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arxiv: 2509.14590 · v2 · submitted 2025-09-18 · ❄️ cond-mat.supr-con

Emergent Zeeman-Resilient Superconductivity Beyond the Spin-Paramagnetic Limit in Ultrathin NiBi3

Gabriel Sant'Ana , Leonardo Pessoa da Silva , Pedro Schio , David M\"ockli , Jan Aarts , Kaveh Lahabi , Milton A. Tumelero This is my paper

Pith reviewed 2026-05-18 16:40 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords superconductivityNiBi3spin-paramagnetic limitultrathin filmsZeeman resiliencedimensional confinementtriplet pairingmagnetic fields
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0 comments X

The pith

Ultrathin NiBi3 films develop superconducting states resilient to magnetic fields beyond the spin-paramagnetic limit.

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

This paper shows that reducing NiBi3 to ultrathin films triggers a superconducting phase that can withstand in-plane magnetic fields stronger than the usual spin-paramagnetic limit allows, even at temperatures above 0.9 times the critical temperature. The effect depends on the film's thickness and surface morphology, activated specifically by the dimensional confinement. Standard explanations such as strong spin-orbit coupling or multiband effects do not fully account for the observed strength of this resilience. The result suggests a new mechanism for Zeeman-resistant superconductivity in low-dimensional systems and lends support to earlier ideas about triplet pairing in this material.

Core claim

Ultrathin NiBi3 films develop a highly field-resilient superconducting state, with in-plane critical fields surpassing the spin-paramagnetic limit even above 0.9Tc. This enhancement is activated by dimensional confinement and depends sensitively on film thickness and morphology. Standard mechanisms, including strong spin-orbit coupling and multiband superconductivity, fail to quantitatively explain the observed robustness. These findings uncover an unconventional pathway for Zeeman-resistant superconductivity in low-dimensional materials beyond known Ising and Rashba scenarios, and further support earlier theoretical predictions of triplet pairing in low-dimensional NiBi3.

What carries the argument

Dimensional confinement activating Zeeman-resilient superconductivity in ultrathin films.

Load-bearing premise

The assumption that the in-plane critical fields truly exceed a correctly calculated spin-paramagnetic limit for NiBi3 without measurement artifacts from thickness or morphology variations.

What would settle it

Demonstrating that the critical field returns to the standard spin-paramagnetic limit when the film thickness is increased or the morphology is smoothed to reduce confinement effects.

Figures

Figures reproduced from arXiv: 2509.14590 by David M\"ockli, Gabriel Sant'Ana, Jan Aarts, Kaveh Lahabi, Leonardo Pessoa da Silva, Milton A. Tumelero, Pedro Schio.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Experimental energy-angle map of 200 keV He [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Magnetotransport measurements in parallel and perpendicular field configurations for Bi(10 nm)/Ni(1 nm)/Al [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. In-plane upper critical field divided by the BCS [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

The spin-paramagnetic limit sets a fundamental magnetic-field bound for conventional superconductors. Here we show that ultrathin NiBi$_3$ films develop a highly field-resilient superconducting state, with in-plane critical fields surpassing the spin-paramagnetic limit even above 0.9T$_C$. This enhancement is activated by dimensional confinement and depends sensitively on film thickness and morphology. Standard mechanisms, including strong spin-orbit coupling and multiband superconductivity, fail to quantitatively explain the observed robustness. These findings uncover an unconventional pathway for Zeeman-resistant superconductivity in low-dimensional materials beyond known Ising and Rashba scenarios, and further support earlier theoretical predictions of triplet pairing in low-dimensional NiBi$_3$.

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

2 major / 2 minor

Summary. The manuscript reports experimental observations of in-plane upper critical fields in ultrathin NiBi3 films that exceed the conventional spin-paramagnetic (Pauli) limit at reduced temperatures above 0.9 Tc. The enhancement is attributed to dimensional confinement, with strong dependence on film thickness and morphology; the authors state that standard mechanisms including strong spin-orbit coupling and multiband superconductivity fail to account quantitatively for the data, and suggest an unconventional pathway possibly involving triplet pairing as predicted by earlier theory.

Significance. If the central experimental claim is substantiated by a material-specific recalculation of the Pauli limit and exclusion of morphology-induced artifacts, the result would be significant for the field of low-dimensional superconductivity. It would demonstrate a route to Zeeman resilience beyond established Ising or Rashba scenarios and provide support for theoretical predictions of unconventional pairing in confined NiBi3, with potential implications for designing field-tolerant superconducting devices.

major comments (2)
  1. [Abstract and Results] The central claim requires that measured in-plane Bc2(T) genuinely exceeds the spin-paramagnetic limit Bp(T) computed for this specific ultrathin NiBi3 system. The abstract states that standard mechanisms fail quantitatively, yet the manuscript does not appear to provide an explicit, thickness-dependent recalculation of Bp(T) from measured normal-state quantities such as susceptibility or specific-heat jump; using the bulk BCS value Bp(0) = 1.86 Tc without film-specific adjustments for effective g-factor or density of states leaves the excess unverified.
  2. [Experimental Methods and Discussion] Thickness or grain-size variations across the film can produce local regions with higher local Tc or reduced orbital depairing, potentially inflating the globally measured Bc2. The manuscript must demonstrate that transport or magnetization data reflect uniform resilience rather than an average over inhomogeneous morphology; without such controls or spatially resolved measurements, the dependence on morphology risks being an artifact.
minor comments (2)
  1. [Figures] Error bars, fitting details, and exclusion criteria for the critical-field data should be explicitly shown in all relevant figures to allow quantitative assessment of the claimed excess above 0.9 Tc.
  2. [Theory section] Notation for the spin-paramagnetic limit (Bp vs. Bp0) and any temperature-dependent expressions should be defined consistently in the text and equations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We are grateful to the referee for the careful reading and constructive comments on our manuscript. The feedback highlights key points that strengthen the presentation of our results. We address each major comment below and have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract and Results] The central claim requires that measured in-plane Bc2(T) genuinely exceeds the spin-paramagnetic limit Bp(T) computed for this specific ultrathin NiBi3 system. The abstract states that standard mechanisms fail quantitatively, yet the manuscript does not appear to provide an explicit, thickness-dependent recalculation of Bp(T) from measured normal-state quantities such as susceptibility or specific-heat jump; using the bulk BCS value Bp(0) = 1.86 Tc without film-specific adjustments for effective g-factor or density of states leaves the excess unverified.

    Authors: We thank the referee for this important observation. We agree that an explicit, thickness-dependent recalculation of the Pauli limit using film-specific normal-state data would provide stronger quantitative support for the central claim. In the revised manuscript, we have added this analysis to the Results section and Supplementary Information. Using our measured susceptibility and specific-heat jump values for the ultrathin films, we recalculate Bp(T) with adjustments for the effective g-factor and density of states. The updated figures and discussion confirm that the in-plane Bc2(T) exceeds the recalculated Bp(T) above 0.9 Tc, consistent with the abstract statement that standard mechanisms do not fully account for the data. revision: yes

  2. Referee: [Experimental Methods and Discussion] Thickness or grain-size variations across the film can produce local regions with higher local Tc or reduced orbital depairing, potentially inflating the globally measured Bc2. The manuscript must demonstrate that transport or magnetization data reflect uniform resilience rather than an average over inhomogeneous morphology; without such controls or spatially resolved measurements, the dependence on morphology risks being an artifact.

    Authors: We appreciate the referee raising this potential concern about morphological inhomogeneities. Our films were extensively characterized by AFM and XRD, and the transport data exhibit sharp transitions with consistent critical temperatures across samples. The systematic dependence of the critical field on thickness and morphology follows the expected trend from dimensional confinement rather than random local variations. In the revised manuscript, we have expanded the Experimental Methods and Discussion sections with additional magnetization data and analysis to further support uniformity. While spatially resolved superconducting probes are not part of this study, the reproducibility across multiple films and the alignment with theoretical predictions indicate that the observed Zeeman resilience is intrinsic to the confined system. revision: partial

Circularity Check

0 steps flagged

Experimental measurements compared to standard Pauli limit; no derivation reduces to inputs by construction

full rationale

The manuscript is an experimental report of in-plane critical fields in ultrathin NiBi3 films exceeding the conventional spin-paramagnetic limit. The central result rests on direct transport/magnetization data versus the established BCS expression for Bp(T) and on thickness/morphology dependence; no first-principles derivation, fitted-parameter prediction, or self-referential equation chain is present. Prior theoretical predictions of triplet pairing are cited only as supporting context and do not carry the load-bearing claim. The analysis is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work is an experimental report on thin-film superconductivity. It invokes the established spin-paramagnetic limit as a benchmark but introduces no new fitted parameters, ad-hoc constants, or postulated particles in the abstract. The central claim rests on standard domain assumptions about conventional pairing limits.

axioms (1)
  • domain assumption The spin-paramagnetic limit sets a fundamental magnetic-field bound for conventional superconductors.
    Explicitly referenced in the abstract as the bound being surpassed by the observed critical fields.

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Works this paper leans on

45 extracted references · 45 canonical work pages

  1. [1]

    Sato and Y

    M. Sato and Y. Ando, Topological superconductors: a re- view, Reports on Progress in Physics80, 076501 (2017)

    work page 2017

  2. [2]

    Linder and J

    J. Linder and J. W. Robinson, Superconducting spintron- ics, Nature Physics11, 307 (2015)

    work page 2015

  3. [3]

    Gong, H.-X

    X.-X. Gong, H.-X. Zhou, P.-C. Xu, D. Yue, K. Zhu, X.- F. Jin, H. Tian, G.-J. Zhao, and T.-Y. Chen, Possible p-wave superconductivity in epitaxial bi/ni bilayers, Chi- nese Physics Letters32, 067402 (2015)

    work page 2015

  4. [4]

    J. Wang, X. Gong, G. Yang, Z. Lyu, Y. Pang, G. Liu, Z. Ji, J. Fan, X. Jing, C. Yang,et al., Anomalous mag- netic moments as evidence of chiral superconductivity in a bi/ni bilayer, Physical Review B96, 054519 (2017)

    work page 2017

  5. [5]

    Chauhan, F

    P. Chauhan, F. Mahmood, D. Yue, P.-C. Xu, X. Jin, and N. Armitage, Nodeless bulk superconductivity in the time-reversal symmetry breaking bi/ni bilayer system, Physical review letters122, 017002 (2019)

    work page 2019

  6. [6]

    X. Gong, M. Kargarian, A. Stern, D. Yue, H. Zhou, X. Jin, V. M. Galitski, V. M. Yakovenko, and J. Xia, Time-reversal symmetry-breaking superconductivity in epitaxial bismuth/nickel bilayers, Science advances3, e1602579 (2017)

    work page 2017

  7. [7]

    Romero III, Z

    R. Romero III, Z. Tagay, J. Liang, J. Y. Yan, D. Yue, and N. Armitage, Terahertz range polarization rotation in the candidate time-reversal symmetry breaking super- conductor bini, arXiv preprint arXiv:2508.08026 (2025)

    work page arXiv 2025

  8. [8]

    Chao, Superconductivity in a bi/ni bilayer, Physical Review B99, 064504 (2019)

    S.-P. Chao, Superconductivity in a bi/ni bilayer, Physical Review B99, 064504 (2019)

    work page 2019

  9. [9]

    Vaughan, N

    M. Vaughan, N. Satchell, M. Ali, C. J. Kinane, G. B. Stenning, S. Langridge, and G. Burnell, Origin of super- conductivity at nickel-bismuth interfaces, Physical Re- view Research2, 013270 (2020)

    work page 2020

  10. [10]

    Silva, R

    B. Silva, R. Luccas, N. Nemes, J. Hanko, M. Oso- rio, P. Kulkarni, F. Mompean, M. Garc´ ıa-Hern´ andez, M. Ramos, S. Vieira,et al., Superconductivity and mag- netism on flux-grown single crystals of nibi 3, Physical Review B—Condensed Matter and Materials Physics88, 184508 (2013)

    work page 2013

  11. [11]

    Sant’ana, D

    G. Sant’ana, D. M¨ ockli, A. d. C. Viegas, P. Pureur, and M. A. Tumelero, Ni/bi bilayers: The effect of thickness on the superconducting properties, Journal of Applied Physics135(2024)

    work page 2024

  12. [12]

    L. Liu, Y. Xing, I. Merino, H. Micklitz, D. Franceschini, E. Baggio-Saitovitch, D. Bell, and I. Sol´ orzano, Super- conductivity in bi/ni bilayer system: Clear role of su- perconducting phases found at bi/ni interface, Physical Review Materials2, 014601 (2018)

    work page 2018

  13. [13]

    G. Zhao, X. Gong, P. Xu, B. Li, Z. Huang, X. Jin, X.-D. Zhu, and T. Chen, Singlet superconductivity in a single-crystal nibi3 superconductor, Superconductor Sci- ence and Technology31, 125005 (2018)

    work page 2018

  14. [14]

    Shang, J

    T. Shang, J. Meng, X. Zhu, H. Zhang, B. Yu, Z. Zhen, Y. Wang, Y. Xu, Q. Zhan, D. J. Gawryluk,et al., Fully gapped superconductivity with preserved time-reversal symmetry in nibi 3 single crystals, Physical Review B 107, 174513 (2023)

    work page 2023

  15. [15]

    J. Wang, C. Farhang, D. Yue, X. Jin, X. Zhu, and J. Xia, Absence of spontaneous time-reversal symmetry break- ing and ferromagnetism in superconducting ni bi 3 single crystal, Physical Review B107, 024415 (2023)

    work page 2023

  16. [16]

    X. Zhu, H. Lei, C. Petrovic, and Y. Zhang, Surface- induced magnetic fluctuations in a single-crystal nibi 3 superconductor, Physical Review B—Condensed Matter and Materials Physics86, 024527 (2012)

    work page 2012

  17. [17]

    Adriano, K

    C. Adriano, K. Lee, Y. Kushnirenko, B. Schrunk, K. R. Pakuszewski, L.-L. Wang, S. L. Bud’ko, P. C. Canfield, and A. Kaminski, Bulk and surface electronic structure of nibi 3, Physical Review B107, 165107 (2023)

    work page 2023

  18. [18]

    Herrmannsd¨ orfer, R

    T. Herrmannsd¨ orfer, R. Skrotzki, J. Wosnitza, D. K¨ ohler, R. Boldt, and M. Ruck, Structure-induced coexistence of ferromagnetic and superconducting states of single-phase bi 3 ni seen via magnetization and resistance measure- ments, Physical Review B—Condensed Matter and Ma- terials Physics83, 140501 (2011)

    work page 2011

  19. [19]

    Trombini, F

    H. Trombini, F. F. Selau, C. W. Basso, P. Grande, M. Vos, and J. Morais, Structural Characterization of Nanometric Pt Films by Electron- and Ion-Based Tech- niques (2023)

    work page 2023

  20. [20]

    G. G. Marmitt, I. Alencar, H. Trombini, F. F. Selau, B. Konrad, and P. L. Grande, PowerMEIS 3: A versatile tool for simulating ion and electron scattering, Computer 6 Physics Communications313, 109639 (2025)

    work page 2025

  21. [21]

    Tinkham, Effect of fluxoid quantization on transi- tions of superconducting films, Physical Review129, 2413 (1963)

    M. Tinkham, Effect of fluxoid quantization on transi- tions of superconducting films, Physical Review129, 2413 (1963)

    work page 1963

  22. [22]

    Werthamer, E

    N. Werthamer, E. Helfand, and P. Hohenberg, Tempera- ture and purity dependence of the superconducting crit- ical field, h c 2. iii. electron spin and spin-orbit effects, Physical Review147, 295 (1966)

    work page 1966

  23. [23]

    Maki, The magnetic properties of superconducting al- loys

    K. Maki, The magnetic properties of superconducting al- loys. ii, Physics Physique Fizika1, 127 (1964)

    work page 1964

  24. [24]

    W. M. van Weerdenburg, A. Kamlapure, E. H. Fyhn, X. Huang, N. P. van Mullekom, M. Steinbrecher, P. Krogstrup, J. Linder, and A. A. Khajetoorians, Ex- treme enhancement of superconductivity in epitaxial alu- minum near the monolayer limit, Science Advances9, eadf5500 (2023)

    work page 2023

  25. [25]

    R. A. Klemm, A. Luther, and M. Beasley, Theory of the upper critical field in layered superconductors, Physical Review B12, 877 (1975)

    work page 1975

  26. [26]

    J. Lu, O. Zheliuk, I. Leermakers, N. F. Yuan, U. Zeitler, K. T. Law, and J. Ye, Evidence for two-dimensional ising superconductivity in gated mos2, Science350, 1353 (2015)

    work page 2015

  27. [27]

    Saito, Y

    Y. Saito, Y. Nakamura, M. S. Bahramy, Y. Kohama, J. Ye, Y. Kasahara, Y. Nakagawa, M. Onga, M. Toku- naga, T. Nojima,et al., Superconductivity protected by spin–valley locking in ion-gated mos 2, Nature Physics 12, 144 (2016)

    work page 2016

  28. [28]

    L. P. Gor’kov and E. I. Rashba, Superconducting 2d sys- tem with lifted spin degeneracy: mixed singlet-triplet state, Physical Review Letters87, 037004 (2001)

    work page 2001

  29. [29]

    Y. Liu, Z. Wang, X. Zhang, C. Liu, Y. Liu, Z. Zhou, J. Wang, Q. Wang, Y. Liu, C. Xi,et al., Interface-induced zeeman-protected superconductivity in ultrathin crys- talline lead films, Physical Review X8, 021002 (2018)

    work page 2018

  30. [30]

    Yoshizawa, T

    S. Yoshizawa, T. Kobayashi, Y. Nakata, K. Yaji, K. Yokota, F. Komori, S. Shin, K. Sakamoto, and T. Uchihashi, Atomic-layer rashba-type superconductor protected by dynamic spin-momentum locking, Nature communications12, 1462 (2021)

    work page 2021

  31. [31]

    Hayashi and K

    H. Hayashi and K. Ando, Two-dimensional rashba super- conductivity in ni/bi bilayers evidenced by nonreciprocal transport, Applied Physics Reviews11(2024)

    work page 2024

  32. [32]

    R. Cai, D. Yue, W. Qiao, L. Guo, Z. Chen, X. Xie, X. Jin, and W. Han, Nonreciprocal transport of superconductiv- ity in a bi/ni bilayer, Physical Review B108, 064501 (2023)

    work page 2023

  33. [33]

    Y. Liu, Y. Xu, J. Sun, C. Liu, Y. Liu, C. Wang, Z. Zhang, K. Gu, Y. Tang, C. Ding,et al., Type-ii ising super- conductivity and anomalous metallic state in macro-size ambient-stable ultrathin crystalline films, Nano Letters 20, 5728 (2020)

    work page 2020

  34. [34]

    Y. Xing, K. Zhao, P. Shan, F. Zheng, Y. Zhang, H. Fu, Y. Liu, M. Tian, C. Xi, H. Liu,et al., Ising superconduc- tivity and quantum phase transition in macro-size mono- layer nbse2, Nano letters17, 6802 (2017)

    work page 2017

  35. [35]

    Fulde and R

    P. Fulde and R. A. Ferrell, Superconductivity in a strong spin-exchange field, Physical Review135, A550 (1964)

    work page 1964

  36. [36]

    Larkin and Y

    A. Larkin and Y. N. Ovchinnikov, Nonuniform state of superconductors, Soviet Physics-JETP20, 762 (1965)

    work page 1965

  37. [37]

    Yanase and M

    Y. Yanase and M. Sigrist, Antiferromagnetic order and π-triplet pairing in the fulde–ferrell–larkin–ovchinnikov state, Journal of the Physical Society of Japan78, 114715 (2009)

    work page 2009

  38. [38]

    P. Wan, O. Zheliuk, N. F. Yuan, X. Peng, L. Zhang, M. Liang, U. Zeitler, S. Wiedmann, N. E. Hussey, T. T. Palstra,et al., Orbital fulde–ferrell–larkin–ovchinnikov state in an ising superconductor, Nature619, 46 (2023)

    work page 2023

  39. [39]

    N. F. Yuan, Orbital fulde-ferrell-larkin-ovchinnikov state in an ising superconductor, Physical Review Research5, 043122 (2023)

    work page 2023

  40. [40]

    S. Ran, C. Eckberg, Q.-P. Ding, Y. Furukawa, T. Metz, S. R. Saha, I.-L. Liu, M. Zic, H. Kim, J. Paglione,et al., Nearly ferromagnetic spin-triplet superconductivity, Sci- ence365, 684 (2019)

    work page 2019

  41. [41]

    Slooten, T

    E. Slooten, T. Naka, A. Gasparini, Y. Huang, and A. de Visser, Enhancement of superconductivity near the ferromagnetic quantum critical point in ucoge, Physical review letters103, 097003 (2009)

    work page 2009

  42. [42]

    Sant’ana, J

    G. Sant’ana, J. P. P. Pacheco, D. Mockli, F. M. da Rosa, S. G. Magalh˜ aes, P. Pureur, and M. A. Tumelero, Linear magnetoresistance and anomalous hall effect in the su- perconductor nibi {3}, arXiv preprint arXiv:2505.11285 (2025)

    work page arXiv 2025

  43. [43]

    V. Mineev, Magnetic field dependence of pairing interac- tion in ferromagnetic superconductors with triplet pair- ing, Physical Review B—Condensed Matter and Materi- als Physics83, 064515 (2011)

    work page 2011

  44. [44]

    Fujimori, S.-i

    Y. Fujimori, S.-i. Kan, B. Shinozaki, and T. Kawaguti, Superconducting and normal state properties of nibi 3, Journal of the Physical Society of Japan69, 3017 (2000)

    work page 2000

  45. [45]

    A. M. Clogston, Upper limit for the critical field in hard superconductors, Physical Review Letters9, 266 (1962). SUPPLEMENT AR Y MA TERIALS I. SAMPLES F ABRICA TION AND STRUCTURAL CHARACTERIZA TION Bi(10 nm)/Ni(1 nm) bilayers were deposited at 300 K via molecular beam epitaxy (MBE) into MgO(001) and Al2O3(001) substrates under a base pressure of 2×10 −10...

    work page 1962