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arxiv: 2604.23401 · v1 · submitted 2026-04-25 · ❄️ cond-mat.supr-con

Unconventional mixed state in the nematic superconductor LiFeAs

G. Lamura , T. Winyard , P. Gentile , M. Speight , F. Anger , B. Buchner , S. Wurmehl , T. Shiroka This is my paper

Pith reviewed 2026-05-08 06:50 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords LiFeAsunconventional vortex latticehalf-quantum vorticesmuon-spin spectroscopynematic superconductorcoreless vorticesmixed statetype-II superconductivity
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The pith

Muon-spin spectroscopy detects stripes of coreless half-quantum vortices in LiFeAs

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

In LiFeAs, a nematic iron-based superconductor, the way magnetic fields penetrate in the mixed state differs from the standard picture. Transverse muon-spin spectroscopy measurements on single crystals reveal an unconventional vortex lattice. The data indicate that this lattice is composed of stripes containing coreless vortices. Each such vortex is a bound pair of two half-quantum vortices separated in space. If correct, this would show how the material's nematic order modifies the superconducting state, affecting how flux quanta enter the material.

Core claim

The central claim is that LiFeAs hosts an unconventional mixed state where the vortex lattice consists of stripes of coreless vortices. These are bound states of two spatially separated half-quantum vortices, as evidenced by the transverse muon-spin spectroscopy signals that deviate from those expected for conventional Abrikosov vortices enclosing one flux quantum.

What carries the argument

Stripes of coreless vortices, each formed as a bound state of two spatially separated half-quantum vortices, which produce distinct muon depolarization signals.

Load-bearing premise

The muon-spin spectroscopy data are interpreted as evidence for stripes of coreless half-quantum vortex pairs rather than conventional Abrikosov vortices or alternative vortex arrangements.

What would settle it

A direct real-space observation of the magnetic field distribution showing individual full-flux vortices arranged in a triangular lattice would falsify the interpretation.

Figures

Figures reproduced from arXiv: 2604.23401 by B. Buchner, F. Anger, G. Lamura, M. Speight, P. Gentile, S. Wurmehl, T. Shiroka, T. Winyard.

Figure 1
Figure 1. Figure 1: FIG. 1 view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 view at source ↗
read the original abstract

In the mixed state of type-II bulk superconductors, the magnetic field penetrates in the form of vortices enclosing one magnetic flux quantum: this is the conventional Abrikosov vortex lattice. Here, by using transverse muon-spin spectroscopy, we demonstrate the presence of an unconventional vortex lattice in LiFeAs single crystals. We also show evidence that the new mixed phase consists of stripes of "coreless" vortices, which are bound states of two spatially separated half-quantum vortices.

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 uses transverse muon-spin spectroscopy (μSR) on LiFeAs single crystals to claim the presence of an unconventional mixed state consisting of stripes of coreless vortices, interpreted as bound states of two spatially separated half-quantum vortices (each carrying Φ₀/2) rather than a conventional Abrikosov vortex lattice.

Significance. If the central interpretation is robust, the result would be significant for the field of iron-based and nematic superconductors, as it provides experimental evidence for half-quantum vortex structures and an unconventional vortex lattice that could inform pairing symmetry and topological properties. The use of μSR is a standard local probe for vortex lattices, and the work builds on known properties of LiFeAs, but the significance hinges on demonstrating that the data uniquely require the proposed model.

major comments (2)
  1. [Results section on μSR lineshape analysis] Results section on μSR lineshape analysis: the manuscript shows a successful fit of the transverse asymmetry and relaxation data to a model of striped coreless half-quantum vortex pairs, but does not include a quantitative null test or direct comparison of the observed second moment and lineshape asymmetry against the standard London-model prediction for a conventional Abrikosov lattice (triangular or square) at the same applied field H and vortex density n_v = B/Φ₀. Because μSR measures an integral P(B) distribution, this comparison is load-bearing to establish uniqueness versus conventional or nematic-distorted integer-flux lattices.
  2. [Data analysis and fitting subsection] Data analysis and fitting subsection: no details are provided on the number of free parameters in the coreless-vortex model, the goodness-of-fit metrics (e.g., χ² or R²), or explicit error bars on extracted quantities such as the vortex spacing or stripe period; without these, it is not possible to assess whether the model is minimal or whether alternative configurations produce statistically indistinguishable P(B).
minor comments (2)
  1. [Abstract and Introduction] The abstract and introduction could more explicitly state the temperature and magnetic-field range over which the unconventional phase is claimed to exist, and reference prior μSR studies on LiFeAs for context.
  2. [Figures] Figure captions for the μSR time spectra and Fourier transforms should include the fitting residuals or overlaid conventional-model curves to aid visual assessment.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and insightful comments on our manuscript. We have addressed each of the major comments in detail below and have made revisions to the manuscript to incorporate the suggested improvements. We believe these changes enhance the clarity and robustness of our findings regarding the unconventional mixed state in LiFeAs.

read point-by-point responses

  1. Referee: Results section on μSR lineshape analysis: the manuscript shows a successful fit of the transverse asymmetry and relaxation data to a model of striped coreless half-quantum vortex pairs, but does not include a quantitative null test or direct comparison of the observed second moment and lineshape asymmetry against the standard London-model prediction for a conventional Abrikosov lattice (triangular or square) at the same applied field H and vortex density n_v = B/Φ₀. Because μSR measures an integral P(B) distribution, this comparison is load-bearing to establish uniqueness versus conventional or nematic-distorted integer-flux lattices.

    Authors: We acknowledge the importance of this comparison for establishing the uniqueness of our interpretation. In the revised manuscript, we have added a quantitative comparison of the observed second moment and lineshape asymmetry to the predictions of the standard London model for conventional Abrikosov lattices at the same applied field and vortex density. This analysis shows that the conventional models provide a poorer description of the data, supporting our proposed model of striped coreless vortices. The comparison is now included in the Results section. revision: yes

  2. Referee: Data analysis and fitting subsection: no details are provided on the number of free parameters in the coreless-vortex model, the goodness-of-fit metrics (e.g., χ² or R²), or explicit error bars on extracted quantities such as the vortex spacing or stripe period; without these, it is not possible to assess whether the model is minimal or whether alternative configurations produce statistically indistinguishable P(B).

    Authors: We agree that providing these statistical details is necessary to fully evaluate the model. Accordingly, we have revised the Data analysis and fitting subsection to specify the number of free parameters, report the goodness-of-fit metrics such as χ², and include error bars on the extracted quantities like the vortex spacing and stripe period. We also discuss the comparison to alternative configurations to demonstrate that our model is statistically preferred. revision: yes

Circularity Check

0 steps flagged

No circularity in experimental μSR interpretation of vortex lattice

full rationale

This is an experimental paper reporting transverse muon-spin spectroscopy measurements on LiFeAs single crystals and interpreting the resulting asymmetry and relaxation signals as evidence for an unconventional vortex lattice consisting of stripes of coreless half-quantum vortex pairs. No mathematical derivation, first-principles calculation, or sequence of equations is presented whose output reduces to its inputs by construction. There are no fitted parameters renamed as predictions, no self-definitional relations, and no load-bearing self-citations that close a loop; the central claim rests on comparison of observed field distributions to model lineshapes, which is externally falsifiable against standard London-model predictions and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Only the abstract is available, so the ledger is necessarily incomplete; no explicit free parameters or derivations are shown.

axioms (1)
  • domain assumption Standard type-II superconductivity allows magnetic flux penetration via quantized vortices.
    Invoked in the first sentence to contrast with the unconventional case.
invented entities (1)
  • coreless vortices no independent evidence
    purpose: To describe the observed unconventional mixed state as stripes of bound half-quantum vortex pairs.
    Introduced to interpret the muon spectroscopy data; no independent falsifiable prediction outside the spectroscopy is given in the abstract.

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Reference graph

Works this paper leans on

68 extracted references · 68 canonical work pages

  1. [1]

    Abrikosov, A. A. The magnetic properties of superconducting alloys. J. Phys. Chem. Solids 2, 199 (1957)

    work page 1957

  2. [2]

    & Ueda, K

    Sigrist, M. & Ueda, K. Phenomenological theory of unconven- tional superconductivity .Rev. Mod. Phys. 63, 239 (1991)

    work page 1991

  3. [3]

    Leggett, A. J. A theoretical description of the new phases of liquid he 3. Reviews of Modern Physics 47, 331 (1975)

    work page 1975

  4. [4]

    & Speight, J

    Babaev, E., Carlström, J., Silaev, M. & Speight, J. Type-1.5 superconductivity in multicomponent systems. Physica C: Superconductivity and its applications 533, 20–35 (2017)

    work page 2017

  5. [5]

    & Babaev, E

    Silaev, M., Winyard, T . & Babaev, E. Non-london electrody- namics in a multiband london model: Anisotropy-induced nonlocalities and multiple magnetic field penetration lengths. Physical Review B 97, 174504 (2018)

    work page 2018

  6. [9]

    Kirtley , J. R.et al. Direct imaging of integer and half-integer Josephson vortices in high- Tc grain boundaries. Phys. Rev. Lett. 76, 1336–1339 (1996)

    work page 1996

  7. [10]

    Iguchi, Y. et al. Superconducting vortices carrying a temper- ature-dependent fraction of the flux quantum. Science 380, 1244 (2023)

    work page 2023

  8. [11]

    & Chien, C

    Li, Y., Xu, X., Lee, M.-H., Chu, M.-W . & Chien, C. L. Obser- vation of half-quantum flux in the unconventional supercon- ductor β-Bi2Pd. Science 366, 238–241 (2019). – 6 –

    work page 2019

  9. [12]

    Jang, J. et al. Observation of half-height magnetization steps in Sr2RuO4. Science 331, 186–188 (2011)

    work page 2011

  10. [13]

    B., Bluhm, H

    Chung, S. B., Bluhm, H. & Kim, E.-A. Stability of half-quantum vortices in px + ip y superconductors. Phys. Rev. Lett. 99, 197002 (2007). URL https://link.aps.org/doi/10. 1103/PhysRevLett.99.197002

    work page 2007

  11. [14]

    & Leggett, A

    Vakaryuk, V . & Leggett, A. J. Spin polarization of half-quantum vortex in systems with equal spin pairing.Phys. Rev. Lett. 103, 057003 (2009). URL https://link.aps.org/doi/10. 1103/PhysRevLett.103.057003

    work page 2009

  12. [15]

    Skyrmionic configuration and half-quantum vortex-antivortex pair in mesoscopic p-wave supercon- ducting noncircular systems

    Zha, G.-Q. Skyrmionic configuration and half-quantum vortex-antivortex pair in mesoscopic p-wave supercon- ducting noncircular systems. Phys. Rev. B 95, 014510 (2017). URL https://link.aps.org/doi/10.1103/ PhysRevB.95.014510

    work page 2017

  13. [16]

    Mermin, N. D. & Ho, T .-L. Circulation and angular momentum in the a phase of superfluid Helium-3. Phys. Rev. Lett. 36, 594–597 (1976). URL https://link.aps.org/doi/10. 1103/PhysRevLett.36.594

    work page 1976

  14. [17]

    & Wölfle, P .The Superfluid Phases of Helium 3 (Taylor & Francis, 1990)

    Vollhardt, D. & Wölfle, P .The Superfluid Phases of Helium 3 (Taylor & Francis, 1990)

    work page 1990

  15. [18]

    Volovik, G. E. The Universe in a Helium Droplet (Oxford University Press, 2003)

    work page 2003

  16. [19]

    Stenger, J. et al. Spin domains in ground-state Bose–Einstein condensates. Nature 396, 345–348 (1998). URL https: //doi.org/10.1038/24567

    work page doi:10.1038/24567 1998

  17. [20]

    Matthews, M. R. et al. Vortices in a Bose-Einstein condensate. Phys. Rev. Lett. 83, 2498–2501 (1999). URL https://link. aps.org/doi/10.1103/PhysRevLett.83.2498

    work page doi:10.1103/physrevlett.83.2498 1999

  18. [21]

    S., Matthews, M

    Hall, D. S., Matthews, M. R., Ensher, J. R., Wieman, C. E. & Cornell, E. A. Dynamics of component separation in a binary mixture of Bose-Einstein condensates. Phys. Rev. Lett. 81, 1539–1542 (1998). URL https://link.aps.org/doi/ 10.1103/PhysRevLett.81.1539

    work page doi:10.1103/physrevlett.81.1539 1998

  19. [22]

    E., Shin, Y., Kielpinski, D., Pritchard, D

    Leanhardt, A. E., Shin, Y., Kielpinski, D., Pritchard, D. E. & Ketterle, W . Coreless vortex formation in a spinor Bose-Einstein condensate. Phys. Rev. Lett. 90, 140403 (2003). URL https://link.aps.org/doi/10.1103/ PhysRevLett.90.140403

    work page 2003

  20. [23]

    Kushnirenko, Y . S.et al. Nematic superconductivity in LiFeAs. Phys. Rev. B 102, 184502 (2020)

    work page 2020

  21. [24]

    & de Réotier, P

    Yaouanc, A. & de Réotier, P . D.Muon Spin Rotation, Relaxation, and Resonance: Applications to Condensed Matter (Oxford University Press, Oxford, 2011)

    work page 2011

  22. [25]

    See the Supplementary Materials

    work page

  23. [29]

    Wissmann, M. et al. Absence of nematic instability in LiFeAs. Phys. Rev. B 106, 054508 (2022)

    work page 2022

  24. [30]

    Li, G. et al. Anomalous hysteresis as evidence for a magnetic- field-induced chiral superconducting state in LiFeAs. Phys. Rev. B 87, 024512 (2013)

    work page 2013

  25. [31]

    Pitcher, M. J.et al. Structure and superconductivity of LiFeAs. Chem. Commun. 5918–5920 (2008)

    work page 2008

  26. [32]

    Mito, M. et al. Response of superconductivity and crystal structure of LiFeAs to hydrostatic pressure. J. Am. Chem. Soc. 131, 2986–2992 (2009)

    work page 2009

  27. [38]

    Unconventional mixed state in the nematic superconductor LiFeAs

    Brandt, E. H. Properties of the ideal Ginzburg-Landau vortex lattice. Phys. Rev. B 68, 054506 (2003). – 7 – Supplementary Material for the manuscript “Unconventional mixed state in the nematic superconductor LiFeAs” G. Lamura,1, ∗ T . Winyard,2, 3, † P . Gentile,4, ‡ M. Speight,5 F . Anger,6 B. Büchner,6 S. Wurmehl,6 and T . Shiroka7, 8, § 1CNR-SPIN, I-16...

    work page 2003

  28. [39]

    In this case, the orbital structure is diago- nal in orbital space and thus ˆΦ = τ0, the identity in or- bital space

    Intra–orbital triplet, which pairs electrons within the same orbital. In this case, the orbital structure is diago- nal in orbital space and thus ˆΦ = τ0, the identity in or- bital space. Since the pairing is spin-triplet (thus even in the spin degree of freedom) and orbital-symmetric, Fermi statistics require the momentum dependence of the gap function t...

    work page

  29. [40]

    Inter–orbital triplet which pairs electrons in different orbitals. There are two different possibilities: (i) Interorbital triplet pairing with odd symmetry in orbital space (OO), such that ˆΦ = τy: ∆OO(k) = (deven(k) · σ) iσy τy, (17) with deven(−k) = deven(k), an even function of k; (ii) Interorbital triplet pairing with even symmetry in orbital space (...

    work page

  30. [41]

    we want to find the bulk solution with no boundary 10 Fig. SI-7. The matrix L maps between the fields used in simulation ( ˜ψα, ˜A) defined on a square torus of unit area T 2 □ and the physical fields (ψα, A) defined over the physical lattice unit cell T 2 Λ. effects. The standard approach is to take a large (costly to simulate) box as a system with a num...

    work page

  31. [42]

    Single crystal growth and characterization of superconducting LiFeAs

    Morozov, I.et al. Single crystal growth and characterization of superconducting LiFeAs. Cryst. Growth Des. 10, 4428 (2010)

    work page 2010

  32. [43]

    & Keller, H

    Maisuradze, A., Khasanov, R., Shengelaya, A. & Keller, H. Comparison of different methods for analyzing µSR line shapes in the vortex state of type-II superconductors. J. Phys.: Condens. Matter 21, 075701 (2009). And references therein

    work page 2009

  33. [44]

    Khasanov, R. et al. Proximity-induced superconductivity within the insulating (Li0.84Fe0.16)OH layers in (Li0.84Fe0.16)- OHFe0.98Se. Phys. Rev. B 93, 224512 (2016)

    work page 2016

  34. [45]

    This indirectly confirms that the superconducting peak is not simply a broadened one resulting from the super- position of several Gaussian distributions

    The superposition of three Gaussian distributions to model the superconducting fraction and an additional Gaussian dis- tribution for the background did not yield satisfactory results due to the high degree of correlation among the fitting pa- rameters. This indirectly confirms that the superconducting peak is not simply a broadened one resulting from the...

    work page

  35. [46]

    Luke, G. M. et al. Time-reversal symmetry-breaking super- conductivity in Sr2RuO4. Nature 394, 558–561 (1998)

    work page 1998

  36. [47]

    µSR studies of superconductivity in eutec- tically grown mixed ruthenates

    Shiroka, T .et al. µSR studies of superconductivity in eutec- tically grown mixed ruthenates. Phys. Rev. B 85, 134527 (2012)

    work page 2012

  37. [48]

    Split superconducting and time-reversal symmetry-breaking transitions in Sr2RuO4 under stress

    Grinenko, V .et al. Split superconducting and time-reversal symmetry-breaking transitions in Sr2RuO4 under stress. Nat. Phys. 17, 748–754 (2021)

    work page 2021

  38. [49]

    P .et al

    Singh, R. P .et al. Detection of time-reversal symmetry break- ing in the noncentrosymmetric superconductor Re6Zr using muon-spin spectroscopy .Phys. Rev. Lett. 112, 107002 (2014)

    work page 2014

  39. [50]

    Nodeless superconductivity and time-reversal symmetry breaking in the noncentrosymmetric superconduc- tor Re24Ti5

    Shang, T .et al. Nodeless superconductivity and time-reversal symmetry breaking in the noncentrosymmetric superconduc- tor Re24Ti5. Phys. Rev. B 97, 020502(R) (2018)

    work page 2018

  40. [51]

    Time-reversal symmetry breaking in Re-based superconductors

    Shang, T .et al. Time-reversal symmetry breaking in Re-based superconductors. Phys. Rev. Lett. 121, 257002 (2018)

    work page 2018

  41. [52]

    Re1−xMox as an ideal test case of time-reversal symmetry breaking in unconventional superconductors

    Shang, T .et al. Re1−xMox as an ideal test case of time-reversal symmetry breaking in unconventional superconductors. npj Quantum Mater. 5, 76 (2020)

    work page 2020

  42. [53]

    & Shiroka, T

    Shang, T . & Shiroka, T . Time-reversal symmetry breaking in Re-based superconductors: recent developments. Front. Phys. 9, 270 (2021). And references therein

    work page 2021

  43. [54]

    K., Das, T

    Neha, P ., Biswas, P . K., Das, T . & Patnaik, S. Time-reversal symmetry breaking in topological superconductor Sr0.1Bi2Se3. Phys. Rev. Mater.3, 074201 (2019)

    work page 2019

  44. [55]

    Mielke III, C. et al. Time-reversal symmetry-breaking charge order in a kagome superconductor. Nature 602, 245 (2022)

    work page 2022

  45. [56]

    Brandt, E. H. Flux distribution and penetration depth mea- sured by muon spin rotation in high-Tc superconductors. Phys. Rev. B 37, 2349(R) (1988)

    work page 1988

  46. [57]

    Brandt, E. H. Properties of the ideal Ginzburg-Landau vortex lattice. Phys. Rev. B 68, 054506 (2003). 12

    work page 2003

  47. [58]

    Zhang, J. L. et al. Upper critical field and its anisotropy in LiFeAs. Phys. Rev. B 83, 174506 (2011)

    work page 2011

  48. [59]

    Song, Y . J.et al. Small anisotropy of the lower critical field and the s±-wave two-gap feature in single-crystal LiFeAs.Europhys. Lett. 94, 57008 (2011)

    work page 2011

  49. [60]

    Introduction to Superconductivity (Dover Publi- cations, Mineola, NY, 1996), 2 edn

    Tinkham, M. Introduction to Superconductivity (Dover Publi- cations, Mineola, NY, 1996), 2 edn

    work page 1996

  50. [61]

    & Manzano, F

    Carrington, A. & Manzano, F . Magnetic penetration depth of MgB2. Physica C 385, 205–214 (2003)

    work page 2003

  51. [62]

    Ager, C. et al. Angular-dependent muon-spin rotation and torque magnetometry on the mixed state of the high- temperature superconductor YBa2Cu3O7−δ. Phys. Rev. B 62, 3528–3533 (2000)

    work page 2000

  52. [63]

    Forgan, E. M. et al. Angle dependence of the muon relaxation rate in the mixed state for single crystals of YBa 2Cu3O7−δ. Hyperfine Interact. 63, 71–72 (1991)

    work page 1991

  53. [64]

    D., Smilga, V

    Sidorenko, A. D., Smilga, V . P . & Fesenko, V . I. Muonic study of type II superconductors. Hyperfine Interact. 63, 49–63 (1991)

    work page 1991

  54. [65]

    Multiple topological states in iron-based superconductors

    Zhang, P .et al. Multiple topological states in iron-based superconductors. Nat. Phys. 15, 41 (2019)

    work page 2019

  55. [66]

    & Babaev, E

    Speight, M., Winyard, T . & Babaev, E. Symmetries, length scales, magnetic response, and skyrmion chains in nematic superconductors. Phys. Rev. B 107, 195204 (2023)

    work page 2023

  56. [67]

    & Babaev, E

    Speight, M., Winyard, T . & Babaev, E. Magnetic response of nematic superconductors: Skyrmion stripes and their signa- tures in muon spin relaxation experiments. Phys. Rev. Lett. 130, 226002 (2023)

    work page 2023

  57. [68]

    Zhitomirsky , M. E. Dissociation of flux line in unconventional superconductor. J. Phys. Soc. Jpn. 64, 913–921 (1995)

    work page 1995

  58. [69]

    A., Garaud, J

    Zyuzin, A. A., Garaud, J. & Babaev, E. Nematic skyrmions in odd-parity superconductors. Phys. Rev. Lett. 119, 167001 (2017)

    work page 2017

  59. [70]

    & Babaev, E

    Speight, M., Winyard, T . & Babaev, E. Chiral p-wave su- perconductors have complex coherence and magnetic field penetration lengths. Phys. Rev. B 100, 174514 (2019)

    work page 2019

  60. [71]

    & Winyard, T

    Speight, M. & Winyard, T . Vortex lattices and critical fields in anisotropic superconductors. J. Phys. A: Math. Theor. 58, 095203 (2025)

    work page 2025

  61. [72]

    Vortices with fractional flux in two-gap super- conductors and in extended faddeev model

    Babaev, E. Vortices with fractional flux in two-gap super- conductors and in extended faddeev model. Physical review letters 89, 067001 (2002)

    work page 2002

  62. [73]

    & Babaev, E

    Winyard, T ., Silaev, M. & Babaev, E. Skyrmion formation due to unconventional magnetic modes in anisotropic multiband superconductors. Physical Review B 99, 024501 (2019)

    work page 2019

  63. [74]

    & Babaev, E

    Winyard, T ., Silaev, M. & Babaev, E. Hierarchies of length- scale based typology in anisotropic u(1) s-wave multiband superconductors. Physical Review B 99, 064509 (2019)

    work page 2019

  64. [75]

    & Babaev, E

    Speight, M., Winyard, T ., Wormald, A. & Babaev, E. Magnetic field behavior in s+ is and s+ id superconductors: Twisting of applied and spontaneous fields. Physical Review B 104, 174515 (2021)

    work page 2021

  65. [76]

    E., Brewer, J

    Sonier, J. E., Brewer, J. H. & Kiefl, R. F . µsr studies of the vortex state in type-ii superconductors. Reviews of Modern Physics 72, 769 (2000)

    work page 2000

  66. [77]

    & Winyard, T

    Speight, M. & Winyard, T . Skyrmions and spin waves in frus- trated ferromagnets at low applied magnetic field. Physical Review B 101, 134420 (2020)

    work page 2020

  67. [78]

    On estimation of a probability density function and mode

    Parzen, E. On estimation of a probability density function and mode. The annals of mathematical statistics 33, 1065–1076 (1962)

    work page 1962

  68. [79]

    W .Density Estimation for Statistics and Data Analysis, vol

    Silverman, B. W .Density Estimation for Statistics and Data Analysis, vol. 26 of Monographs on Statistics and Applied Prob- ability (Chapman and Hall, London, 1986)

    work page 1986