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REVIEW 3 major objections 5 minor 67 references

A ferromagnet that collapses its magnetization on photon impact can lift infrared single-photon detectors to 3.25–3.75 K.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-02 11:06 UTC pith:K4K3C3WT

load-bearing objection New dynamic idea, but the magnetization collapse is an input assumption; worth reviewing to force the energy budget. the 3 major comments →

arxiv 2606.17177 v3 pith:K4K3C3WT submitted 2026-06-15 cond-mat.supr-con quant-ph

Hybrid Ferromagnet-SNSPDs: Single photon induced order-to-disorder transition in ferromagnets coupled to thin film superconductors

Leif Bauer , Daien He , Sathwik Bharadwaj , Zubin Jacob This is my paper
classification cond-mat.supr-con quant-ph
keywords superconducting nanowire single-photon detectorferromagnet/superconductor bilayervortex crossing barrierdark count ratemid-infrared single-photon detectionCurie temperature engineeringnoise equivalent powerNiCu alloy
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper proposes a hybrid ferromagnet/superconductor single-photon detector in which a magnetic layer both suppresses dark counts and loses its magnetization when a photon is absorbed. A static ferromagnet would reduce dark noise but also block real photon signals; the central idea is to make the magnetic barrier collapse on photon impact by setting the ferromagnet's Curie temperature just above the operating temperature. With this hybrid phase transition, the vortex crossing barrier stays high in the dark and drops sharply after photon absorption, preserving detection efficiency. The authors predict single-photon sensitivity at 3.25–3.75 K for 3–14 µm light, with noise equivalent power below the single-photon limit, which would allow simpler liquid-helium cryocooling instead of dilution refrigeration.

Core claim

The central claim is that a ferromagnet/superconductor bilayer can simultaneously achieve a low dark count rate and high single-photon detection efficiency in the mid- and longwave infrared, raising the operating temperature to 3.25–3.75 K. The detection sequence is: an incident photon creates a hotspot in the superconductor; heat spreads into the ferromagnet, which sits near its Curie temperature, triggering an order-to-disorder transition that reduces the magnetization and therefore the magnetic field in the superconductor; the reduced field lowers the vortex crossing barrier enough for one vortex to cross, producing a 2π phase slip and a normal-state transition that registers as a count.

What carries the argument

The enabling mechanism is the hybrid ferromagnet–superconductor phase transition: a ferromagnet with perpendicular magnetic anisotropy and a Curie temperature close to the operating temperature produces a static field Hi that raises the vortex crossing barrier Umax and suppresses dark counts; after photon absorption, the magnetization follows an exponential collapse H(t) = Hi(1 − a e^(−t/τ)), lowering the barrier during the 5–15 ps vortex crossing window and triggering a count. The analysis rests on the single-vortex model, with the crossing rate Γv = αv exp(−Umax/kBT) and SDE obtained from the time-integrated crossing probability.

Load-bearing premise

The whole prediction rests on one infrared photon measurably heating the ferromagnet: the paper assumes a single absorbed 0.09–0.4 eV photon drops the magnetization enough to cut the magnetic field by up to ~95% within 5–15 ps, while the same film still supplies 10–40 mT in the dark; the post-photon temperature T(0) that would justify this drop is never quantified in the main text.

What would settle it

Measure the magnetization of a 6 nm Ni0.44Cu0.56 film at 3–4 K immediately after absorption of a single 5 µm photon, or calculate T(0) − Ti from the film's heat capacity and the photon energy. A collapse of only a few percent, or a thermal time constant much longer than the 5–15 ps vortex-crossing window, would move the SDE plateau to bias currents above Ic and erase the predicted NEP improvement.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Midwave/longwave infrared single-photon detection could run at 3.25–3.75 K, replacing dilution refrigerators and 3He cryogens with simpler helium-compressor cryostats.
  • The ferromagnet's static field suppresses dark counts while the photon-induced magnetization collapse keeps the SDE plateau above 0.99, pushing noise equivalent power below the single-photon limit.
  • Visible-to-SWIR hybrid detectors could operate near 4.25 K, roughly at liquid-helium temperature.
  • Candidate ferromagnets such as CuVP2S6, TmNiAl2, and Eu3Sb4Se9, along with engineered NixCu1−x alloys, provide tunable Curie temperatures and perpendicular anisotropy for the required operating range.
  • The proximity effect of a thin NiCu layer on NbN is predicted to be small at high copper concentrations, so the ferromagnet layer does not destroy superconductivity.

Where Pith is reading between the lines

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

  • If the magnetization-collapse mechanism works as modeled, the same bilayer concept could be extended to other wavelengths and detector materials by matching the ferromagnet's Curie temperature and thermal time constant to the vortex-crossing window; the key tunable parameter is the fractional collapse a of the magnetic field.
  • A practical device may need an absorber or waveguide that deposits the photon energy directly in the ferromagnet, since the paper's model assumes heat flows from the hotspot into the magnetic layer; whether a single 0.1 eV photon can heat a 6 nm film enough is the open experimental question.
  • The design principle emerging from this work is to choose ferromagnets with a sharp magnetization slope near the operating point, not merely a low Curie temperature, because the SDE plateau is recovered only when the photon-induced field reduction is large relative to the initial field.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The manuscript proposes a hybrid ferromagnet/superconductor SNSPD in which a static magnetic field from the ferromagnetic layer suppresses thermally activated vortex crossing (dark counts), while an absorbed infrared photon heats the ferromagnet near its Curie temperature, transiently collapses the field, and restores detection efficiency. Using a vortex-crossing rate model (Eqs. 1–6), TDGL simulations, atomistic spin dynamics, and proximity-effect calculations, it predicts single-photon operation at 3.25–3.75 K for MWIR/LWIR wavelengths. The central claim is that the photon-induced order-to-disorder transition in the ferromagnet causes a vortex-induced phase transition in the superconductor. The quantitative predictions hinge on Eq. (8), where the fractional field reduction parameter a is an input, not a derived quantity.

Significance. If fully established, the proposed mechanism would be significant: it could replace dilution refrigeration with closed-cycle helium cryostats for mid- and long-wave infrared single-photon detection. The vortex-crossing rate model is standard, and the qualitative direction—magnetic field raises the vortex barrier and suppresses dark counts, while reducing the field restores the SDE plateau—is coherent with existing experiments and the TDGL result in Fig. 3. The paper also includes concrete ASD and Usadel calculations for a NiCu ferromagnet. However, the predicted operating temperatures are not currently supported because the single-photon magnetization collapse is assumed rather than calculated; the headline NEP/SDE results reduce to the hand-set parameter a.

major comments (3)
  1. [§III B, Eq. (8), Fig. 5] The enabling mechanism is not derived. Eq. (7) defines T(t) with T(0) unspecified, and Eq. (8) states without derivation that the magnetization follows the same exponential relaxation. The fractional field reduction a is a free parameter. The headline calculations in Fig. 5 use a = 0.95 (H_i → 0.05H_i) and τ = 100 ps, and the NEP/SDE curves reduce to these choices. No energy-budget calculation translates a 0.09–0.4 eV photon into a ~95% magnetization collapse within the 5–15 ps vortex-crossing window. The Supplementary Material is cited as containing 'Analysis of single-photon induced changes in magnetization' but that material is absent from this version. This is the load-bearing step of the paper, so it must be supplied and justified before the operating-temperature predictions can be evaluated.
  2. [§III B, Eq. (7), thermal response] The thermal model is too schematic to support the ps-time-scale field collapse. T(0) is never quantified; the heat capacity, volume, and interface conductance of the ferromagnet are not used; and no estimate shows that heat deposited in the superconducting nanowire is transferred to the ferromagnet on the 5–15 ps timescale required. The assumption that magnetization follows the temperature relaxation (Eq. 8) ignores spin-lattice and critical-slowing-down physics. As written, τ is another free parameter; Fig. 5 chooses τ = 100 ps. The authors should provide at least an order-of-magnitude heat budget and a justification of the magnetization–temperature mapping, including the time scale of magnetization response near T_Curie.
  3. [§III C, §IV, Fig. 2 vs Fig. 6] The material designs in Fig. 2 are difficult to reconcile with the inputs in Fig. 5. To have H_i = 40 mT idle, the ferromagnet must be below T_Curie with substantial order; to have a ≈ 0.95 after a single photon, it must be very close to T_Curie. Fig. 2's LWIR design uses CuVP2S6 with T_Curie = 3.3 K at T ≈ 3.25 K, where the equilibrium magnetization is already small, whereas the ASD example Ni0.44Cu0.56 (T_Curie ~17 K) has large dM/dT only near ~10 K (Fig. 6c), not in the 3.25–3.75 K window. The paper acknowledges in Sec. III C that large H_i require proportionally larger reductions, but no single material or parameter set is shown to satisfy both conditions simultaneously.
minor comments (5)
  1. [General] There are typographical issues: 'F erromagnet' in the Section III B heading, and 'L WIR' spacing throughout.
  2. [Eq. (8)] Define a before it is used, state units for τ, and connect the Fig. 5 caption notation H_i → 0.05H_i explicitly to a = 0.95.
  3. [Ref. 29] The reference is a placeholder ('URL-will-be-inserted-by-publisher') and the Supplementary Material, which is essential for the central claim, is not included in the arXiv version. This should be resolved before review.
  4. [Fig. 5] The reduced T_c values (12.47 K, 8 K, 6 K) are used but the method of reduction is not specified beyond a general mention of disorder. A reference or equation would clarify the assumed material parameters.
  5. [Fig. 4] λ_p is used in the captions but never defined; presumably it is the photon wavelength.

Circularity Check

2 steps flagged

The 3.25-3.75 K operating-temperature prediction is set by the assumed 95% magnetization-collapse parameter a in Eq. 8; the central result reduces to hand-set inputs.

specific steps
  1. fitted input called prediction [Sec. III B, Eq. (8); Sec. III D, Fig. 5 caption]
    "We take the ferromagnet magnetization after heating to follow a similar trend as (Eq. 7) [50]. Therefore, the time-varying magnetic field will follow H(t) =Hi(1−ae−t/τ) (8) where Hi is the initial magnetic field, and Hi(1−a) is the magnetic field after heating from the incident photon."

    The headline NEP and 3.25-3.75 K operating temperatures are obtained by inserting a=0.95 (Hi→0.05Hi), Hi=40 mT, and τ=100 ps into Eqs. (3)-(6) and (8). Parameter a is never derived from photon energy, heat capacity, or the magnetization curve: T(0) in Eq. (7) is never quantified, and the magnetization is 'taken' to follow the temperature exponential, not calculated. The listed Supplementary Material 'Analysis of single-photon induced changes in magnetization' is not present, so the decisive calculation is missing. Thus the claimed hybrid phase transition is an assumed input, not an output: the 'prediction' is generated from the chosen value of a by construction.

  2. self citation load bearing [Sec. II, Eq. (3); refs. 13, 25]
    "We employ the single vortex model of SNSPD detection to model device metrics, which has recently been demonstrated to be effective in modeling dark count rate, system detection efficiency, and timing jitter [24, 25]. ... Γv =αv exp(−Umax/kBT) (3) where αv is the vortex attempt rate (a material dependent fitting parameter)."

    The quantitative rate law used for both DCR and SDE is justified by the authors' own 'Unified theory' (ref. [25]) and the same group's ref. [13]; αv is a material-dependent fitting parameter carried from that framework. Since DCR = Γv ∝ αv and NEP = hf sqrt(2DCR)/SDE, the numerical single-photon-limit curves inherit a self-cited fit. This is secondary: the direction of dark-count suppression is externally anchored by refs. 17-20 and the TDGL simulation, but the quantitative predictions are not independent of the authors' prior fitted model.

full rationale

The paper is not globally circular: dark-count suppression by magnetic field is externally supported (refs. 17-20), the TDGL/ASD/proximity analyses are independent modeling components, and the vortex barrier formula is from external theory. The circularity is localized to the central headline claim. The NEP-based single-photon-limit temperatures (Fig. 5 and abstract) are computed from explicitly assumed inputs: Hi=40 mT, Hi→0.05Hi, τ=100 ps in the caption, and a in Eq. (8) is acknowledged only as 'we take', not derived. No energy-budget or magnetization calculation connects a 0.09-0.4 eV photon to a ~95% field collapse; the relevant Supplementary Material item is listed but absent. The secondary dependence on α_v from the authors' own fitted model further means the quantitative NEP values are not independently derived. Hence the headline prediction reduces by construction to hand-set parameters, meriting a partial-circularity score of 6, rather than 8-10 because the model framework and materials analysis contain substantial independent content.

Axiom & Free-Parameter Ledger

7 free parameters · 6 axioms · 0 invented entities

The model (Eqs. 1-6) is standard from prior literature; the paper's contribution is the proposed dynamic field reduction, which enters as assumed parameters 'a', τ, and T(0), plus material-specific simulations whose exchange parameters are fitted to experimental Curie temperatures. The headline 3.25-3.75K operating temperatures are direct outputs of these assumed inputs.

free parameters (7)
  • a (fractional field reduction after photon) = 0.95 in headline Fig. 5; 0.5-0.9 in Fig. 4 variants
    Eq. 8. The reduction in magnetic field after photon incidence is assumed, not computed. This parameter sets the size of the hybrid effect.
  • τ (thermal time constant of ferromagnet) = 100 ps in headline; 1, 10 ps scanned
    Eqs. 7-8. Chosen from geometry/sound-velocity estimates; gates whether the barrier drop co-occurs with the vortex-crossing window.
  • Hi (initial magnetic field) = 40 mT in headline; 10-50 mT stated as required
    Eq. 8 and Fig. 5. Must be 10-40 mT to suppress dark counts per ref. 17; assumed reachable by a ferromagnet simultaneously sitting near its Curie temperature.
  • T(0) (post-photon ferromagnet temperature) = not specified
    Eq. 7. The temperature after heating from the incident photon is never quantified; the entire magnetization reduction depends on it.
  • α_v (vortex attempt rate) = not stated numerically
    Eq. 3. 'Material dependent fitting parameter'; taken from the authors' own unified theory (ref. 25).
  • E_xc (ferromagnet exchange potential) = obtained from fits to experimental Curie temperatures
    Sec. IV B, Eq. 10b. Fit to literature data; used in the Usadel proximity calculation.
  • Reduced superconducting T_c values = 6 K (LWIR), 8 K (MWIR), 12.47 K (SWIR)
    Fig. 2/5. Chosen per wavelength band; motivates defect-engineering of NbN (ref. 37).
axioms (6)
  • domain assumption The single-vortex crossing model with barrier Eq. 1 describes SNSPD detection and dark counts.
    Sec. II, Eqs. 1-5, refs. 13, 16, 24, 25. The whole device analysis stands on this model being valid for thin-film NbN at the proposed temperatures.
  • domain assumption Vortex crossing is a thermally activated process with rate Γ = α_v exp(-U_max/k_BT) (Kramers theory).
    Eq. 3, ref. 28.
  • domain assumption Ferromagnet temperature follows lumped-capacitance exponential relaxation (Eq. 7).
    Sec. III B. No finite-element heat transport across the S/F interface or phonon bottleneck is modeled.
  • ad hoc to paper Ferromagnet magnetization follows the same exponential relaxation as temperature (Eq. 8).
    Sec. III B: 'We take the ferromagnet magnetization after heating to follow a similar trend as (Eq. 7)'. This is the step that produces the dynamic barrier reduction; it is assumed, not derived (no LLG dynamics with a thermal transient, no critical dynamics near T_Curie).
  • domain assumption A ferromagnet with perpendicular anisotropy, Curie temperature within ~0.1 K of the operating temperature, enough moment to give 10-40 mT when nearly disordered, and ps-scale magnetization response exists or can be engineered.
    Secs. II and IV. The requirements are mutually strained near T_Curie: a small order parameter means a small field, and critical slowing-down conflicts with the ps response.
  • domain assumption Usadel self-consistency (Eq. 9) governs the proximity-suppressed superconducting critical temperature.
    Sec. IV B, refs. 63, 64.

pith-pipeline@v1.3.0-alltime-deepseek · 5101 in / 5271 out tokens · 291873 ms · 2026-08-02T11:06:45.542715+00:00 · methodology

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read the original abstract

The development of midwave and longwave infrared single photon detectors is crucial for their emerging applications in spectroscopy, remote sensing, exoplanet detection, and free space quantum communications. However, existing sensors need to be operated at extremely low temperatures (0.08-0.9K) to reduce dark noise and hence require the use of advanced cryogenics such as dilution refrigerators or $^3$He cryogens, significantly limiting applications. Here we propose a vortex-engineering approach based on a hybrid phase transition in a ferromagnet/superconductor bilayer to increase the operating temperature of infrared single photon detectors up to 3.75K. We show that the introduction of a ferromagnetic layer produces a local magnetic field which impedes vortex crossing in the superconductor, reducing dark noise. When a single photon is incident, the photon-induced hotspot causes an order-to-disorder transition in the ferromagnet, leading to a vortex-induced phase transition in the superconducting layer. By engineering the ferromagnet's Curie temperature to be close to the device's operating temperature, single photon sensitivity can be achieved at increased operating temperatures. We predict at midwave/longwave infrared wavelengths (3-14$\mu$m) the operating temperature can be raised to 3.25-3.75K, enabling significantly simpler cooling systems.

Figures

Figures reproduced from arXiv: 2606.17177 by Daien He, Leif Bauer, Sathwik Bharadwaj, Zubin Jacob.

Figure 1
Figure 1. Figure 1: FIG. 1. Hybrid phase transition in a ferromagnet/superconductor (FM-S) bilayer. (a) When no photons are incident the vortex [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Potential hybrid FM-SNSPD designs for LWIR, MWIR, visible-SWIR, and high temperature operations where [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Dark count behavior of SNSPDs and FM-SNSPDs. (a-b) Time dependent Ginzburg-Landau simulation of vortex [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Effect of time-varying ferromagnet temperature on SNSPD sensitivity. (a) An incident IR photon causes a change [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Impact of ferromagnet/superconductor bilayers on infrared NEP. (a-c) Solid lines indicate hybrid FM-SNSPDs, while [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Synthetic ferromagnet design. (a) Atomistic spin dynamics (ASD) simulation of Ni [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

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Reference graph

Works this paper leans on

67 extracted references

  1. [1]

    J. A. Lau, V. B. Verma, D. Schwarzer, and A. M. Wodtke, Superconducting single-photon detectors in the mid-infrared for physical chemistry and spectroscopy, Chem. Soc. Rev.52, 921 (2023)

    2023

  2. [2]

    F. Bao, L. Bauer, A. Rubio Lopez, Z. Yang, X. Wang, and Z. Jacob, Photon discerner: Adaptive quantum op- tical sensing near the shot noise limit, New J. Phys.26, 10.1088/1367-2630/ad6584 (2024)

    doi:10.1088/1367-2630/ad6584 2024

  3. [3]

    Baudis, A

    L. Baudis, A. Bismark, N. Brugger, C. Capelli, I. Charaev, J. C. Garc ´ ıa, G. D. Hadas, Y. Hochberg, J. K. Hohmann, A. Kavner, C. Koos, A. Kuzmin, B. V. Lehmann, S. N¨ ageli, T. Neupert, B. Penning, D. R. Garc ´ ıa, and A. Schilling, First Sub-MeV Dark Matter Search with the QROCODILE Experiment Using Su- perconducting Nanowire Single-Photon Detectors, P...

    2025

  4. [4]

    E. E. Wollman, V. B. Verma, A. B. Walter, J. Chiles, B. Korzh, J. P. Allmaras, Y. Zhai, A. E. Lita, A. N. McCaughan, E. Schmidt, S. Frasca, R. P. Mirin, S.-W. Nam, and M. D. Shaw, Recent advances in superconduct- ing nanowire single-photon detector technology for exo- planet transit spectroscopy in the mid-infrared, JATIS7, 011004 (2021), publisher: SPIE

    2021

  5. [5]

    Dello Russo, A

    S. Dello Russo, A. Elefante, D. Dequal, D. K. Pal- lotti, L. Santamaria Amato, F. Sgobba, and M. Siciliani De Cumis, Advances in Mid-Infrared Single-Photon De- tection, Photonics9, 470 (2022)

    2022

  6. [6]

    Cherednichenko, N

    S. Cherednichenko, N. Acharya, E. Novoselov, and V. Drakinskiy, Low kinetic inductance superconducting MgB 2 nanowires with a 130 ps relaxation time for single- photon detection applications, Supercond. Sci. Technol. 34, 044001 (2021)

    2021

  7. [7]

    Korzh, Q.-Y

    B. Korzh, Q.-Y. Zhao, J. P. Allmaras, S. Frasca, T. M. Autry, E. A. Bersin, A. D. Beyer, R. M. Briggs, B. Bum- ble, M. Colangelo, G. M. Crouch, A. E. Dane, T. Gerrits, A. E. Lita, F. Marsili, G. Moody, C. Pe˜ na, E. Ramirez, J. D. Rezac, N. Sinclair, M. J. Stevens, A. E. Velasco, V. B. Verma, E. E. Wollman, S. Xie, D. Zhu, P. D. Hale, M. Spiropulu, K. L. ...

    2020

  8. [8]

    D. V. Reddy, R. R. Nerem, S. W. Nam, R. P. Mirin, and V. B. Verma, Superconducting nanowire single-photon detectors with 98% system detection efficiency at 1550 nm, Optica7, 1649 (2020)

    2020

  9. [9]

    Colangelo, A

    M. Colangelo, A. B. Walter, B. A. Korzh, E. Schmidt, B. Bumble, A. E. Lita, A. D. Beyer, J. P. Allmaras, R. M. Briggs, A. G. Kozorezov, E. E. Wollman, M. D. Shaw, and K. K. Berggren, Large-Area Superconduct- ing Nanowire Single-Photon Detectors for Operation at Wavelengths up to 7.4 um, Nano Lett.22, 5667 (2022), publisher: American Chemical Society

    2022

  10. [10]

    V. B. Verma, B. Korzh, A. B. Walter, A. E. Lita, R. M. Briggs, M. Colangelo, Y. Zhai, E. E. Wollman, A. D. Beyer, J. P. Allmaras, H. Vora, D. Zhu, E. Schmidt, A. G. Kozorezov, K. K. Berggren, R. P. Mirin, S. W. Nam, and M. D. Shaw, Single-photon detection in the mid- infrared up to 10 um wavelength using tungsten silicide superconducting nanowire detector...

    2021

  11. [11]

    Q. Chen, R. Ge, L. Zhang, F. Li, B. Zhang, F. Jin, H. Han, Y. Dai, G. He, Y. Fei, X. Wang, H. Wang, X. Jia, Q. Zhao, X. Tu, L. Kang, J. Chen, and P. Wu, Mid-infrared single photon detector with superconductor Mo0.8Si0.2 nanowire, Science Bulletin66, 965 (2021)

    2021

  12. [12]

    G. G. Taylor, A. B. Walter, B. Korzh, B. Bumble, S. R. Patel, J. P. Allmaras, A. D. Beyer, R. O’Brient, M. D. Shaw, and E. E. Wollman, Low-noise single-photon counting superconducting nanowire detectors at infrared wavelengths up to 29 um, Optica10, 1672 (2023)

    2023

  13. [13]

    Jahani, L.-P

    S. Jahani, L.-P. Yang, A. Buganza Tepole, J. C. Bardin, H. X. Tang, and Z. Jacob, Probabilistic vortex crossing criterion for superconducting nanowire single-photon de- tectors, Journal of Applied Physics127, 143101 (2020)

    2020

  14. [14]

    Abrikosov, The magnetic properties of superconduct- ing alloys, Journal of Physics and Chemistry of Solids2, 199 (1957)

    A. Abrikosov, The magnetic properties of superconduct- ing alloys, Journal of Physics and Chemistry of Solids2, 199 (1957). 10

    1957

  15. [15]

    Tinkham,Introduction to superconductivity, 2nd ed., Dover books on physics (Dover Publ, Mineola, NY, 2015)

    M. Tinkham,Introduction to superconductivity, 2nd ed., Dover books on physics (Dover Publ, Mineola, NY, 2015)

    2015

  16. [16]

    L. N. Bulaevskii, M. J. Graf, and V. G. Kogan, Vortex- assisted photon counts and their magnetic field depen- dence in single-photon superconducting detectors, Phys. Rev. B85, 014505 (2012)

    2012

  17. [17]

    Charaev, A

    I. Charaev, A. Semenov, K. Ilin, and M. Siegel, Magnetic- Field Enhancement of Performance of Superconducting Nanowire Single-Photon Detector, IEEE Trans. Appl. Supercond.29, 1 (2019)

    2019

  18. [18]

    B. J. Lawrie, C. E. Marvinney, Y.-Y. Pai, M. A. Feld- man, J. Zhang, A. J. Miller, C. Hua, E. Dumitrescu, and G. B. Halasz, Multifunctional Superconducting Nanowire Quantum Sensors, Phys. Rev. Appl.16, 064059 (2021), publisher: American Physical Society

    2021

  19. [19]

    Engel, A

    A. Engel, A. Schilling, K. Il’in, and M. Siegel, Depen- dence of count rate on magnetic field in superconducting thin-film TaN single-photon detectors, Phys. Rev. B86, 140506 (2012)

    2012

  20. [20]

    Cristiano, L

    R. Cristiano, L. Parlato, U. Nasti, M. Ejrnaes, H. My- oren, T. Taino, R. Sobolewski, and G. P. Pepe, Supercon- ductor/Ferromagnet Nanowires for Optical Photon De- tection, IEEE Transactions on Applied Superconductiv- ity26, 1 (2016)

    2016

  21. [21]

    Chang, J

    J. Chang, J. W. N. Los, R. Gourgues, S. Steinhauer, S. N. Dorenbos, S. F. Pereira, H. P. Urbach, V. Zwiller, and I. Esmaeil Zadeh, Efficient mid-infrared single-photon detection using superconducting NbTiN nanowires with high time resolution in a Gifford-McMahon cryocooler, Photon. Res.10, 1063 (2022)

    2022

  22. [22]

    A. Azem, D. V. Morozov, D. Kuznesof, C. Bruscino, R. H. Hadfield, L. Chrostowski, and J. F. Young, Mid-infrared characterization of NbTiN superconducting nanowire single-photon detectors on silicon-on-insulator, Applied Physics Letters125, 211102 (2024)

    2024

  23. [23]

    Marsili, F

    F. Marsili, F. Bellei, F. Najafi, A. E. Dane, E. A. Dauler, R. J. Molnar, and K. K. Berggren, Efficient Single Photon Detection from 500 nm to 5 um Wavelength, Nano Lett. 12, 4799 (2012)

    2012

  24. [24]

    Engel, J

    A. Engel, J. J. Renema, K. Il’in, and A. Semenov, De- tection mechanism of superconducting nanowire single- photon detectors, Supercond. Sci. Technol.28, 114003 (2015)

    2015

  25. [25]

    D. He, L. Bauer, S. Bharadwaj, and Z. Jacob, Unified theory of dark count rate and system detection efficiency for nbn, wsi based superconducting single photon detec- tors, Journal of Applied Physics139, 063901 (2026)

    2026

  26. [26]

    Qiu and T

    C. Qiu and T. Qian, Numerical study of the phase slip in two-dimensional superconducting strips, Phys. Rev. B 77, 174517 (2008)

    2008

  27. [27]

    L. N. Bulaevskii, M. J. Graf, C. D. Batista, and V. G. Kogan, Vortex-induced dissipation in narrow current- biased thin-film superconducting strips, Phys. Rev. B83, 144526 (2011)

    2011

  28. [28]

    H¨ anggi, P

    P. H¨ anggi, P. Talkner, and M. Borkovec, Reaction-rate theory: fifty years after Kramers, Rev. Mod. Phys.62, 251 (1990)

    1990

  29. [29]

    See Supplemental Material at URL-will-be-inserted-by- publisher for additional simulation details

  30. [30]

    Engel and A

    A. Engel and A. Schilling, Numerical analysis of detection-mechanism models of superconducting nanowire single-photon detector, Journal of Applied Physics114, 214501 (2013)

    2013

  31. [31]

    R. H. Hadfield, Single-photon detectors for optical quan- tum information applications, Nature Photon3, 696 (2009)

    2009

  32. [32]

    J. W. Xu, X. Q. Zheng, S. X. Yang, S. H. Shao, J. Q. Liu, J. Y. Zhang, S. G. Wang, Z. Y. Xu, L. C. Wang, S. Zhang, Z. Q. Zhang, and B. G. Shen, Low working temperature near liquid helium boiling point of RNiAl2 (R=Tm, Tb and Gd) compounds with large magnetocaloric effect, J. Appl. Phys.125, 225102 (2019)

    2019

  33. [33]

    L. Li, K. Nishimura, W. D. Hutchison, Z. Qian, D. Huo, and T. NamiKi, Giant reversible magnetocaloric effect in ErMn2Si2 compound with a second order magnetic phase transition, Applied Physics Letters100, 152403 (2012)

    2012

  34. [34]

    S. Wang, Y. Wu, T. Cao, X. Wang, Y.-Z. Long, D. Chen, and B. Teng, Magnetic properties of a pseudo-one- dimensional ferrimagnetic semiconductor Eu3Sb4Se9, Applied Physics Letters117, 232405 (2020)

    2020

  35. [35]

    G. A. Jacob and R. J. Joseyphus, Enhanced Curie Temperature and Critical Exponents of Fe-Substituted NiCu Alloy, physica sta- tus solidi (a)218, 2100050 (2021), eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/pssa.202100050

    doi:10.1002/pssa.202100050 2021

  36. [36]

    T. J. Hicks, B. Rainford, J. S. Kouvel, G. G. Low, and J. B. Comly, Giant Moments in Ni-Cu Alloys Near the Critical Composition, Phys. Rev. Lett.22, 531 (1969)

    1969

  37. [37]

    Zhang, Q

    W. Zhang, Q. Jia, L. You, X. Ou, H. Huang, L. Zhang, H. Li, Z. Wang, and X. Xie, Saturating Intrinsic De- tection Efficiency of Superconducting Nanowire Single- Photon Detectors via Defect Engineering, Phys. Rev. Ap- plied12, 044040 (2019)

    2019

  38. [38]

    C. Wang, B. Lichtenwalter, A. Friebel, and H. X. Tang, A closed-cycle 1 K refrigeration cryostat, Cryogenics64, 5 (2014)

    2014

  39. [39]

    P. Liu, D. Yuan, C. Dong, G. Lin, E. G. Villora, J. Qi, X. Zhao, K. Shimamura, J. Ma, J. Wang, Z. Zhang, and B. Li, Ultralow-field magnetocaloric materials for compact magnetic refrigeration, NPG Asia Mater15, 41 (2023), publisher: Nature Publishing Group

    2023

  40. [40]

    R. Xie, Z. Lin, Y. Cao, C. Yun, Z. Zhang, S. Fan, Y. Peng, X. Ma, K. Li, C. Shi, D. Zhou, R. Han, H. Du, X. Liu, Z. Luo, J. Yang, and W. Yang, Cu-driven ferroionic structure and pressure-tunable magnetism in layered thiophosphate cuvp2s6, Advanced Materials38, e20850 (2026)

    2026

  41. [41]

    Z. Mo, J. Jiang, L. Tian, H. Xie, Y. Li, X. Zheng, L. Zhang, X. Gao, Z. Li, G. Liu, L. Li, and J. Shen, Ferro- magnetic Eu2SiO4 Compound with a Record Low-Field Magnetocaloric Effect and Excellent Thermal Conduc- tivity Near Liquid Helium Temperature, J. Am. Chem. Soc.147, 14684 (2025), publisher: American Chemical Society

    2025

  42. [42]

    ´Cwik, Y

    J. ´Cwik, Y. Koshkid’ko, K. Nenkov, E. Tereshina, and K. Rogacki, Structural, magnetic and magnetocaloric properties of HoNi2 and ErNi2 compounds ordered at low temperatures, Journal of Alloys and Compounds735, 1088 (2018)

    2018

  43. [43]

    J. S. Dyck, C. Drasar, P. Lost’ak, and C. Uher, Low- temperature ferromagnetic properties of the diluted mag- netic semiconductor Sb 2 - x Cr x Te 3, Phys. Rev. B71, 115214 (2005)

    2005

  44. [44]

    T. S. Alstrøm, M. P. Sørensen, N. F. Pedersen, and S. Madsen, Magnetic Flux Lines in Complex Geometry Type-II Superconductors Studied by the Time Depen- dent Ginzburg-Landau Equation, Acta Appl Math115, 11 63 (2011)

    2011

  45. [45]

    V. A. Schweigert and F. M. Peeters, Flux penetration and expulsion in thin superconducting disks, Phys. Rev. Lett.83, 2409 (1999)

    1999

  46. [46]

    COMSOL Multiphysics ® ver. 6.1. COMSOL AB, Stock- holm, Sweden, (2022)

    2022

  47. [47]

    A. N. Zotova and D. Y. Vodolazov, Photon detec- tion by current-carrying superconducting film: A time- dependent Ginzburg-Landau approach, Phys. Rev. B85, 024509 (2012)

    2012

  48. [48]

    Rogalski,Infrared and terahertz detectors, third edi- tion ed

    A. Rogalski,Infrared and terahertz detectors, third edi- tion ed. (CRC Press, Taylor & Francis Group, Boca Ra- ton, FL, 2019)

    2019

  49. [49]

    J. H. Lienhard and J. H. Lienhard, eds.,A heat transfer textbook, 4th ed., Dover Civil and Mechanical Engineering (Dover Publications, Mineola, N.Y, 2011)

    2011

  50. [50]

    Taneda, G

    T. Taneda, G. P. Pepe, L. Parlato, A. A. Golubov, and R. Sobolewski, Time-resolved carrier dynamics and electron-phonon coupling strength in proximized weak ferromagnet-superconductor nanobilayers, Phys. Rev. B 75, 174507 (2007)

    2007

  51. [51]

    Besse, A

    V. Besse, A. Golov, V. Vlasov, A. Alekhin, D. Kuzmin, I. Bychkov, L. Kotov, and V. Temnov, Generation of ex- change magnons in thin ferromagnetic films by ultrashort acoustic pulses, Journal of Magnetism and Magnetic Ma- terials502, 166320 (2020)

    2020

  52. [52]

    R. F. Evans, W. J. Fan, P. Chureemart, T. A. Ostler, M. O. Ellis, and R. W. Chantrell, Atomistic spin model simulations of magnetic nanomaterials, Journal of Physics: Condensed Matter26, 103202 (2014)

    2014

  53. [53]

    available from http://vampire.york.ac.uk/

    Vampire software package, version 6. available from http://vampire.york.ac.uk/

  54. [54]

    Lyberatos, D

    A. Lyberatos, D. V. Berkov, and R. W. Chantrell, A method for the numerical simulation of the thermal magnetization fluctuations in micromagnetics, Journal of Physics: Condensed Matter5, 8911 (1993)

    1993

  55. [55]

    Nowak, O

    U. Nowak, O. N. Mryasov, R. Wieser, K. Guslienko, and R. W. Chantrell, Spin dynamics of magnetic nanopar- ticles: Beyond brown’s theory, Physical Review B72, 172410 (2005)

    2005

  56. [56]

    Brown, Thermal fluctuation of fine ferromagnetic par- ticles, IEEE Transactions on Magnetics15, 1196 (1979)

    W. Brown, Thermal fluctuation of fine ferromagnetic par- ticles, IEEE Transactions on Magnetics15, 1196 (1979)

    1979

  57. [57]

    J. L. Garc ´ ıa-Palacios and F. J. L´ azaro, Langevin- dynamics study of the dynamical properties of small mag- netic particles, Physical Review B58, 14937 (1998)

    1998

  58. [58]

    Colarieti-Tosti, S

    M. Colarieti-Tosti, S. Simak, R. Ahuja, L. Nordstr¨ om, O. Eriksson, D. ˚Aberg, S. Edvardsson, and M. S. Brooks, Origin of magnetic anisotropy of gd metal, Physical re- view letters91, 157201 (2003)

    2003

  59. [59]

    Ikeda and K

    K. Ikeda and K. Tanosaki, Origin of anomalous resistivity in ni–cu alloys, Transactions of the Japan institute of metals25, 447 (1984)

    1984

  60. [60]

    Ahmad and D

    H. Ahmad and D. Greig, The electrical resistivity and thermopower of nickel-copper alloys, Le Journal de Physique Colloques35, C4 (1974)

    1974

  61. [61]

    Aitken and J

    R. Aitken and J. Kouvel, Spin-glass-like distribution of interaction fields in a nearly ferromagnetic Ni-Cu alloy, Journal of Magnetism and Magnetic Materials12, 215 (1979)

    1979

  62. [62]

    Ododo and B

    J. Ododo and B. Coles, The critical concentration for the onset of ferromagnetism in cuni alloys, Journal of Physics F: Metal Physics7, 2393 (1977)

    1977

  63. [63]

    K. D. Usadel, Generalized diffusion equation for su- perconducting alloys, Physical Review Letters25, 507 (1970)

    1970

  64. [64]

    A. I. Buzdin, Proximity effects in superconductor- ferromagnet heterostructures, Reviews of modern physics 77, 935 (2005)

    2005

  65. [65]

    Zdravkov, A

    V. Zdravkov, A. Sidorenko, G. Obermeier, S. Gsell, M. Schreck, C. M¨ uller, S. Horn, R. Tidecks, and L. R. Tagirov, Reentrant Superconductivity in Nb / Cu 1 - x Ni x Bilayers, Phys. Rev. Lett.97, 057004 (2006)

    2006

  66. [66]

    V. V. Ryazanov, V. A. Oboznov, A. S. Prokof’ev, and S. V. Dubonos, Proximity effect and spontaneous vortex phase in planar SF structures, Jetp Lett.77, 39 (2003)

    2003

  67. [67]

    X. He, N. Helbig, M. J. Verstraete, and E. Bousquet, TB2J: A python package for computing magnetic inter- action parameters, Computer Physics Communications 264, 107938 (2021)

    2021