Magnonic Combinatorial Memory (MCM)

• Magnonic Combinatorial Memory is a memory device where data is stored in collective spin-wave paths instead of discrete bits.
• It employs an active-ring network and auto-oscillation mechanisms based on amplitude gain and phase conditions to realize superlinear storage scaling.
• Experimental studies demonstrated room-temperature operation with On/Off ratios exceeding 50 dB, highlighting its potential for ROM-like applications.

Magnonic Combinatorial Memory (MCM) is a proposed memory paradigm in which information is stored not in discrete cells but in the set of signal propagation paths sustained by a wave-based network, specifically a magnonic network embedded in an active ring circuit. In this formulation, the relevant state variables are the allowed auto-oscillation routes, their frequencies, and their port-resolved output signatures, rather than the binary state of isolated capacitors, transistors, or magnetic tunnel junctions. The central claim is that the number of distinguishable paths and path combinations can greatly exceed the number of physical elements, yielding superlinear and, in some constructions, factorial scaling of capacity with system size (Balinskiy et al., 11 Sep 2025). A 2025 experimental study reported room-temperature operation with an On/Off ratio for path detection exceeding 50 dB in a four-terminal magnonic element, extending the earlier 2023 proof-of-concept that had demonstrated route-based storage with three magnets and an On/Off ratio exceeding 35 dB (Balinskiy et al., 11 Sep 2025, Balynskyy et al., 2023).

1. Conceptual basis and historical placement

MCM was introduced as a route-based alternative to conventional memories, whose storage capacity scales approximately linearly with the number of cells because each cell stores one or a few bits. In MCM, the stored object is instead the collective routing structure of spin-wave propagation through a mesh, together with the frequency and phase conditions under which particular routes sustain auto-oscillation in a closed-loop active ring (Balynskyy et al., 2023). The 2025 formulation sharpened this idea by expressing the device as a network of frequency-dependent multiport elements whose information content is encoded in their $S$-parameters and in the arrangement of those elements within the network (Balinskiy et al., 11 Sep 2025).

The concept sits within a broader lineage of distributed magnonic information processing. Earlier magnonic holographic memories stored information in interference patterns shaped by junction magnets and phase-coded spin-wave inputs, and were developed for pattern recognition rather than route-addressable storage (Gertz et al., 2014, Kozhevnikov et al., 2014). Related combinatorial devices used essentially the same active-ring logic to select valid routes in a magnetic mesh for traveling-salesman-type optimization, with frequency filters, phase shifters, and attenuators encoding graph structure and route costs (Balinskiy et al., 2023). MCM differs from both by treating the route-selection mechanism itself as the storage primitive.

A recurrent misconception is to interpret MCM as a faster or denser version of random-access RAM. The published description does not support that reading. The stored data are collective, route-defined, and global; once the magnet arrangement is fixed, the device is effectively read-only, and changing a single logical bit may require reconfiguring many or all magnets (Balinskiy et al., 11 Sep 2025).

2. Active-ring architecture and auto-oscillation mechanism

MCM is realized as an active ring composed of electric and magnonic parts connected in series. The electric part contains a broadband amplifier $G(V)$, voltage-tunable band-pass filters $f(V)$, voltage-tunable phase shifters $\Psi(V)$, and directional couplers with power sensors. The magnonic part is a YIG-based multiport structure with micro-antennas for RF–magnon conversion and micro-magnets that create a spatially non-uniform internal field landscape. Together, the magnonic section behaves as a frequency-dependent multiport characterized by an $S$-matrix $S_{ij}(f)$ (Balinskiy et al., 11 Sep 2025).

Auto-oscillation is governed by Barkhausen-type amplitude and phase conditions. For a simple transmission channel, the paper writes

$G(V) + \text{abs}[S(f)] \ge 0,$

which corresponds in linear notation to $|G(f)S_{21}(f)| \ge 1$, and

$\Psi(V) + \arg[S(f)] = 2\pi k,\quad k=1,2,3,\dots$

so only those frequencies and paths whose round-trip gain compensates loss and whose round-trip phase is an integer multiple of $2\pi$ survive and build up (Balinskiy et al., 11 Sep 2025). In a multiport element, channels such as $G(V)$0, $G(V)$1, and $G(V)$2 correspond to propagation from one input antenna to multiple outputs; each port can therefore represent a separate route-conditioned bit.

Because the ring closes electronically while propagation occurs magnonically, the selection is collective. The wave initially explores the admissible spectral and spatial manifold of the network; the loop then amplifies only the subset of modes that simultaneously satisfy amplitude and phase matching. In multi-input cases, the phase at a given output depends not only on individual transmission coefficients but also on their superposition, so switch combinations such as 01, 10, and 11 generate different phase-versus-frequency curves and therefore different oscillation conditions (Balinskiy et al., 11 Sep 2025).

3. Encoding model: $G(V)$3-parameters, topology, addresses, and states

The 2025 paper formalizes MCM as a network model in which information is encoded at two coupled levels. At the element level, each device has a complex $G(V)$4-matrix whose entries $G(V)$5 depend on material, geometry, and magnet placement. At the network level, the arrangement of elements in the mesh determines the set of admissible routes, including multiple reflections and inter-element couplings (Balinskiy et al., 11 Sep 2025).

The memory address is not a geometric cell coordinate. It is a composite control word comprising which input switches are ON or OFF, the selected filter frequencies, and the selected phase-shifter states. The memory state is the vector of logic values at the output ports, determined by whether auto-oscillation appears at each output. The paper defines logic 1 as $G(V)$6 and logic 0 as $G(V)$7, with example thresholds such as powers above $G(V)$8 dBm for ON and below $G(V)$9 dBm for OFF in the demonstrated system (Balinskiy et al., 11 Sep 2025).

For a network with $f(V)$0 input ports, $f(V)$1 output ports, $f(V)$2 available frequencies, and $f(V)$3 distinct phase states per output, the number of address combinations is estimated as

$f(V)$4

and the maximum number of stored bits as

$f(V)$5

The same work also introduces a second combinatorial layer: if $f(V)$6 distinct elements can be arranged in $f(V)$7 positions, the number of arrangements is

$f(V)$8

This factorial dependence is central to the claimed density advantage, because each arrangement induces a different global $f(V)$9-parameter landscape and therefore a different address-to-state truth table (Balinskiy et al., 11 Sep 2025).

4. Physical realization and experimental demonstration

The experimental magnonic element reported in 2025 uses a single-crystal YIG film $\Psi(V)$0 on a GGG substrate. The YIG thickness is $\Psi(V)$1, the GGG substrate is thinned to $\Psi(V)$2, the saturation magnetization is $\Psi(V)$3, and the ferromagnetic resonance linewidth is $\Psi(V)$4 at 3 GHz. A pair of bulk NdFeB permanent magnets beneath the PCB supplies an in-plane bias field of approximately 375 Oe (Balinskiy et al., 11 Sep 2025).

Four short microstrip antennas, about $\Psi(V)$5 long and $\Psi(V)$6 wide, are placed under the film. Antenna #1 is the input, while antennas #2, #3, and #4 are outputs. Above the film, a plastic plate contains 16 pits for micro-magnets. Four NdFeB micro-magnets of volumes 0.02, 0.03, 0.045, and $\Psi(V)$7 were permuted among four selected pits, giving 24 distinct arrangements, all of which were characterized (Balinskiy et al., 11 Sep 2025).

The active ring combined this magnonic element with a phase shifter on the input branch, three YIG-sphere-based tunable band-pass filters, three output phase shifters, directional couplers, and three cascaded broadband amplifiers. Two filter sets were used: $\Psi(V)$8, and $\Psi(V)$9, with bandwidth about 15 MHz (Balinskiy et al., 11 Sep 2025).

The main reported findings were threefold. First, passive VNA measurements showed strong configuration dependence of $S$0, $S$1, $S$2, and their phases. Second, in the active ring, the presence or absence of oscillation at each output varied systematically with magnet arrangement, frequency set, and phase setting. Third, across three address sets—frequency set 1 with phases 0, frequency set 2 with phases 0, and frequency set 2 with phases $S$3—all 3-bit combinations from 000 to 111 were realized by suitable magnet arrangements (Balinskiy et al., 11 Sep 2025).

The reported On/Off ratio exceeded 50 dB at room temperature, with ON states above $S$4 dBm and OFF states below $S$5 dBm. Comparison of passive $S$6-parameter-based predictions with active-ring observations showed good overall agreement, with two mismatches attributed to additional amplifier phase shifts, nonlinear effects, and imperfections in phase control and measurement (Balinskiy et al., 11 Sep 2025).

5. Operation as a memory device, capacity claims, and physical limits

Programming in the demonstrated architecture consists of arranging the magnets in selected pits. That arrangement fixes a specific mapping from addresses—defined by switch states, frequencies, and phases—to output bit patterns. Storage is non-volatile because the NdFeB magnets are permanent and the YIG film is passive; no DC power is required to maintain the state. Reading consists of energizing the ring, waiting for the allowed mode or modes to grow, and thresholding the output powers. The reported time to reach saturation is less than 1 ms, and the estimated energy is about $S$7 per 3-bit retrieval in the demonstrated device (Balinskiy et al., 11 Sep 2025).

The most widely cited density claims are combinatorial rather than prototype-density measurements. In the earlier 2023 formulation, the authors argued that MCM with just 25 magnets could store as much as $S$8 bits, described there as “10 Yotta” bits, because the number of ordered magnet arrangements scales factorially (Balynskyy et al., 2023). In the 2025 work, the experimental prototype used four magnets and the authors estimated that more than 9 bits could be encoded with only four magnets and a suitable network, with the possibility of exceeding 1 kB if the full combinatorial space of frequencies, phases, and arrangements were exploited (Balinskiy et al., 11 Sep 2025). No explicit bits-per-area figure was reported for the demonstrated prototype.

The limits are also collective rather than cell-local. Spin-wave attenuation restricts usable path length; frequency crowding limits the number of independently addressable spectral channels; phase resolution is limited by phase shifter resolution, given there as about $S$9, and by oscillator phase noise; fabrication and alignment tolerances affect $S_{ij}(f)$0-parameters; thermal noise and material losses set practical thresholds for discriminating ON and OFF routes (Balinskiy et al., 11 Sep 2025). The authors explicitly state that a complete high-fidelity model connecting magnet arrangements, $S_{ij}(f)$1-parameters, and ultimate capacity limits remains future work.

6. Relation to adjacent magnonic paradigms and outlook

MCM belongs to a family of distributed magnonic information systems but is technically distinct from each of its nearest neighbors. Magnonic holographic memory uses phase-coded inputs and passive interference in a magnetic matrix to recognize stored patterns, with the internal magnet configuration defining the transfer function of the matrix (Gertz et al., 2014, Kozhevnikov et al., 2014). Magnonic combinatorial devices for optimization use an active ring, frequency filters, and phase conditions to select low-loss routes representing valid combinatorial solutions (Balinskiy et al., 2023). MCM combines these two strands: holographic-style distributed encoding with active-ring route selection.

Its most natural application class is therefore ROM-like, lookup-table-like, or associative, rather than mutable RAM. The architecture is attractive when storage can be embedded into a collective wave-routing fabric and read many times, but not when fine-grained random rewriting is required. That trade-off is explicit in the published work (Balinskiy et al., 11 Sep 2025).

Several recent magnonic developments suggest possible engineering directions without yet constituting MCM proper. Phase-insensitive, self-normalized cascaded magnonic logic addresses two problems that large MCM fabrics would also face—phase robustness and signal restoration—though that work concerns logic gates rather than memory (Guo et al., 6 Jan 2026). Multiferroic and magnetoelectric magnonic logic-in-memory cells provide non-volatile local state variables and electrically controlled magnon-mediated operations, which suggests hybrid architectures in which route-based MCM is combined with more conventional cell-based write and read support (Chai et al., 2023, Cong et al., 15 Feb 2026). A plausible implication is that practical large-scale MCM, if realized, will be a heterogeneous system rather than a purely passive mesh.

In its present form, MCM remains a proposal validated by small-scale experiments rather than a mature memory technology. Its significance lies in reframing storage density as a property of collective path combinatorics, spectral selectivity, and topology-sensitive $S_{ij}(f)$2-parameter engineering, rather than of cell miniaturization alone (Balinskiy et al., 11 Sep 2025).