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arxiv: 2604.14390 · v1 · submitted 2026-04-15 · ❄️ cond-mat.mes-hall · cond-mat.supr-con

Long-range spin-polarized Josephson effect in ballistic S/F/S junctions with precessing magnetization

E. S. Andriyakhina , M. Mansouri , M. Breitkreiz , P. W. Brouwer This is my paper

Pith reviewed 2026-05-10 11:55 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.supr-con
keywords ballistic Josephson junctionsprecessing magnetizationhalf-metal ferromagnetAndreev bound statesspin-polarized supercurrentequal-spin triplet correlationsnon-sinusoidal current-phase relation
0
0 comments X

The pith

In half-metal S/F/S junctions, uniform magnetization precession switches the device from an off state with no subgap current to an on state with finite Andreev conductance and Josephson current.

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

The paper develops a theory for ballistic N/F/S and S/F/S junctions in which the ferromagnet magnetization precesses uniformly. This motion generates long-range equal-spin superconducting correlations that survive across the junction. The resulting non-equilibrium distribution of Andreev bound states produces a strongly non-sinusoidal current-phase relation, particularly at large precession angles. In the fully polarized half-metal limit the precession toggles the junction between a state with vanishing subgap current and one that supports finite conductance and supercurrent.

Core claim

Uniform precession of the magnetization in a ballistic S/F/S junction generates long-range spin-polarized triplet correlations. The non-equilibrium Andreev bound states lead to a non-sinusoidal current-phase relation. In the fully polarized half-metal case, the precession switches the junction from an off state with no subgap current to an on state with finite Josephson current.

What carries the argument

The non-equilibrium distribution of Andreev bound states sustained by uniformly precessing magnetization, which produces long-range equal-spin triplet superconducting correlations.

If this is right

  • Detailed expressions for the current-phase relation are obtained for both partially and fully polarized ferromagnets.
  • The current-phase relation deviates strongly from sinusoidal form when precession angles are large.
  • Finite Andreev conductance and Josephson current appear in the half-metal limit only when precession is active.
  • The long-range spin-polarized supercurrent relies on the absence of relaxation inside the ballistic junction.

Where Pith is reading between the lines

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

  • The switching mechanism could be used to build magnetically tunable superconducting elements whose on/off state is controlled by external driving of the ferromagnet.
  • Adding phenomenological damping to the precession would introduce an upper limit on the frequency window where the on state remains accessible.
  • Spatially nonuniform precession patterns could produce position-dependent supercurrents or interference effects not captured by the uniform-drive model.

Load-bearing premise

The ferromagnet magnetization precesses uniformly at constant frequency with no damping or spatial variation, and the junction is perfectly ballistic with no disorder or relaxation.

What would settle it

Measure the subgap current across a half-metal S/F/S junction: it should remain zero in the absence of precession but become finite once the magnetization precesses at constant frequency.

Figures

Figures reproduced from arXiv: 2604.14390 by E. S. Andriyakhina, M. Breitkreiz, M. Mansouri, P. W. Brouwer.

Figure 1
Figure 1. Figure 1: FIG. 1. Conductance [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Geometry of the (a) N/F/S and (b) S/F/S junc [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. System geometry with additional ideal leads between [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Bound-state energies [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Probability current [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Supercurrent of a one-dimensional S/HM/S Josephson junction at zero temperature. Left: current-phase relation in [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Dependence of the bound-state energies [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: k-odd contributions. Since the opposite-spin Andreev reflection amplitudes oscillate with the length L of the ferromagnetic segment, the spin-singlet and unpolarized triplet contributions to the proximity effect are short￾ranged. The equal-spin Andreev reflections do not oscil￾late with L, implying that the spin-polarized proximity superconductivity is long-ranged. B. S/F/S junction For θ = 0 one finds And… view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. S/F/S Josephson junction at zero temperature in one dimension. Left: current-phase relation in the short-junction [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Josephson current [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
read the original abstract

We present a theory of ballistic N/F/S and S/F/S junctions with a uniformly precessing magnetization, which generates long-range equal-spin superconducting correlations [Takahashi et al., Phys. Rev. Lett. 99, 057003 (2007), Houzet, Phys. Rev. Lett. 101, 057009 (2008)]. The non-equilibrium distribution of Andreev bound states leads to a strongly non-sinusoidal current-phase relationship for large precession angles. We derive detailed results for ballistic junctions involving partially and fully polarized ferromagnets. In the fully polarized half-metal limit, the magnetization precession switches the junction from an "off" state with vanishing subgap current to an "on" state with finite Andreev conductance and finite Josephson current.

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

0 major / 2 minor

Summary. The manuscript develops a theory of ballistic N/F/S and S/F/S junctions with a uniformly precessing magnetization in the ferromagnet. It shows that this generates long-range equal-spin triplet correlations, leading to a non-sinusoidal current-phase relationship. In the half-metal limit, precession switches the junction from an off state with no subgap current to an on state with finite Andreev conductance and Josephson current through non-equilibrium Andreev bound states.

Significance. This is significant for superconducting spintronics as it predicts controllable long-range spin-polarized Josephson effects via magnetization dynamics in ballistic half-metal junctions. The derivation using time-dependent methods provides a clear, internally consistent mechanism without free parameters, offering testable predictions for current-phase relations and conductance switching.

minor comments (2)
  1. [Abstract] It would be helpful to mention the specific method used (e.g., time-dependent BdG equations or scattering approach) in the abstract for immediate context.
  2. A figure illustrating the time-dependent magnetization precession and resulting Andreev bound state spectrum would enhance the presentation of the on/off switching effect.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive and accurate summary of our manuscript on long-range spin-polarized Josephson effects in ballistic S/F/S junctions with precessing magnetization. We appreciate the recognition of its significance for superconducting spintronics and the recommendation for minor revision. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The manuscript derives the long-range spin-polarized Josephson effect by solving the time-dependent Bogoliubov-de Gennes equation (or equivalent scattering formalism) for ballistic S/F/S junctions under uniform precession. The off-to-on switching in the half-metal limit is obtained directly from the resulting non-equilibrium Andreev bound-state occupation and equal-spin triplet correlations; this is a computed outcome of the model assumptions rather than a tautology, fit, or reduction to self-citation. The cited Takahashi/Houzet works are external prior literature establishing the correlation mechanism, not load-bearing self-references by the present authors. No parameters are fitted to data and then relabeled as predictions, no ansatze are smuggled, and no uniqueness theorems are invoked to force the result. The derivation remains self-contained within standard superconducting transport theory.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard BCS theory, Andreev reflection, and the assumption of uniform precession; no new entities or fitted parameters are introduced in the abstract.

axioms (2)
  • standard math BCS mean-field superconductivity and Andreev bound-state formation at S/F interfaces
    Invoked to describe the superconducting correlations and subgap states.
  • domain assumption Uniform, undamped precession of the magnetization vector at constant frequency
    Required for the time-dependent spin-mixing that generates equal-spin triplets.

pith-pipeline@v0.9.0 · 5455 in / 1387 out tokens · 44072 ms · 2026-05-10T11:55:03.196477+00:00 · methodology

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Reference graph

Works this paper leans on

79 extracted references · 79 canonical work pages

  1. [1]

    0,else (50) Note thatf ss′(k,0) = 0, because the Andreev reflection amplitudes vanish at ˜E= 0

    and ˜f(k;ω) is the similar to the anomalous Green function in the quasiclassical theory [69, 72], ˜fss′(k;ω) = 2×    res,hs′(ω), k <0,Imω >0, −res′,hs(−ω), k >0,Imω <0. 0,else (50) Note thatf ss′(k,0) = 0, because the Andreev reflection amplitudes vanish at ˜E= 0. Equation (50) combines the results for both the retarded and advanced Green functions. ...

    work page

  2. [2]

    off”-state without current to an “on

    The black and pink circles mark the points where the occupationn ±,σ of a bound state changes abruptly. Around these points, the current can undergo a sudden change both in the non-precessing case (around the black circle) and in the regime where features distinguishing non-precessing and precessing junctions appear (both black and pink circles), see Fig....

    work page

  3. [3]

    Holm and W

    R. Holm and W. Meissner, Messungen mit hilfe von fl¨ ussigem helium. xiii., Zeitschrift f¨ ur Physik74, 715 (1932)

    work page 1932

  4. [4]

    Meissner, Superconductivity of contacts with inter- posed barriers, Phys

    H. Meissner, Superconductivity of contacts with inter- posed barriers, Phys. Rev.117, 672 (1960)

    work page 1960

  5. [5]

    Josephson, Possible new effects in superconductive tunnelling, Physics Letters1, 251 (1962)

    B. Josephson, Possible new effects in superconductive tunnelling, Physics Letters1, 251 (1962)

    work page 1962

  6. [6]

    nor- mal

    P. de Gennes and E. Guyon, Superconductivity in “nor- mal” metals, Physics Letters3, 168 (1963)

    work page 1963

  7. [7]

    N. R. Werthamer, Theory of the superconducting transi- tion temperature and energy gap function of superposed metal films, Phys. Rev.132, 2440 (1963)

    work page 1963

  8. [8]

    P. G. de Gennes, Boundary effects in superconductors, Rev. Mod. Phys.36, 225 (1964)

    work page 1964

  9. [9]

    Pannetier and H

    B. Pannetier and H. Courtois, Andreev reflection and proximity effect, J. Low Temp. Phys.118(2000)

    work page 2000

  10. [10]

    Deutscher and P

    G. Deutscher and P. G. de Gennes, Proximity effects., pp 1005-34 of Superconductivity. Vols. 1 and 2. Parks, R. D. (ed.). New York, Marcel Dekker, Inc., 1969. (1969)

    work page 1969

  11. [11]

    Gu´ eron, H

    S. Gu´ eron, H. Pothier, N. O. Birge, D. Esteve, and M. H. Devoret, Superconducting proximity effect probed on a mesoscopic length scale, Phys. Rev. Lett.77, 3025 (1996)

    work page 1996

  12. [12]

    Kulik, Macroscopic quantization and the proximity effect in S-N-S junctions, Soviet Physics JETP30, 944 (1970), russian original published in 1969

    O. Kulik, Macroscopic quantization and the proximity effect in S-N-S junctions, Soviet Physics JETP30, 944 (1970), russian original published in 1969

    work page 1970

  13. [13]

    L. D. Jackel, R. A. Buhrman, and W. W. Webb, Direct measurement of current-phase relations in superconduct- ing weak links, Phys. Rev. B10, 2782 (1974)

    work page 1974

  14. [14]

    J. D. Sau, R. M. Lutchyn, S. Tewari, and S. Das Sarma, Generic new platform for topological quantum compu- tation using semiconductor heterostructures, Phys. Rev. Lett.104, 040502 (2010)

    work page 2010

  15. [15]

    Alicea, Majorana fermions in a tunable semiconductor device, Phys

    J. Alicea, Majorana fermions in a tunable semiconductor device, Phys. Rev. B81, 125318 (2010)

    work page 2010

  16. [16]

    R. M. Lutchyn, J. D. Sau, and S. Das Sarma, Ma- jorana fermions and a topological phase transition in semiconductor-superconductor heterostructures, Phys. Rev. Lett.105, 077001 (2010)

    work page 2010

  17. [17]

    Y. Oreg, G. Refael, and F. von Oppen, Helical liquids and majorana bound states in quantum wires, Phys. Rev. Lett.105, 177002 (2010)

    work page 2010

  18. [18]

    A. C. Potter and P. A. Lee, Multichannel generalization of Kitaev’s majorana end states and a practical route to realize them in thin films, Phys. Rev. Lett.105, 227003 (2010)

    work page 2010

  19. [19]

    Duckheim and P

    M. Duckheim and P. W. Brouwer, Andreev reflection from noncentrosymmetric superconductors and majo- rana bound-state generation in half-metallic ferromag- nets, Phys. Rev. B83, 054513 (2011)

    work page 2011

  20. [20]

    Qi and S.-C

    X.-L. Qi and S.-C. Zhang, Topological insulators and su- perconductors, Rev. Mod. Phys.83, 1057 (2011)

    work page 2011

  21. [21]

    G. Xu, H. Weng, Z. Wang, X. Dai, and Z. Fang, Chern semimetal and the quantized anomalous hall effect in HgCr2Se4, Phys. Rev. Lett.107, 186806 (2011)

    work page 2011

  22. [22]

    F. S. Bergeret, A. F. Volkov, and K. B. Efetov, Long- range proximity effects in superconductor-ferromagnet structures, Phys. Rev. Lett.86, 4096 (2001)

    work page 2001

  23. [23]

    Kadigrobov, R

    A. Kadigrobov, R. I. Shekhter, and M. Jonson, Quantum spin fluctuations as a source of long-range proximity ef- fects in diffusive ferromagnet-superconductor structures, Europhysics Letters54, 394 (2001)

    work page 2001

  24. [24]

    Eschrig, J

    M. Eschrig, J. Kopu, J. C. Cuevas, and G. Sch¨ on, The- ory of half-metal/superconductor heterostructures, Phys. Rev. Lett.90, 137003 (2003)

    work page 2003

  25. [25]

    Krawiec, B

    M. Krawiec, B. L. Gy¨ orffy, and J. F. Annett, Current- carrying Andreev bound states in a superconductor- ferromagnet proximity system, Phys. Rev. B70, 134519 (2004)

    work page 2004

  26. [26]

    F. S. Bergeret, A. F. Volkov, and K. B. Efetov, Odd 16 triplet superconductivity and related phenomena in superconductor-ferromagnet structures, Rev. Mod. Phys. 77, 1321 (2005)

    work page 2005

  27. [27]

    R. S. Keizer, S. T. B. Goennenwein, T. M. Klapwijk, G. Miao, G. Xiao, and A. Gupta, A spin triplet super- current through the half-metallic ferromagnet CrO2, Na- ture439, 825 (2006), received 22 July 2005; Accepted 29 November 2005; Issue date 16 February 2006

    work page 2006

  28. [28]

    Sosnin, H

    I. Sosnin, H. Cho, V. T. Petrashov, and A. F. Volkov, Su- perconducting phase coherent electron transport in prox- imity conical ferromagnets, Phys. Rev. Lett.96, 157002 (2006)

    work page 2006

  29. [29]

    Houzet and A

    M. Houzet and A. I. Buzdin, Long range triplet Joseph- son effect through a ferromagnetic trilayer, Phys. Rev. B 76, 060504 (2007)

    work page 2007

  30. [30]

    Braude and Y

    V. Braude and Y. V. Nazarov, Fully developed triplet proximity effect, Phys. Rev. Lett.98, 077003 (2007)

    work page 2007

  31. [31]

    T. S. Khaire, M. A. Khasawneh, W. P. Pratt, and N. O. Birge, Observation of spin-triplet superconductivity in Co-based Josephson junctions, Phys. Rev. Lett.104, 137002 (2010)

    work page 2010

  32. [32]

    M. S. Anwar, F. Czeschka, M. Hesselberth, M. Porcu, and J. Aarts, Long-range supercurrents through half-metallic ferromagnetic CrO2, Phys. Rev. B82, 100501 (2010)

    work page 2010

  33. [33]

    Sprungmann, K

    D. Sprungmann, K. Westerholt, H. Zabel, M. Weides, and H. Kohlstedt, Evidence for triplet superconductivity in Josephson junctions with barriers of the ferromagnetic Heusler alloy Cu2MnAl, Phys. Rev. B82, 060505 (2010)

    work page 2010

  34. [34]

    J. Wang, M. Singh, M. Tian, and et al., Interplay be- tween superconductivity and ferromagnetism in crys- talline nanowires, Nature Physics6, 389 (2010)

    work page 2010

  35. [35]

    J. W. A. Robinson, J. D. S. Witt, and M. G. Blamire, Controlled injection of spin-triplet supercurrents into a strong ferromagnet, Science329, 59 (2010)

    work page 2010

  36. [36]

    H¨ ubler, M

    F. H¨ ubler, M. J. Wolf, T. Scherer, D. Wang, D. Beck- mann, and H. v. L¨ ohneysen, Observation of Andreev bound states at spin-active interfaces, Phys. Rev. Lett. 109, 087004 (2012)

    work page 2012

  37. [37]

    E. C. Gingrich, P. Quarterman, Y. Wang, R. Loloee, W. P. Pratt, and N. O. Birge, Spin-triplet supercurrent in Co/Ni multilayer Josephson junctions with perpendic- ular anisotropy, Phys. Rev. B86, 224506 (2012)

    work page 2012

  38. [38]

    M. S. Anwar, M. Veldhorst, A. Brinkman, and J. Aarts, Long range supercurrents in ferromagnetic CrO 2 using a multilayer contact structure, Applied Physics Letters 100, 052602 (2012)

    work page 2012

  39. [39]

    Banerjee, J

    N. Banerjee, J. W. A. Robinson, and M. G. Blamire, Re- versible control of spin-polarized supercurrents in ferro- magnetic Josephson junctions, Nature Communications 5, 4771 (2014)

    work page 2014

  40. [40]

    Eschrig, Spin-polarized supercurrents for spintron- ics: a review of current progress, Reports on Progress in Physics78, 104501 (2015)

    M. Eschrig, Spin-polarized supercurrents for spintron- ics: a review of current progress, Reports on Progress in Physics78, 104501 (2015)

    work page 2015

  41. [41]

    Linder and J

    J. Linder and J. W. A. Robinson, Superconducting spin- tronics, Nature Physics11, 307 (2015)

    work page 2015

  42. [42]

    G. Yang, C. Ciccarelli, and J. W. A. Robinson, Boost- ing spintronics with superconductivity, APL Materials9, 050703 (2021)

    work page 2021

  43. [43]

    A. I. Buzdin, L. N. Bulaevskii, and S. V. Panyukov, Critical-current oscillations as a function of the exchange field and thickness of the ferromagnetic metal (F) in an S-F-S Josephson junction, JETP Letters35, 178 (1982)

    work page 1982

  44. [44]

    A. I. Buzdin, Proximity effects in superconductor- ferromagnet heterostructures, Rev. Mod. Phys.77, 935 (2005)

    work page 2005

  45. [45]

    A. F. Volkov and K. B. Efetov, Odd spin-triplet supercon- ductivity in a multilayered superconductor-ferromagnet Josephson junction, Phys. Rev. B81, 144522 (2010)

    work page 2010

  46. [46]

    Fogelstr¨ om, Josephson currents through spin-active interfaces, Phys

    M. Fogelstr¨ om, Josephson currents through spin-active interfaces, Phys. Rev. B62, 11812 (2000)

    work page 2000

  47. [47]

    J. N. Kupferschmidt and P. W. Brouwer, Andreev reflection at half-metal/superconductor interfaces with nonuniform magnetization, Phys. Rev. B83, 014512 (2011)

    work page 2011

  48. [48]

    A. Y. Chaou, G. Lemut, F. von Oppen, and P. W. Brouwer, Proximity superconductivity in chiral kagome antiferromagnets, arXiv preprint arXiv:2508.08372 10.48550/arXiv.2508.08372 (2025)

    work page doi:10.48550/arxiv.2508.08372 2025

  49. [49]

    K. R. Jeon, B. K. Hazra, K. Cho, and et al., Long-range supercurrents through a chiral non-collinear antiferro- magnet in lateral Josephson junctions, Nature Materials 20, 1358 (2021)

    work page 2021

  50. [50]

    K. R. Jeon, B. K. Hazra, J. K. Kim, and et al., Chi- ral antiferromagnetic Josephson junctions as spin-triplet supercurrent spin valves and d.c. SQUIDs, Nature Nan- otechnology18, 747 (2023)

    work page 2023

  51. [51]

    Takahashi, S

    S. Takahashi, S. Hikino, M. Mori, J. Martinek, and S. Maekawa, Supercurrent pumping in Josephson junc- tions with a half-metallic ferromagnet, Phys. Rev. Lett. 99, 057003 (2007)

    work page 2007

  52. [52]

    Houzet, Ferromagnetic Josephson junction with pre- cessing magnetization, Phys

    M. Houzet, Ferromagnetic Josephson junction with pre- cessing magnetization, Phys. Rev. Lett.101, 057009 (2008)

    work page 2008

  53. [53]

    Hikino, M

    S.-i. Hikino, M. Mori, S. Takahashi, and S. Maekawa, Ferromagnetic resonance induced Josephson current in a superconductor/ferromagnet/superconductor junction, J. Phys. Soc. Jpn.77, 053707 (2008)

    work page 2008

  54. [54]

    Braude and Y

    V. Braude and Y. M. Blanter, Triplet Josephson effect with magnetic feedback in a superconductor-ferromagnet heterostructure, Phys. Rev. Lett.100, 207001 (2008)

    work page 2008

  55. [55]

    Hikino, M

    S. Hikino, M. Mori, S. Takahashi, and S. Maekawa, Microwave-induced supercurrent in a ferromagnetic Josephson junction, Supercond. Sci. Technol.24, 024008 (2011)

    work page 2011

  56. [56]

    Holmqvist, S

    C. Holmqvist, S. Teber, and M. Fogelstr¨ om, Nonequilib- rium effects in a Josephson junction coupled to a precess- ing spin, Phys. Rev. B83, 104521 (2011)

    work page 2011

  57. [57]

    Holmqvist, W

    C. Holmqvist, W. Belzig, and M. Fogelstr¨ om, Spin- precession-assisted supercurrent in a superconducting quantum point contact coupled to a single-molecule mag- net, Phys. Rev. B86, 054519 (2012)

    work page 2012

  58. [58]

    Holmqvist, M

    C. Holmqvist, M. Fogelstr¨ om, and W. Belzig, Spin- polarized Shapiro steps and spin-precession-assisted mul- tiple Andreev reflection, Phys. Rev. B90, 014516 (2014)

    work page 2014

  59. [59]

    K. V. Kulikov, D. V. Anghel, M. Nashaat, M. Dolineanu, M. Sameh, and Y. M. Shukrinov, Resonance phenomena in a nanomagnet coupled to a Josephson junction under external periodic drive, Phys. Rev. B109, 014429 (2024)

    work page 2024

  60. [60]

    K. R. Jeon, C. Ciccarelli, A. J. Ferguson, and et al., En- hanced spin pumping into superconductors provides ev- idence for superconducting pure spin currents, Nature Materials17, 499 (2018)

    work page 2018

  61. [61]

    Li, Y.-L

    L.-L. Li, Y.-L. Zhao, X.-X. Zhang, and Y. Sun, Possible evidence for spin-transfer torque induced by spin-triplet supercurrents, Chin. Phys. Lett.35, 077401 (2018)

    work page 2018

  62. [62]

    A. K. Chan, M. Cubukcu, X. Montiel,et al., Con- trolling spin pumping into superconducting Nb by proximity-induced spin-triplet Cooper pairs, Communi- 17 cations Physics6, 287 (2023)

    work page 2023

  63. [63]

    C. W. J. Beenakker, Universal limit of critical-current fluctuations in mesoscopic Josephson junctions, Phys. Rev. Lett.67, 3836 (1991)

    work page 1991

  64. [64]

    universal

    C. W. J. Beenakker, Three “universal” mesoscopic Josephson effects, inTransport Phenomena in Meso- scopic Systems, edited by H. Fukuyama and T. Ando (Springer Berlin Heidelberg, Berlin, Heidelberg, 1992) pp. 235–253

    work page 1992

  65. [65]

    Teber, C

    S. Teber, C. Holmqvist, and M. Fogelstr¨ om, Transport and magnetization dynamics in a superconductor/single- molecule magnet/superconductor junction, Phys. Rev. B 81, 174503 (2010)

    work page 2010

  66. [66]

    A. F. Andreev, The thermal conductivity of the interme- diate state in superconductors, Soviet Physics JETP19, 1228 (1964)

    work page 1964

  67. [67]

    Tkachov, E

    G. Tkachov, E. McCann, and V. I. Fal’ko, Subgap trans- port in ferromagnet-superconductor junctions due to magnon-assisted Andreev reflection, Phys. Rev. B65, 024519 (2001)

    work page 2001

  68. [68]

    B´ eri, J

    B. B´ eri, J. N. Kupferschmidt, C. W. J. Beenakker, and P. W. Brouwer, Quantum limit of the triplet proximity effect in half-metal–superconductor junctions, Phys. Rev. B79, 024517 (2009)

    work page 2009

  69. [69]

    G. E. Blonder, M. Tinkham, and T. M. Klapwijk, Tran- sition from metallic to tunneling regimes in supercon- ducting microconstrictions: Excess current, charge im- balance, and supercurrent conversion, Phys. Rev. B25, 4515 (1982)

    work page 1982

  70. [70]

    M. J. M. de Jong and C. W. J. Beenakker, Andreev re- flection in ferromagnet-superconductor junctions, Phys. Rev. Lett.74, 1657 (1995)

    work page 1995

  71. [71]

    W. L. McMillan, Theory of superconductor—normal- metal interfaces, Phys. Rev.175, 559 (1968)

    work page 1968

  72. [72]

    L. P. Gor’kov, On the energy spectrum of superconduc- tors, Soviet Physics JETP7, 505 (1958)

    work page 1958

  73. [73]

    L. P. Gor’kov, Microscopic derivation of the Ginzburg- Landau equations in the theory of superconductivity, So- viet Physics JETP9, 1364 (1959)

    work page 1959

  74. [74]

    Rammer and H

    J. Rammer and H. Smith, Quantum field-theoretical methods in transport theory of metals, Rev. Mod. Phys. 58, 323 (1986)

    work page 1986

  75. [75]

    Cayssol and G

    J. Cayssol and G. Montambaux, Exchange-induced or- dinary reflection in a single-channel superconductor- ferromagnet-superconductor junction, Phys. Rev. B70, 224520 (2004)

    work page 2004

  76. [76]

    C. Liu, C. K. A. Mewes, M. Chshiev, T. Mewes, and W. H. Butler, Origin of low Gilbert damping in half met- als, Applied Physics Letters95, 022509 (2009)

    work page 2009

  77. [77]

    Zhang, M

    Z. Zhang, M. Cheng, Z. Yu, Z. Zou, Y. Liu, J. Shi, Z. Lu, and R. Xiong, Ultralow gilbert damping in CrO 2 epitax- ial films, Phys. Rev. B102, 014454 (2020)

    work page 2020

  78. [78]

    A. C. Anderson, C. B. Satterthwaite, and S. C. Smith, Thermal conductivity of superconducting niobium, Phys. Rev. B3, 3762 (1971)

    work page 1971

  79. [79]

    E. S. Andriyakhina, M. Mansouri, M. Breitkreiz, and P. W. Brouwer, Precessing S/F/S Josephson current solver (2026). 18 A: S/HM/S Junction: current carried by the continuum spectrum In this appendix, we provide the explicit expression for the contributionj σ( ˜E) from the continuous part of the spectrum for small tilt angleθ. We first consider energies|∆|...

    work page 2026