arxiv: 2605.10139 · v1 · submitted 2026-05-11 · ❄️ cond-mat.supr-con

Recognition: 2 theorem links

· Lean Theorem

Superconductivity Mediated Long Range Magnetic Coupling

Ming Yan Wang , Yi Liu , Yao Lu

Authors on Pith no claims yet

Pith reviewed 2026-05-12 04:30 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con

keywords Rashba superconductorferromagnetic insulatorslong-range magnetic interactionscircular supercurrentspower-law decaysuperconducting spintronicsstatic vs dynamic coupling

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The pith

Ferromagnetic insulators on a Rashba superconductor generate circular supercurrents that mediate long-range magnetic interactions decaying as power laws.

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

The paper examines a Rashba superconductor thin film with ferromagnetic insulators placed directly on top. The insulators induce circular supercurrents in the film that produce magnetic interactions between the insulators. These interactions decay according to power laws rather than exponentially. In the static case the coupling can be ferromagnetic, which differs from earlier results that found only antiferromagnetic interactions with exponential decay. The dynamic case shows a distinct distance dependence for the interaction.

Core claim

We show that the ferromagnetic insulators generate circular super-currents, enabling long-range magnetic interactions (LRMI), decaying in power laws. In the static case, the long-range magnetic interaction can be ferromagnetic, in contrast to previous studies showing that superconductor mediates anti-ferromagnetic interactions decaying exponentially. Surprisingly, we find that in the dynamic case, the LRMI has a different distance dependence.

What carries the argument

Circular super-currents induced in the Rashba superconductor thin film by the ferromagnetic insulators, which act as the mediator for the long-range magnetic interactions.

If this is right

In the static case the long-range magnetic interaction is ferromagnetic and decays as a power law.
In the dynamic case the long-range magnetic interaction follows a different distance dependence.
The mechanism offers potential applications in superconducting spintronics.

Where Pith is reading between the lines

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

Hybrid devices could exploit the power-law decay to achieve magnetic coupling across larger separations than exponential mechanisms allow.
Similar circular-current effects might appear in other superconductors that host strong Rashba-type spin-orbit coupling.
Varying the film thickness or the strength of the ferromagnetic moments could provide experimental control over the interaction range.

Load-bearing premise

The model assumes an ideal Rashba superconductor thin film with ferromagnetic insulators placed directly on top and that the induced supercurrents produce the claimed long-range interactions without significant contributions from disorder, finite temperature, or other unmodeled effects.

What would settle it

Measure the effective magnetic coupling strength or force between two ferromagnetic insulators at varying separation distances on the superconductor film and check whether the dependence follows a power law instead of exponential decay.

Figures

Figures reproduced from arXiv: 2605.10139 by Ming Yan Wang, Yao Lu, Yi Liu.

**Figure 3.** Figure 3: FIG. 3: Spatial distribution of the total induced current [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

read the original abstract

We study a Rashba superconductor thin film with ferromagnetic insulators (FIs) placed on top of it. We show that the ferromagnetic insulators generate circular super-currents, enabling long-range magnetic interactions (LRMI), decaying in power laws. In the static case, the long-range magnetic interaction can be ferromagnetic, in contrast to previous studies showing that superconductor mediates anti-ferromagnetic interactions decaying exponentially. Surprisingly, we find that in the dynamic case, the LRMI has a different distance dependence. Our results have potential applications in superconducting spintronics.

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

The abstract describes a Rashba-SC thin film with top FIs that induce circular supercurrents, producing static ferromagnetic power-law LRMI instead of the usual exponential AF decay, plus a different dynamic distance dependence.

read the letter

The main thing here is the claim that ferromagnetic insulators on a Rashba superconductor thin film create circular supercurrents that mediate long-range magnetic interactions with power-law decay, and that these interactions are ferromagnetic in the static limit. That sign flip and the power-law form are presented as different from earlier work on superconductor-mediated coupling. If the derivation holds up, it could be relevant for spintronic ideas that want longer-range ferromagnetic links inside a superconducting platform. The paper also notes a distinct distance dependence in the dynamic case, which adds a bit of new territory. The abstract is clear on the setup and the contrast with prior exponential AF results, so the direction is straightforward to follow. The potential applications in superconducting spintronics are mentioned without overclaiming. The soft spot is the handling of electromagnetic screening. The stress-test note flags that finite London penetration depth should turn the interaction exponential beyond roughly lambda, yet the abstract gives no sign that the model keeps a finite lambda or solves the coupled Maxwell-London equations self-consistently. If the calculation effectively takes lambda to infinity or skips the vector-potential feedback, the reported power-law and ferromagnetic sign could be an artifact. The weakest assumption listed is the ideal thin-film Rashba SC without disorder or temperature effects, which is common but still needs checking against the actual equations. The work is for readers who follow hybrid superconductor-magnet systems and are looking for mechanisms that could extend magnetic range. It is coherent on its own terms and engages the cited literature, so it deserves a serious referee even if the screening issue turns out to require revision. I would send it to review rather than desk-reject.

Referee Report

2 major / 2 minor

Summary. The manuscript studies a Rashba superconductor thin film with ferromagnetic insulators placed on top. It claims that the FIs induce circular supercurrents, which mediate long-range magnetic interactions (LRMI) decaying as power laws. In the static case these interactions can be ferromagnetic, in contrast to prior work reporting antiferromagnetic coupling with exponential decay; the dynamic case exhibits a different distance dependence. Potential applications in superconducting spintronics are noted.

Significance. If the central claims hold after including realistic screening, the work would offer a mechanism for power-law ferromagnetic coupling mediated by a Rashba superconductor, potentially enabling longer-range interactions than the exponential decay found in conventional treatments. This could be relevant for hybrid spintronic devices, though the result's robustness hinges on whether the power-law form survives the full electrodynamics.

major comments (2)

[Model description and derivation of LRMI] The power-law LRMI and the static-case sign reversal to ferromagnetic (abstract and main derivation) rest on the generation of circular supercurrents. The model description gives no indication that the full Maxwell-London equations with finite London penetration depth λ are solved self-consistently; a finite λ introduces Meissner screening that converts the interaction to exponential decay beyond ~λ. This approximation is load-bearing for the central 'long-range' and 'power-law' claims.
[Dynamic-case analysis] The distinction between static (ferromagnetic, power-law) and dynamic (different distance dependence) LRMI is presented as a key result. Without explicit expressions for the dynamic interaction (e.g., the frequency-dependent kernel or the resulting radial dependence), it is unclear whether the difference survives inclusion of finite λ or is an artifact of the same approximation used in the static case.

minor comments (2)

[Introduction] Explicit citations to the 'previous studies' that found antiferromagnetic exponential decay would allow readers to assess the precise contrast claimed in the abstract.
[Abstract] The abstract states 'decaying in power laws' without specifying the exponent; including the functional form (e.g., 1/r^n) in the abstract or a summary table would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each major comment below.

read point-by-point responses

Referee: [Model description and derivation of LRMI] The power-law LRMI and the static-case sign reversal to ferromagnetic (abstract and main derivation) rest on the generation of circular supercurrents. The model description gives no indication that the full Maxwell-London equations with finite London penetration depth λ are solved self-consistently; a finite λ introduces Meissner screening that converts the interaction to exponential decay beyond ~λ. This approximation is load-bearing for the central 'long-range' and 'power-law' claims.

Authors: We appreciate the referee pointing out the importance of screening. Our derivation employs the London relation for supercurrents in the thin-film geometry of the Rashba superconductor, where the 2D nature of the system and the Rashba-induced circular currents produce the reported power-law decay and ferromagnetic sign. We did not perform a full self-consistent 3D Maxwell-London solution with finite λ. We agree this is a relevant approximation and will revise the manuscript to state the thin-film limit explicitly, discuss the range of validity (distances ≪ λ), and add a qualitative estimate of how Meissner screening modifies the interaction at larger distances. revision: partial
Referee: [Dynamic-case analysis] The distinction between static (ferromagnetic, power-law) and dynamic (different distance dependence) LRMI is presented as a key result. Without explicit expressions for the dynamic interaction (e.g., the frequency-dependent kernel or the resulting radial dependence), it is unclear whether the difference survives inclusion of finite λ or is an artifact of the same approximation used in the static case.

Authors: The dynamic interaction is obtained from the frequency-dependent electromagnetic response of the superconductor. The change in distance dependence originates from retardation effects in the dynamic regime. We will include the explicit form of the frequency-dependent kernel and the resulting radial dependence in the revised manuscript. We will also note that finite-λ screening primarily affects the static contribution while the retarded dynamic part retains a distinct functional form over the relevant length scales. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained theoretical analysis.

full rationale

The paper presents a direct calculation of supercurrents induced by ferromagnetic insulators in a Rashba superconductor thin film, leading to power-law decaying LRMI with a sign change in the static limit. No load-bearing step reduces by construction to a fitted parameter, self-citation, or ansatz imported from the authors' prior work. The central results follow from solving the model's equations (London relation, Rashba SOC, etc.) under stated approximations, without tautological redefinition of outputs as inputs. External benchmarks like prior exponential-decay results are contrasted rather than presupposed. This is the normal non-circular outcome for a first-principles theoretical manuscript.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract supplies insufficient technical detail to enumerate free parameters, axioms, or invented entities; all fields are therefore left empty.

pith-pipeline@v0.9.0 · 5379 in / 1045 out tokens · 31698 ms · 2026-05-12T04:30:18.419352+00:00 · methodology

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.

We solve the London-Maxwell equations... jy(x) ≈ (e² D a_y / π r0) (r0/x)² ∝ 1/x²
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

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

The supercurrent is governed by... ∇²ϕ = 0 with boundary conditions j·n=0

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

30 extracted references · 30 canonical work pages

[1]

Anderson and H

P. Anderson and H. Suhl, Phys. Rev.116, 898 (1959)

work page 1959
[2]

A. I. Buzdin, Rev. Mod. Phys.77, 935 (2005)

work page 2005
[3]

F. S. Bergeret, A. F. Volkov, and K. Efetov, Phys. Rev. B69, 174504 (2004)

work page 2004
[4]

J. Xia, V. Shelukhin, M. Karpovski, A. Kapitulnik, and A. Palevski, Phys. Rev. Lett.102, 087004 (2009)

work page 2009
[5]

Eilenberger, Z

G. Eilenberger, Z. Phys. A214, 195 (1968)

work page 1968
[6]

K. D. Usadel, Phys. Rev. Lett.25, 507 (1970)

work page 1970
[7]

L. P. Gor’kov, Sov. Phys. JETP7, 158 (1958)

work page 1958
[8]

F. S. Bergeret, A. F. Volkov, and K. B. Efetov, Rev. Mod. Phys.77, 1321 (2005)

work page 2005
[9]

Ryazanov, V

V. Ryazanov, V. Oboznov, A. Y. Rusanov, A. Vereten- nikov, A. A. Golubov, and J. Aarts, Phys. Rev. Lett.86, 2427 (2001)

work page 2001
[10]

T. S. Khaire, M. A. Khasawneh, W. P. Pratt, Jr., and N. O. Birge, Phys. Rev. Lett.104, 137002 (2010)

work page 2010
[11]

Robinson, J

J. Robinson, J. Witt, and M. Blamire, Science329, 59 (2010)

work page 2010
[12]

Fiebig, J

M. Fiebig, J. Phys. D38, R123 (2005)

work page 2005
[13]

Levitov, Y

L. Levitov, Y. V. Nazarov, and G. Eliashberg, JETP Lett.41, 365 (1985)

work page 1985
[14]

Yip, Phys

S. Yip, Phys. Rev. B65, 144508 (2002)

work page 2002
[15]

Fujimoto, Phys

S. Fujimoto, Phys. Rev. B72, 024515 (2005)

work page 2005
[16]

F. Ando, Y. Miyasaka, T. Li, J. Ishizuka, T. Arakawa, Y. Shiota, T. Moriyama, Y. Yanase, and T. Ono, Nature 584, 373 (2020)

work page 2020
[17]

Daido, Y

A. Daido, Y. Ikeda, and Y. Yanase, Phys. Rev. Lett.128, 037001 (2022)

work page 2022
[18]

Linder and J

J. Linder and J. W. Robinson, Nat. Phys.11, 307 (2015)

work page 2015
[19]

Eschrig, Rep

M. Eschrig, Rep. Prog. Phys.78, 104501 (2015)

work page 2015
[20]

K.-R. Jeon, C. Ciccarelli, A. J. Ferguson, H. Kure- bayashi, L. F. Cohen, X. Montiel, M. Eschrig, J. W. Robinson, and M. G. Blamire, Nat. Mater.17, 499 (2018)

work page 2018
[21]

A. I. Buzdin, Phys. Rev. Lett.101, 107005 (2008)

work page 2008
[22]

D. Qiu, C. Gong, S. Wang, M. Zhang, C. Yang, X. Wang, and J. Xiong, Adv. Mater.33, 2006124 (2021)

work page 2021
[23]

Y. Lu, I. Tokatly, and F. S. Bergeret, Phys. Rev. B108, L180506 (2023)

work page 2023
[24]

Pearl, Appl

J. Pearl, Appl. Phys. Lett.5, 65 (1964). 7 Appendix A: Derivation of current in Fourier space for static case In the static limit, the supercurrent density is governed by the relation [23]: j=−e 2D(A+a t).(A1) The vector potentialAsatisfies the Maxwell equation∇ 2A=−µ 0j(x, y)δ(z). Applying a two-dimensional Fourier transform in thexy-plane, the equation ...

work page 1964
[25]

We parameterize the integration path by settingq=k 0 +is, wheres∈(0,∞) is a real variable representing the coordinate along the cut, and dq=ids

Parameterization and Discontinuity Evaluation The branch cut is defined as a vertical line extending from the branch pointk 0 tok 0 +i∞in the complexq-plane. We parameterize the integration path by settingq=k 0 +is, wheres∈(0,∞) is a real variable representing the coordinate along the cut, and dq=ids. The hairpin contour Γ cut consists of two paths: a dow...

work page
[26]

r0 p q2 −k 2 0 1 +r 0 p q2 −k 2 0 # J1(qr) qr ,(F10a) jθ(r, θ) =−e 2Daθ Z ∞ 0 q dq 2π

Analytical Form of the Final Integral Substituting the derived discontinuity into Eq. (D3), and factoring out the constants, we have: I(x) =i 2eiπ/4eik0x Z ∞ 0 √se−sxds.(D7) 11 The integral overscan be evaluated using the the Gamma function, R ∞ 0 sne−sxds= Γ(n+ 1)/x n+1. Forn= 1/2: Z ∞ 0 s1/2e−sxds= Γ(3/2) x3/2 = √π 2x3/2 .(D8) By applying Euler’s formul...

work page
[27]

Far-Field Approximation We evaluate the asymptotic behavior of Eq. (F7). The asymptotic expressions for the radial and azimuthal current components are: jr(r, θ)≈ −e 2Dar −ik0r0 1−ik 0r0 1 2πr2 ,(F11a) jθ(r, θ)≈e 2Daθ −ik0r0 1−ik 0r0 1 2πr2 −i e2Daθk0r0 2πr2 eik0r.(F11b) It is crucial to note that, in the strict static limit, all the terms of Eq. (F11b) v...

work page
[28]

r0 p q2 −k 2 0 1 +r 0 p q2 −k 2 0 # J1(qr) qr ,(H10) jθ(r, θ) =−e 2Daθ Z ∞ 0 q dq 2π

Different Topology Case To explore the effects of different boundary topologies, we transition from a large superconductor film to a spherical. Assume the radial Rashba spin-orbit coupling is isotropic. We consider a localized magnetic impurity located at the coordinates (R, θ 0, φ0), where ˆr0 denotes the unit radial vector pointing from the origin to th...

work page
[29]

Consequently, at theq= 0 limit, we haveκ(0) =−ik 0

To satisfy causality, we applyω→ω+i0 +, which ensuresk 0 →k 0 +i0 +. Consequently, at theq= 0 limit, we haveκ(0) =−ik 0. The zero-momentum limit of the kernel evaluates to: f(0) = −ik0r0 1−ik 0r0 .(I2) The integral expression for the radial current is: jr(r, θ) =−e 2Dar Z ∞ 0 q dq 2π f(q) J1(qr) qr =−e 2Dar 1 2πr Z ∞ 0 f(q)J 1(qr)dq.(I3) In the far-field ...

work page
[30]

Substituting this result back into Eq

The corresponding evaluation on the right side yields: ∂2 ∂z2 eik0 √ r2+z2 √ r2 +z 2 ! z=0 = 1 r ∂ ∂r eik0r r = ik0 r2 eik0r − 1 r3 eik0r.(I10) Retaining the leading order 1/r 2 term for the far-field expansion, the integral simplifies toik 0eik0r/r2. Substituting this result back into Eq. (I8) gives: Irad =−i e2Daθk0r0 2πr2 eik0r.(I11) 18 Summing the two...

work page