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arxiv: 2605.21004 · v1 · pith:BH56K7RXnew · submitted 2026-05-20 · ❄️ cond-mat.mtrl-sci

Attached Split Ring Resonator Cavity for Magnon Photon Coupling

Aram Akoi , Liubov Ivzhenko , Maciej Krawczyk This is my paper

Pith reviewed 2026-05-21 04:00 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords split ring resonatormagnon photon couplingyttrium iron garnethybrid magnonic deviceson-chip cavitymicrowave magnetic fieldstrong coupling
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The pith

Geometry of the yttrium iron garnet element controls magnon-photon coupling strength more than its volume in an attached split ring resonator cavity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper introduces a compact chip-scale cavity based on an attached split ring resonator integrated with yttrium iron garnet structures to reach strong magnon-photon coupling. The resonator is optimized through adjustments to inter-ring spacing, gap width, substrate thickness, and permittivity to achieve a quality factor of 190 at 5.48 GHz. Simulations then compare coupling to three YIG shapes: full ring, half ring, and disk. The disk geometry delivers the strongest interaction at 135 MHz with cooperativity 25.30 thanks to better field overlap, while the ring shapes yield around 110 MHz with cooperativities near 13. A reader would care because the work frames geometry as a practical design knob for building lithography-compatible hybrid magnonic devices on chip.

Core claim

The paper establishes that an attached split ring resonator cavity, after numerical optimization for high quality factor and field confinement, couples to yttrium iron garnet elements of three geometries with the disk shape producing the highest coupling strength of 135 MHz and cooperativity of 25.30 at lower bias fields due to improved microwave magnetic field overlap, the full ring giving 115 MHz and 13.10 cooperativity, and the half ring giving 108 MHz and 13.50 cooperativity despite edge demagnetizing effects, thereby showing that geometry rather than magnetic volume alone serves as the key parameter for tailoring the interaction.

What carries the argument

The attached split ring resonator (ASRR) cavity, tuned by inter-ring spacing and gap width to confine the microwave magnetic field and reduce radiative losses while achieving a quality factor of 190 at 5.48 GHz.

If this is right

  • The disk YIG geometry achieves the strongest coupling of 135 MHz and cooperativity of 25.30 at lower bias magnetic fields.
  • The full ring YIG geometry delivers balanced performance with 115 MHz coupling strength and 13.10 cooperativity.
  • The half ring YIG geometry maintains comparable coupling of 108 MHz and 13.50 cooperativity despite edge-induced demagnetizing effects.
  • The platform supplies a practical framework for lithography-compatible on-chip hybrid magnonic and quantum devices.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Shape optimization of the YIG element could enable device operation at reduced magnetic field strengths for lower power consumption.
  • The ASRR approach may combine with other on-chip components such as superconducting resonators for quantum hybrid systems.
  • Testing additional substrate permittivities could further raise the quality factor above 190 while preserving compact size.

Load-bearing premise

The electromagnetic simulations accurately predict the coupling strengths and cooperativities for the three YIG geometries without significant unmodeled losses or fabrication imperfections.

What would settle it

Fabricate the optimized ASRR cavity with the three YIG geometries and measure the actual magnon-photon coupling strengths and cooperativities to compare against the simulated values of 115 MHz, 108 MHz, and 135 MHz.

read the original abstract

We present a chip scale planar cavity platform based on an attached split ring resonator (ASRR) integrated with yttrium iron garnet (YIG) structures to achieve strong magnon photon coupling in a compact hybrid system. The ASRR geometry was numerically optimized by tuning inter ring spacing, gap width, substrate thickness, and permittivity, resulting in a quality factor of Q = 190 at 5.48 GHz, enabling strong microwave magnetic field confinement and reduced radiative losses. The optimized cavity was coupled to YIG elements of three geometries: full ring, half ring, and disk. Full electromagnetic simulations show that the full ring geometry exhibits balanced performance with coupling strength 115 MHz and cooperativity 13.10, while the half ring shows a comparable coupling strength of 108 MHz and slightly higher cooperativity 13.50, despite edge induced demagnetizing effects. In contrast, the disk geometry couples at lower bias magnetic fields and achieves the strongest interaction (135 MHz, 25.30), enabled by improved microwave magnetic field overlap. These results demonstrate that geometry, rather than magnetic volume alone, is a key design parameter for tailoring magnon photon coupling, providing a practical framework for lithography compatible, on chip hybrid magnonic and quantum devices.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript presents a chip-scale planar cavity using an attached split ring resonator (ASRR) integrated with yttrium iron garnet (YIG) structures for strong magnon-photon coupling. The ASRR is numerically optimized by tuning inter-ring spacing, gap width, substrate thickness, and permittivity to achieve Q = 190 at 5.48 GHz. Full-wave electromagnetic simulations then evaluate coupling to three YIG geometries—full ring (115 MHz coupling, cooperativity 13.10), half ring (108 MHz, 13.50), and disk (135 MHz, 25.30)—with the authors concluding that geometry is a key design parameter beyond magnetic volume alone for lithography-compatible on-chip hybrid devices.

Significance. If the central claims hold after addressing the noted issues, the work would provide a practical computational framework for tailoring magnon-photon interactions in compact hybrid systems, with the reported coupling values and cavity optimization serving as concrete guidance for future on-chip magnonic and quantum devices. The comparative full-wave simulations across geometries are a strength, offering reproducible numerical benchmarks.

major comments (1)
  1. [Results section on coupling to YIG geometries (and abstract)] The central claim in the abstract that 'geometry, rather than magnetic volume alone, is a key design parameter' is load-bearing but unsupported by the presented data. The three YIG geometries are compared with specific coupling strengths (full ring 115 MHz, half ring 108 MHz, disk 135 MHz) and cooperativities, yet the manuscript provides neither the physical volumes of the YIG elements nor a volume-normalized metric such as g/√V. This prevents isolating geometry effects (e.g., improved microwave field overlap for the disk or edge demagnetization for the half ring) from possible volume differences, especially since the disk result occurs at lower bias fields.
minor comments (2)
  1. [Abstract] The abstract and results report specific performance numbers (coupling strengths and cooperativities) derived solely from simulations with an assumed Q = 190, but do not mention experimental validation, error bars, or comparison to analytic cavity-magnon formulas. Clarifying the scope as simulation-based would help set reader expectations.
  2. [Cavity optimization section] The optimization parameters (inter-ring spacing, gap width, substrate thickness, permittivity) are listed but the manuscript would benefit from a table or explicit values showing how each contributes to the final Q = 190 and field confinement.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive critique of our manuscript on the attached split ring resonator cavity for magnon-photon coupling. The major comment on the support for our central claim is well taken, and we address it directly below.

read point-by-point responses

  1. Referee: [Results section on coupling to YIG geometries (and abstract)] The central claim in the abstract that 'geometry, rather than magnetic volume alone, is a key design parameter' is load-bearing but unsupported by the presented data. The three YIG geometries are compared with specific coupling strengths (full ring 115 MHz, half ring 108 MHz, disk 135 MHz) and cooperativities, yet the manuscript provides neither the physical volumes of the YIG elements nor a volume-normalized metric such as g/√V. This prevents isolating geometry effects (e.g., improved microwave field overlap for the disk or edge demagnetization for the half ring) from possible volume differences, especially since the disk result occurs at lower bias fields.

    Authors: We agree that the current manuscript does not report the physical volumes of the three YIG elements or include a volume-normalized metric such as g/√V, which limits the ability to fully separate geometric effects from possible volume variations. In the revised version we will add the volumes for the full-ring, half-ring, and disk geometries and compute g/√V for each case. We will also expand the discussion in the results section to address the lower bias-field condition for the disk and clarify how field overlap and demagnetization contribute to the observed coupling differences. These changes will be made to strengthen the evidential basis for the claim. revision: yes

Circularity Check

0 steps flagged

No circularity: coupling values obtained from independent EM simulations of distinct geometries

full rationale

The manuscript derives coupling strengths (115 MHz, 108 MHz, 135 MHz) and cooperativities directly from full-wave electromagnetic simulations of three separate YIG shapes after numerical optimization of the ASRR cavity parameters. These outputs do not reduce to any self-referential definitions, fitted inputs renamed as predictions, or self-citation chains within the paper's equations. The geometry-vs-volume claim rests on comparative simulation results rather than any internal loop or ansatz smuggled via prior work. The derivation chain is self-contained against external simulation benchmarks.

Axiom & Free-Parameter Ledger

4 free parameters · 2 axioms · 0 invented entities

The work relies on standard electromagnetic simulation assumptions and geometry tuning parameters; no new physical entities are introduced.

free parameters (4)
  • inter ring spacing
    Tuned numerically to optimize quality factor and field confinement
  • gap width
    Tuned numerically to optimize quality factor and field confinement
  • substrate thickness
    Tuned numerically to optimize quality factor and field confinement
  • permittivity
    Tuned numerically to optimize quality factor and field confinement
axioms (2)
  • standard math Maxwell's equations govern the electromagnetic fields in the cavity and YIG structures
    Invoked implicitly for all full electromagnetic simulations
  • domain assumption YIG material parameters (saturation magnetization, damping) are known from prior literature and correctly implemented
    Required for magnon resonance modeling in the simulations

pith-pipeline@v0.9.0 · 5757 in / 1483 out tokens · 34616 ms · 2026-05-21T04:00:41.466654+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    Full electromagnetic simulations show that the full ring geometry exhibits balanced performance with coupling strength 115 MHz and cooperativity 13.10, while the half ring shows a comparable coupling strength of 108 MHz and slightly higher cooperativity 13.50... the disk geometry... achieves the strongest interaction (135 MHz, 25.30)

  • IndisputableMonolith/Foundation/ArithmeticFromLogic.lean embed_injective unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    The coupling strength g depends on the number of spins... normalized using g = g0 √N... N = n0 V

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages

  1. [1]

    (𝐵"+𝜇"𝑀#) (3) where 𝑓! is the resonance frequency, 𝛾 is the gyromagnetic ratio, 𝜇.𝑀1 is the saturation magnetization, 𝜇

    Ferromagnetic Resonance of YIG In conventional ferromagnetic resonance (FMR) analysis, the Kittel formula is widely used to estimate the FMR frequency based on the applied static magnetic field 𝐵₀ and the saturation magnetization 𝑀1 [28]. For the in-plane magnetized thin ferromagnetic film, it reads 𝑓! =𝛾/2𝜋'𝐵"(𝐵"+𝜇"𝑀#) (3) where 𝑓! is the resonance frequ...

    work page

  2. [2]

    (,%#=6,)!#,! , 𝜅=,,

    Magnon-Photon Coupling Analysis The strength of magnon-photon coupling of the ASRR loaded with elements of different shapes was examined using COMSOL Multiphysics with RF module, solving the electromagnetic wave equation, Eq. (1), with standard boundary conditions on the YIG surface. The Polder permeability tensor was used to introduce the description of ...

    work page doi:10.1088/1361-648x/ae1ab9 2020

  3. [3]

    Banholzer, A., Narkowicz, R., Hassel, C., Meckenstock, R. et al. (2011) ‘Visualization of spin dynamics in single nanosized magnetic elements’, Nanotechnology, 22(29), p. 295713. https://doi.org/10.1088/0957-4484/22/29/295713. [20] Lenz, K. et al. (2019) ‘Magnetization dynamics of an individual single-crystalline Fe-filled carbon nanotube’, Small, 15, p. ...

    work page doi:10.1088/0957-4484/22/29/295713 2011

  4. [4]

    and Bertotti, G

    Lin, Z., d’Aquino, M., Serpico, C., Devolder, T. and Bertotti, G. (2019) ‘Computational methods based on the linearized Landau–Lifshitz–Gilbert equation’, Journal of Magnetism and Magnetic Materials, 491, p. 165545. https://doi.org/10.1016/j.jmmm.2019.165545. [32] Ivzhenko, L., Polevoy, S., Nedukh, S. and Krawczyk, M. (2025) ‘Influence of photon–magnon co...

    work page doi:10.1016/j.jmmm.2019.165545 2019