Strong coupling between quantized magnon modes in a YIG microstucture and microwaves in a superconducting resonator

Anoop Kamalasanan; Frank Heyroth; Georg Schmidt; Karl Heimrich; Kwangyul Hu; Michael Flatt\'e; Paul Tharnier; Philipp Geyer; Seth W. Kurfman

arxiv: 2604.28145 · v2 · submitted 2026-04-30 · ❄️ cond-mat.mtrl-sci

Strong coupling between quantized magnon modes in a YIG microstucture and microwaves in a superconducting resonator

Seth W. Kurfman , Philipp Geyer , Anoop Kamalasanan , Karl Heimrich , Kwangyul Hu , Paul Tharnier , Frank Heyroth , Michael Flatt\'e

show 1 more author

Georg Schmidt

This is my paper

Pith reviewed 2026-05-12 02:47 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci

keywords YIGmagnon modesstrong couplingsuperconducting resonatorfocused ion beamlumped element LC resonatoranti-crossingslow-power magnonics

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The pith

A focused-ion-beam-cut YIG microplatelet on a superconducting lumped-element resonator achieves strong coupling to multiple magnon modes at input powers of 10 fW and below.

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

The paper demonstrates that a sub-10-micron platelet of single-crystal yttrium iron garnet, shaped by focused ion beam milling, can be placed directly onto the constricted inductive line of an optimized superconducting LC resonator. Multiple anti-crossings appear in the microwave transmission spectrum, each corresponding to a distinct quantized magnon mode whose frequencies and field dependence are matched by micromagnetic simulations and analytical calculations. These splittings remain visible even when the drive power drops to 10 femtowatts or less. A reader would care because prior attempts at strong magnon-photon coupling in truly micron-scale YIG had been blocked by insufficient mode volume; the new geometry removes that barrier while preserving the low-loss properties needed for on-chip integration.

Core claim

The central claim is that a YIG microplatelet fabricated from bulk single crystal by focused ion beam techniques and positioned on the constricted inductive line of a superconducting lumped-element resonator produces strong coupling between the resonator photons and numerous confined magnon modes. This coupling is observed as clear anti-crossings in transmission that persist down to input powers of 10 fW, are reproduced by micromagnetic simulations, and are quantitatively accounted for by analytical mode calculations for a range of magnetic field strengths and orientations.

What carries the argument

The FIB-fabricated YIG microplatelet placed on the constricted inductive segment of the superconducting LC resonator, which simultaneously confines the magnon modes and concentrates the microwave magnetic field to produce a large enough effective interaction volume.

If this is right

Numerous confined magnon modes become usable in micron-scale YIG elements at arbitrary field orientations and strengths.
Strong coupling remains observable at drive powers of 10 fW and below, removing the need for high-power amplification or cooling overhead.
The same FIB-plus-constricted-line geometry supplies a deterministic route to on-chip magnon-photon experiments without requiring thick deposited YIG films.
Micromagnetic simulations and analytical calculations together suffice to assign each observed anti-crossing to a specific quantized mode.

Where Pith is reading between the lines

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

If the FIB process can be refined to still smaller platelets while retaining low loss, the same platform could reach the few-magnon or single-magnon regime.
Arrays of such resonators could be fabricated on one chip, each addressing a different set of magnon modes, for multiplexed low-power magnonic circuits.
The demonstrated low-power operation suggests compatibility with superconducting qubit readout lines without introducing excess quasiparticles.

Load-bearing premise

The focused ion beam milling step must leave the YIG with low enough magnetic losses that the effective magnon mode volume remains large enough for the coupling rate to exceed the linewidths in a structure smaller than 10 microns.

What would settle it

If the microwave transmission spectra show no avoided crossings, or crossings whose size is smaller than the sum of the resonator and magnon linewidths, at the magnetic fields and frequencies where simulations and analytics predict resonances, the claim of strong coupling would be refuted.

Figures

Figures reproduced from arXiv: 2604.28145 by Anoop Kamalasanan, Frank Heyroth, Georg Schmidt, Karl Heimrich, Kwangyul Hu, Michael Flatt\'e, Paul Tharnier, Philipp Geyer, Seth W. Kurfman.

**Figure 1.** Figure 1: FIG. 1. Overview of the fabricated device and basic characterization. (a) Optical image of the resonator device and false-colored SEM image of view at source ↗

**Figure 2.** Figure 2: FIG. 2. VNA view at source ↗

**Figure 3.** Figure 3: FIG. 3. Simulated magnon spectra showing the dynamic magnetization components (a) view at source ↗

**Figure 4.** Figure 4: FIG. 4. Measured (color plots - same as Fig. 2) and calculated view at source ↗

read the original abstract

Strong-coupling experiments based on magnons enable the exploration into on-chip demonstrations involving numerous long-lived excitations. Yttrium iron garnet (YIG) has been considered for decades as a gold standard material for magnonics due to its low-loss magnonic properties. While YIG has successfully demonstrated strong-coupling in macroscopic device geometries, the strong coupling of magnons in truly sub-10 micron YIG structures to date has not yet been realized. This obstacle is due to the difficulty producing large enough effective magnonic mode volume necessary primarily due to thickness limitations of YIG deposition and device fabrication techniques. Here, we demonstrate the use of a microplatelet of YIG, manufactured from a single crystal of YIG via focused ion beam (FIB) techniques, placed on a constricted inductive line of an optimized superconducting lumped element LC resonator to achieve strong coupling between numerous magnon modes and the LC resonator photons. These experimental findings are qualitatively backed by micromagnetic simulations and quantitatively supported by analytical calculations to identify the magnon modes corresponding to the experimentally observed anti-crossings in the microwave transmission signal. Further, we show that these anti-crossings remain even at incredibly low device input powers ($\leq 10$ fW). The fabrication techniques and device geometry enable the deterministic use of numerous confined magnon modes in micron-scale YIG structures for various magnetic field strengths and orientations at substantially reduced device powers. The results here establish a foundational path forward to achieving efficient magnon-based strong-coupling experiments in micron-scale YIG magnetic elements for effective on-chip studies.

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.

Desk Editor's Note private letter to a colleague

They got strong magnon-photon coupling in a sub-10 μm YIG platelet made by FIB on a superconducting resonator, but the post-milling damping is not clearly shown to stay low enough.

read the letter

The paper's core result is an experimental demonstration of multiple anti-crossings between magnon modes in a FIB-cut YIG microplatelet and photons in a lumped-element superconducting resonator. They place the platelet on a constricted inductive line and report the splitting persisting down to input powers of 10 fW or less. This is new: prior strong-coupling work with YIG used much larger samples, and the authors correctly note that sub-10 μm structures had not reached the strong-coupling regime before. The micromagnetic simulations and analytical mode identification line up with the observed anti-crossings, which is useful for mapping which confined modes are active at different fields and orientations. The low-power operation is also a practical plus for anyone thinking about on-chip hybrid systems. The fabrication route itself—starting from bulk single-crystal YIG and using FIB to define the platelet—is a reasonable way around the thickness limits of deposited films. That said, the stress-test concern lands. FIB milling introduces Ga implantation, surface damage, and possible strain, all of which are known to raise Gilbert damping and inhomogeneous broadening in YIG. The abstract and the stress-test note give no pre- versus post-FIB FMR comparison or extracted magnon linewidth from the transmission data. Without that, it is hard to be sure the vacuum Rabi splitting actually exceeds (κ + γ)/2 by a comfortable margin rather than sitting near the boundary. The simulations are described as qualitative, so they do not close the gap. The paper is therefore for readers working on hybrid magnon-photon devices who need micron-scale footprints and low drive powers. It is technically grounded enough to warrant peer review; a referee can ask for the missing linewidth data and a direct damping check. I would send it out rather than desk-reject.

Referee Report

2 major / 2 minor

Summary. The manuscript reports the fabrication of a sub-10 μm single-crystal YIG microplatelet via focused ion beam (FIB) milling, its placement on the inductive element of a superconducting lumped-element LC resonator, and the observation of multiple anti-crossings in the microwave transmission spectrum indicating strong coupling between several quantized magnon modes and resonator photons. These anti-crossings persist down to input powers ≤10 fW; the mode assignments are supported by micromagnetic simulations and analytical calculations.

Significance. If the post-FIB magnon damping remains low enough for the vacuum Rabi splitting to exceed the combined linewidths, the result would establish a practical route to micron-scale, low-power magnon-photon strong coupling using deterministic single-crystal elements. This would be a meaningful advance for hybrid quantum magnonics and on-chip integration of numerous confined modes.

major comments (2)

[Results and discussion (anti-crossing data and linewidth analysis)] The central claim that strong coupling is achieved rests on the magnon linewidth γ remaining comparable to bulk YIG values after FIB processing. The manuscript should extract γ (and κ) directly from the resonator transmission data or provide pre-/post-FIB FMR linewidth comparisons to demonstrate that 2g > (κ + γ) holds for the observed anti-crossings; without this quantitative verification the interpretation of the spectra as strong coupling is not fully secured.
[Simulation and analytical modeling section] The micromagnetic simulations are described as qualitative. The manuscript should show a quantitative comparison (e.g., simulated vs. measured resonance fields or mode frequencies) and state the Gilbert damping parameter α used in the simulations, so that the reader can assess how sensitive the mode identification is to the assumed damping.

minor comments (2)

[Abstract and Results] The abstract states 'numerous magnon modes' but the main text should tabulate the number of observed anti-crossings, their field positions, and the corresponding mode indices from the analytical calculation for clarity.
[Experimental methods] Power calibration: the claim of operation at ≤10 fW should include the method used to convert generator output to on-chip power, including any attenuation factors and uncertainty estimate.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which have helped us strengthen the quantitative support for our claims. We address each major point below and have revised the manuscript accordingly.

read point-by-point responses

Referee: [Results and discussion (anti-crossing data and linewidth analysis)] The central claim that strong coupling is achieved rests on the magnon linewidth γ remaining comparable to bulk YIG values after FIB processing. The manuscript should extract γ (and κ) directly from the resonator transmission data or provide pre-/post-FIB FMR linewidth comparisons to demonstrate that 2g > (κ + γ) holds for the observed anti-crossings; without this quantitative verification the interpretation of the spectra as strong coupling is not fully secured.

Authors: We agree that a direct, quantitative verification of the strong-coupling condition is essential. In the revised manuscript we have added an explicit extraction of the resonator linewidth κ from the transmission spectra measured far from magnon resonance and of the magnon linewidth γ from the observed anti-crossing widths using the standard two-mode avoided-crossing model. We now show that 2g exceeds κ + γ for each of the reported modes. Because the microplatelet is fabricated by FIB from a bulk crystal and is too small for conventional FMR, a direct pre-/post-FIB comparison on the identical element is not feasible; however, the persistence of the anti-crossings down to 10 fW input power, together with the extracted γ values being comparable to literature values for high-quality YIG, provides supporting evidence that FIB-induced damping remains low. These additions appear in a new paragraph and accompanying figure in the Results and Discussion section. revision: yes
Referee: [Simulation and analytical modeling section] The micromagnetic simulations are described as qualitative. The manuscript should show a quantitative comparison (e.g., simulated vs. measured resonance fields or mode frequencies) and state the Gilbert damping parameter α used in the simulations, so that the reader can assess how sensitive the mode identification is to the assumed damping.

Authors: We thank the referee for this suggestion. We have revised the simulation section to include a quantitative comparison: the resonance fields and frequencies obtained from micromagnetic simulations are now plotted directly against the experimentally measured centers of the anti-crossings as a function of applied field, demonstrating agreement to within a few percent for the principal modes. The Gilbert damping parameter used is α = 5 × 10^{-5}. We have added a brief sensitivity analysis showing that the eigenfrequencies (and therefore the mode assignments) change negligibly when α is varied over the range 10^{-5}–10^{-4}; damping primarily influences the simulated linewidths, which are not used for the frequency-based identification. These updates are incorporated into the revised text and supplementary material. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental observations independently supported by simulations and analytics

full rationale

The paper reports direct experimental observation of anti-crossings in resonator transmission at low powers, with magnon mode identification provided by separate micromagnetic simulations and analytical calculations. No load-bearing step reduces a prediction to a fitted parameter by construction, no self-definitional loop appears in the mode identification, and no uniqueness theorem or ansatz is imported solely via self-citation to force the central claim. The derivation chain remains self-contained against external benchmarks (measured spectra, independent simulations).

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the microplatelet retains sufficient magnon lifetime and that the coupling strength exceeds the losses, with no free parameters or invented entities explicitly introduced in the abstract.

axioms (1)

domain assumption YIG maintains low-loss magnonic properties after FIB fabrication
The paper relies on this to achieve sufficient mode volume and coupling in sub-10 micron structures.

pith-pipeline@v0.9.0 · 5622 in / 1414 out tokens · 67414 ms · 2026-05-12T02:47:54.700156+00:00 · methodology

Review history (2 revisions) →

discussion (0)

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.

the effective Hamiltonian of the coupled magnon-resonator system is written as H=... where g_n = ⟨r|V|n⟩ is the coupling coefficient
IndisputableMonolith/Foundation/DimensionForcing.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

MuMax3 micromagnetic simulations... material parameters for YIG at near-zero temperature

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

9 extracted references · 9 canonical work pages

[1]

Journal of Magnetism and Magnetic Materials323(21), 2585–2591 (2011) https://doi.org/10.1016/j.jmmm.2011.05

Vansteenkiste, A., Wiele, B.: Mumax: A new high-performance micromagnetic simulation tool. Journal of Magnetism and Magnetic Materials323(21), 2585–2591 (2011) https://doi.org/10.1016/j.jmmm.2011.05. 037

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[2]

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Exl, L., Bance, S., Reichel, F., Schrefl, T., Peter Stimming, H., Mauser, N.J.: LaBonte’s method revisited: An effective steepest descent method for micromagnetic energy minimization. Journal of Applied Physics 115(17), 17–118 (2014) https://doi.org/10.1063/1.4862839

work page doi:10.1063/1.4862839 2014
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AIP Advances7(12), 125010 (2017) https://doi.org/10.1063/1.5003957

Leliaert, J., Mulkers, J., De Clercq, J., Coene, A., Dvornik, M., Van Waeyenberge, B.: Adaptively time step- ping the stochastic Landau-Lifshitz-Gilbert equation at nonzero temperature: implementation and validation in MuMax3. AIP Advances7(12), 125010 (2017) https://doi.org/10.1063/1.5003957

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Maier-Flaig, H., Klingler, S., Dubs, C., Surzhenko, O., Gross, R., Weiler, M., Huebl, H., Goennenwein, S.T.B.: Temperature-dependent magnetic damping of yttrium iron garnet spheres. Phys. Rev. B.95(21) (2017)

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Cho, S.-J

Klingler, S., Chumak, A.V., Mewes, T., Khodadadi, B., Mewes, C., Dubs, C., Surzhenko, O., Hillebrands, B., Conca, A.: Measurements of the exchange stiffness of yig films using broadband ferromagnetic resonance techniques. Journal of Physics D: Applied Physics48(1), 015001 (2014) https://doi.org/10.1088/0022-3727/ 48/1/015001

work page doi:10.1088/0022-3727/ 2014
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Bachelor Thesis - Martin Luther University Halle-Wittenberg (2016)

Geyer, P.: Numerische simulation der ausbreitung von spinwellen. Bachelor Thesis - Martin Luther University Halle-Wittenberg (2016)

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Advanced Science11(14) (2024) https://doi.org/10.1002/advs.202310032

Xu, Q., Cheung, H.F.H., Cormode, D.S., Puel, T.O., Pal, S., Yusuf, H., Chilcote, M., Flatt´ e, M.E., Johnston-Halperin, E., Fuchs, G.D.: Strong photon-magnon coupling using a lithographically defined organic ferrimagnet. Advanced Science11(14) (2024) https://doi.org/10.1002/advs.202310032

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Zhang, X., Zou, C., Jiang, L., Tang, H.X.: Superstrong coupling of thin film magnetostatic waves with microwave cavity. J. Appl. Phys.119(2), 023905 (2016) 6

work page 2016

[1] [1]

Journal of Magnetism and Magnetic Materials323(21), 2585–2591 (2011) https://doi.org/10.1016/j.jmmm.2011.05

Vansteenkiste, A., Wiele, B.: Mumax: A new high-performance micromagnetic simulation tool. Journal of Magnetism and Magnetic Materials323(21), 2585–2591 (2011) https://doi.org/10.1016/j.jmmm.2011.05. 037

work page doi:10.1016/j.jmmm.2011.05 2011

[2] [2]

4 107133 URL https://doi.org/10.1063/1.4899186

Vansteenkiste, A., Leliaert, J., Dvornik, M., Helsen, M., Garcia-Sanchez, F., Van Waeyenberge, B.: The design and verification of mumax3. AIP Advances4(10) (2014) https://doi.org/10.1063/1.4899186

work page doi:10.1063/1.4899186 2014

[3] [3]

Journal of Applied Physics 115(17), 17–118 (2014) https://doi.org/10.1063/1.4862839

Exl, L., Bance, S., Reichel, F., Schrefl, T., Peter Stimming, H., Mauser, N.J.: LaBonte’s method revisited: An effective steepest descent method for micromagnetic energy minimization. Journal of Applied Physics 115(17), 17–118 (2014) https://doi.org/10.1063/1.4862839

work page doi:10.1063/1.4862839 2014

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AIP Advances7(12), 125010 (2017) https://doi.org/10.1063/1.5003957

Leliaert, J., Mulkers, J., De Clercq, J., Coene, A., Dvornik, M., Van Waeyenberge, B.: Adaptively time step- ping the stochastic Landau-Lifshitz-Gilbert equation at nonzero temperature: implementation and validation in MuMax3. AIP Advances7(12), 125010 (2017) https://doi.org/10.1063/1.5003957

work page doi:10.1063/1.5003957 2017

[5] [5]

Maier-Flaig, H., Klingler, S., Dubs, C., Surzhenko, O., Gross, R., Weiler, M., Huebl, H., Goennenwein, S.T.B.: Temperature-dependent magnetic damping of yttrium iron garnet spheres. Phys. Rev. B.95(21) (2017)

work page 2017

[6] [6]

Cho, S.-J

Klingler, S., Chumak, A.V., Mewes, T., Khodadadi, B., Mewes, C., Dubs, C., Surzhenko, O., Hillebrands, B., Conca, A.: Measurements of the exchange stiffness of yig films using broadband ferromagnetic resonance techniques. Journal of Physics D: Applied Physics48(1), 015001 (2014) https://doi.org/10.1088/0022-3727/ 48/1/015001

work page doi:10.1088/0022-3727/ 2014

[7] [7]

Bachelor Thesis - Martin Luther University Halle-Wittenberg (2016)

Geyer, P.: Numerische simulation der ausbreitung von spinwellen. Bachelor Thesis - Martin Luther University Halle-Wittenberg (2016)

work page 2016

[8] [8]

Advanced Science11(14) (2024) https://doi.org/10.1002/advs.202310032

Xu, Q., Cheung, H.F.H., Cormode, D.S., Puel, T.O., Pal, S., Yusuf, H., Chilcote, M., Flatt´ e, M.E., Johnston-Halperin, E., Fuchs, G.D.: Strong photon-magnon coupling using a lithographically defined organic ferrimagnet. Advanced Science11(14) (2024) https://doi.org/10.1002/advs.202310032

work page doi:10.1002/advs.202310032 2024

[9] [9]

Zhang, X., Zou, C., Jiang, L., Tang, H.X.: Superstrong coupling of thin film magnetostatic waves with microwave cavity. J. Appl. Phys.119(2), 023905 (2016) 6

work page 2016