g., colors) to each cell, defining a set of rules based on the values encountered along each path, and constructing a Boolean function that determines the state of each path. . The coding procedure is illustrated by several examples. The design space scales of the CRF scale fundamentally faster compared to conventional memory. This apparent advantage arises from the use of rule-based and functional representations but is accompanied by increased hardware complexity. A possible hardware realization of the CRF framework is discussed. Importantly, the hardware overhead can be substantially reduced through the use of customized modules. The examples of the customized design are described in the text. The combination of CRF coding with customized module design may lead to a practical advantage in data storage density. According to the estimates, the data storage density may exceed Exabit per centimeter squared. A key problem that requires further investigation is related to the minimum Hamming distance between an arbitrary target bit sequence and the closest sequence realizable within the CRF framework under fixed hardware constraints.

Magnonic Combinatorial Memory (MCM) is a type of memory where the bits of information are encoded in the signal propagation paths in the network. In this work, we consider MCM based on the network of a coupled active ring circuit (ARC). Each circuit includes a broadband amplifier, a magnonic delay line, an adjustable frequency filter, an adjustable phase shifter, and a power detector. The coupling between the circuits is via spin waves propagating in the common delay line - ferrite film. There may or may not be auto-oscillations in the active ring circuits, depending on the combination of circuit parameters and circuit coupling. The address of MCM is defined as the combination of the states of the phase shifters and frequency filters, while the MCM state is defined as the presence/absence of the auto-oscillations. The coupling between the circuits is achieved by placing micromagnets on top of the ferrite film. The number of bits that can be encoded in the network increases quadratically with the number of coupled circuits. This scaling provides a fundamental advantage over conventional memory. We present experimental data obtained for three magnonic ARCs connected via a single-crystal yttrium iron garnet Y3Fe2(FeO4)3 (YIG) film. The data illustrate an example of encoding a 27-bit binary response pattern, corresponding to the 27 experimentally accessible phase combinations. The results demonstrate a robust operation of MCM with an On/Off ratio exceeding 30 dB at room temperature. The advantages and shortcomings of the proposed approach are discussed.

In this work, we describe Magnonic Combinatorial Memory (MCM), where the bits of information are stored in the signal propagation paths in the network. MCM is an active ring circuit consisting of electric and magnonic parts. The electric part includes a broadband amplifier, phase shifters, and frequency filters. The magnonic part is a mesh of frequency-dependent elements. Signal propagation path(s) in the mesh depend on the amplitude/phase matching between the electric and magnetic parts. The operation of the MCM is described based on the network model, where information is encoded in the S-parameters of the network elements as well as in the element arrangement in the network. We present experimental data for MCM with a four-terminal magnonic element. The element consists of a single-crystal yttrium iron garnet Y3Fe2(FeO4)(3) film and magnets on top of the film. The results demonstrate a robust operation of MCM with an On/Off ratio for path detection exceeding 50 dB at room temperature. The number of possible arrangements scales factorially with the number of magnets, which allows us to drastically increase the data storage density. Physical limits of MCM are also discussed.

Magnonics is an emerging field of modern magnetism that aims to benefit spin waves (magnons) for information transport and processing. There are many interesting proposals describing the possible pathways to practically valuable devices. Some of these paths have been explored, and some are waiting to be explored. Here, we would like to go over the development of spin wave logic devices, refer to the most notable works, and discuss the perspectives of magnonic memory and logic devices.

We consider a three-plate parallel plate capacitor where the middle plate is made of graphene and negatively charged. The electric forces of attraction acting on the electrons on the middle plate are compensated, as the electric fields on both sides of the plate are not screened. However, it brings the system to an unstable equilibrium state. To make the system stable, we consider fast oscillations similar to those in the Kapitza pendulum. AC electric current through the middle graphene plane creates a magnetic field. In turn, the Lorentz force squeezes moving electrons towards the center of the middle plane. We present the results of numerical modeling showing the effect of AC electric current on electron movement. According to the estimates, the pseudopotential produced by the AC current may exceed 60 eV at room temperature. Such a large value of the pseudopotential is due to the high mobility and large current density in graphene. The electric field intensity between the edge plates and the middle plate may exceed the breakdown value for a conventional double-plate capacitor. It may be possible to enhance the volume electric energy density above the gasoline 34 MJ/L.

There is an urgent need to enhance the storage density of memory devices to accommodate the exponentially increasing amount of data generated by humankind. In this work, we describe Magnonic Combinatorial Memory (MCM), where the bits of information are stored in the signal propagation paths in the network. The number of paths among the elements of the network is much larger compared to the number of elements, which makes it possible to enhance the data storage density compared to conventional memory devices. MCM is an active ring circuit consisting of electric and magnonic parts. The electric part includes a broadband amplifier, phase shifters, and frequency filters. The magnonic part is a mesh of frequency-dependent elements. Signal propagation path(s) in the mesh depend on the amplitude/phase matching between the electric and magnetic parts. The operation of the MCM is described based on the network model, where information is encoded in the S-parameters of the network elements as well as in the element arrangement in the network. We present experimental data for MCM with a four-terminal magnonic element. The element consists of a single-crystal yttrium iron garnet Y3Fe2(FeO4)3 (YIG) film and magnets on top of the film. There are four micro antennas aimed to convert electromagnetic waves into spin waves and vice versa. One of the antennas is used as an input port while the other three are the output ports. Experimental data show the prominent dependence of the element S-parameters on the magnet arrangement. The number of possible arrangements scales factorially with the number of magnets. There is a number of bits that can be encoded into one magnet arrangement. The results demonstrate a robust operation of MCM with an On/Off ratio for path detection exceeding 50 dB at room temperature. Physical limits and practical constraints of MCM are also discussed.

Spin pumping by surface and backward volume magnetostatic waves in YIG/Pt structures is experimentally studied and analyzed. It is shown that at frequencies corresponding to van Hove singularities in the density of states of the spin wave spectrum, an increase in the efficiency of electron-magnon scattering and spin current generation takes place. The obtained results are important for spin wave-based spintronic devices development.

In this work, we consider a type of magnetic memory where information is encoded into the mutual arrangement of magnets. The device is an active ring circuit comprising magnetic and electric parts connected in series. The electric part includes a broadband 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 path(s) in the magnetic part depends on the mutual arrangement of magnets in the mesh. The propagation path is detected with a set of power sensors. The correlation between circuit parameters and spin wave path is the basis 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 the power sensors is the memory state. We present experimental data on the proof-of-the-concept experiments on the prototype with three magnets placed on top of a single-crystal yttrium iron garnet Y 3 Fe 2 (FeO 4 ) 3 (YIG) film. There are three selected places for the magnets to be placed. There is a variety of spin wave propagation paths for each configuration of magnets. The results demonstrate a robust operation with an On/Off ratio for path detection exceeding 35 dB at room temperature. The number of possible magnet arrangements scales factorially with the size of the magnetic part. The number of possible paths per one configuration scales factorial as well. It makes it possible to drastically increase the data storage density compared to conventional memory devices. Magnonic combinatorial memory with an array of 100 × 100 magnets can store all information generated by humankind. Physical limits and constraints are also discussed.

In this work, we consider the possibility of building a magnonic co-processor for special task data processing. Its principle of operation is based on the natural property of an active ring circuit to self-adjust to the resonant frequency. The co-processor comprises a multi-path active ring circuit where the magnetic part is a mesh of magnonic waveguides. Each waveguide acts as a phase shifter and a frequency filter at the same time. Being connected to the external electric part, the system naturally searches for the path which matches the phase of the electric part. This property can be utilized for solving a variety of mathematical problems including prime factorization, bridges of the Konigsberg problem, traveling salesman, etc. We also present experimental data on the proof-of-the-concept experiment demonstrating the spin wave signal re-routing inside a magnonic matrix depending on the position of the electric phase shifter. The magnetic part is a 3 × 3 matrix of waveguides made of single-crystal yttrium iron garnet Y3Fe2(FeO4)3 films. The results demonstrate a prominent change in the output power at different ports depending on the position of the electric phase shifter. The described magnonic co-processor is robust, deterministic, and operates at room temperature. The ability to exploit the unique physical properties inherent in spin waves and classical wave superposition may be translated into a huge functional throughput that may exceed 1060 operations per meter squared per second for 50×50 magnetic mesh. Physical limits and constraints are also discussed.

Magnonic holographic memory is a type of memory that uses spin waves for magnetic bit read-in and read-out. Its operation is based on the interaction between magnets and propagating spin waves where the phase and the amplitude of the spin wave are sensitive to the magnetic field produced by the magnet. Memory states 0 and 1 are associated with the presence/absence of the magnet in a specific location. In this work, we present experimental data showing the feasibility of magnetic bit location using spin waves. The testbed consists of four micro-antennas covered by Y3Fe2(FeO4)3 yttrium iron garnet (YIG) film. A constant in-plane bias magnetic field is provided by NdFeB permanent magnet. The magnetic bit is made of strips of magnetic steel to maximize interaction with propagating spin waves. In the first set of experiments, the position of the bit was concluded by the change produced in the transmittance between two antennas. The minima appear at different frequencies and show different depths for different positions of the bit. In the second set of experiments, two input spin waves were generated, where the phase difference between the waves is controlled by the phase shifter. The minima in the transmitted spectra appear at different phases for different positions of magnetic bit. The utilization of the structured bit enhances its interaction with propagating spin waves and improves recognition fidelity compared to a regular-shaped bit. The recognition accuracy is further improved by exploiting spin wave interference. The depth of the transmission minima corresponding to different magnet positions may exceed 30 dB. All experiments are accomplished at room temperature. Overall, the presented data demonstrate the practical feasibility of using spin waves for magnetic bit red-out. The practical challenges are also discussed.

Prime factorization is a procedure of determining the prime factors of a given number N that requires super-polynomial time for conventional digital computers. Peter Shor developed a polynomial-time algorithm for quantum computers. Period finding is the key part of the algorithm, which is accomplished with the help of quantum superposition of states and quantum entanglement. The period finding can be also accomplished using classical wave superposition. In this study, we present experimental data obtained on a multi-port spin wave interferometer made of Y3Fe2(FeO4)3. Number 817 was factorized by a sequence of phase measurements. We also present the results of numerical modeling on the prime factorization of larger numbers 334597,1172693,3377663,and9363239. The results of numerical modeling reveal significant shortcomings of the period-based approach. The major problems are associated with an inability to predict the period of the modular function, significant overhead over classical digital computers in some cases, and phase accuracy requirements. We argue that the same problems are inherent in classical analog and quantum computers.

Prime factorization is a procedure of determining the prime factors of a given number N that requires super-polynomial time for conventional digital computers. In this work, we describe an approach to prime factorization using coupled oscillators with positive feedback. The approach includes several steps, where some of the steps are accomplished on a general type computer, and some steps are accomplished using coupled oscillators. We present experimental data on finding the primes of N = 817. The experiment is performed on a system of two coupled active ring oscillators. Each of the oscillators possesses its own set of eigenfrequencies that can be independently controlled by the external phase shifter. The coupling allows us to check on any common frequency that leads to the phase lock-in and power increase in the circuit. One of the ring oscillators includes a spin wave magnetic delay line made of Y3Fe2(FeO4)3, while the second oscillator includes an ordinary coaxial cable as a delay line. There are 22 eigenfrequencies for the spin wave oscillator and 4 eigenfrequencies for the oscillator with coaxial cable in the frequency band of operation. It takes less than 10 μs for the system to find the common frequency (if any). The most appealing property of the proposed circuit is that the processing time does not scale with the number of eigenfrequencies. Potentially, circuits with coupled active ring oscillators can be utilized to solve a variety of computational problems.

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. We also present experimental data on the proof-of-the-concept experiment for the two-path device. The magnetic part consists of two waveguides made of single-crystal yttrium iron garnet Y 3 Fe 2 (FeO 4 ) 3 (YIG) films. Different phase shifts per delay line are achieved by adjusting the magnitude and direction of the bias magnetic field. The auto-oscillation signal changes the propagation path in the magnetic matrix depending on the position of the outer electric phase shifter. The power difference between the active and passive paths exceeds 40 dBm at room temperature. The described logic devices are robust, deterministic, and operate at room temperature. The number of possible paths increases factorial with the size of the mesh. It may be possible to encode information in paths and retrieve it using the external phase shifters and attenuators. Potentially, combinatorial logic devices may compete with quantum computers in functional throughput. Physical limits and constraints are also discussed.

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.

Yttrium iron garnet Y3Fe2(FeO4)(3) (YIG) has a uniquely low magnetic damping for spin waves, which makes it a perfect material for magnonic devices. Spin waves typically exist in the microwave frequency range, and their wavelength can be decreased to the nanoscale. Their dispersion in YIG waveguides depends on the strength and orientation of the bias magnetic field. It may be possible to exploit YIG waveguides as field-controlled filters and delay lines. In this work, we describe combinatorial logic and memory devices to benefit YIG properties. An act of computation in the combinatorial device is associated with finding a route connecting the input and output ports. We present experimental data demonstrating the pathfinding in the active ring circuit with YIG waveguide. The ability to search in parallel through multiple paths is the most appealing property of combinatorial devices. Potentially, they may compete with quantum computers in functional throughput.

Using micromagnetic simulations, we show the possibility to build spin logic devices based on films of yttrium iron garnet and permalloy where energy channeling of spin waves is achieved due to excitation of focused and narrow-directed wave beams with used antennas. We studied the methods to construct a majority logic gate based on the interference of caustics of spin waves excited with the rectilinear transducers directed at an angle to the in-plane magnetic field. We propose the approach that allows using of amplitude detector to build a truth table and that consists in adding a reference signal with the fixed initial phase to three information signals. The possibility to scale the device on the example of its work in the range of spin waves with micron and submicron wavelengths is demonstrated.

In this work, we present experimental data demonstrating the feasibility of magnetic object location using spin waves. The test structure includes a Y3Fe2(FeO4)3 film with four micro-antennas placed on the edges. A constant in-plane bias magnetic field is provided by the 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 micro magnet on the top of the film. The micro 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 micro 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 readout. The disadvantages and physical constraints of this approach are also discussed.

Microwaveguides for spin waves based on yttrium iron garnet films and cross-like structures built on such waveguides are experimentally studied. Effects of the waveguides geometry, location of the microantennas for excitation and detection of the spin waves, and geometry of the waveguides junctions on the spin wave excitation and propagation efficiency are discussed.

In this work, we present experimental data on the interference of backward volume magnetostatic wave (BVMSW) counter-propagating in the structure with two exchange-coupled yttrium iron garnet layers. The layers are engineered to have different saturation magnetization that gives a possibility to BVMSW resonantly interacting with exchange modes of the two-layer structure. The BVMSW is excited by two antennas placed on top of the structure, while the third one placed between them is used for the detection of inductive voltage V generated by waves superposition. It is shown that maximal changes of the output inductive signal δV with the variation of magnetic field δH occur if, first, the waves interfere destructively and, second, the frequency corresponds to the resonant interaction of BVMSW with the exchange waves. In this case, obtained data reveal large sensitivity S = δV/δH approaching S ≈ 267 dB/Oe in the vicinity ±0.1 Oe of the resonant field H. The observed high sensitivity is of great importance for the development of compact sensitive magnetometers operating at room temperature.