pith. sign in

arxiv: 2606.10162 · v1 · pith:7PLPURISnew · submitted 2026-06-08 · ❄️ cond-mat.supr-con

Microscopic Investigation of the Superconducting State in CuCo₂S₄: Evidence for an Intermediate-Coupling Fully Gapped Superconductor

K. Panda , A. Bhattacharyya , Liang-Wen Ji , Jing Li , R. Stewart , D. T. Adroja , Guang-Han Cao This is my paper

Pith reviewed 2026-06-27 14:26 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords superconductivitymuon spin rotationCuCo2S4thiospinelfully gappedintermediate couplings-wavetime-reversal symmetry
0
0 comments X

The pith

Transverse-field μSR measurements establish that CuCo2S4 is a fully gapped superconductor in the intermediate electron-phonon coupling regime.

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

The paper reports the first microscopic probe of superconductivity in the thiospinel CuCo2S4 using muon spin rotation. Temperature-dependent depolarization rates from transverse-field measurements fit a model of a fully gapped s-wave order parameter. The resulting gap-to-transition-temperature ratio of 3.95 exceeds the weak-coupling BCS value, indicating intermediate coupling. Zero-field data show no spontaneous fields, though impurity effects limit sensitivity to time-reversal symmetry breaking. Thermodynamic measurements support the picture of conventional superconductivity.

Core claim

The temperature dependence of the superconducting depolarization rate obtained from transverse-field μSR measurements indicates a fully gapped superconducting order parameter with 2Δ(0)/(k_B T_SC) = 3.95(2), placing CuCo2S4 in the intermediate electron-phonon coupling regime and consistent with conventional s-wave superconductivity.

What carries the argument

The temperature dependence of the muon depolarization rate in the superconducting state, analyzed within the London limit for a fully gapped s-wave superfluid density.

Load-bearing premise

The ferromagnetic impurity phase does not distort the extracted temperature dependence of the depolarization rate in a way that mimics a fully gapped behavior.

What would settle it

Observation of a temperature dependence of the depolarization rate that fits a nodal gap model or yields a gap ratio of exactly 3.53 would falsify the fully gapped intermediate-coupling claim.

Figures

Figures reproduced from arXiv: 2606.10162 by A. Bhattacharyya, D. T. Adroja, Guang-han Cao, Jing Li, K. Panda, Liang-Wen Ji, R. Stewart.

Figure 1
Figure 1. Figure 1: (a) Crystal structure of CuCo2S4, illustrating the arrangement of tetrahedral (CuS4) and octahedral (CoS6) units. In this depiction, copper (Cu) atoms are represented as green spheres (large), cobalt (Co) atoms as red spheres (medium), and sulfur (S) atoms as violet spheres (small). (b) Temperature-dependent magnetic susceptibility measured under zero-field-cooled (ZFC) and field-cooled (FC) conditions in … view at source ↗
Figure 2
Figure 2. Figure 2: (a) Temperature dependence of the heat capacity, [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Transverse-field µSR asymmetry spectra for CuCo2S4 collected at an applied magnetic field of 30 mT, comparing the field-cooled state at 0.25 K (below the critical temperature, TSC) and 5.2 K (above TSC). The solid lines represent fits using Eq. 1. TSC under a 30 mT external magnetic field is consistent with established behavior in the vortex state of superconductors. To gain deeper insight into the superco… view at source ↗
Figure 4
Figure 4. Figure 4: Superconducting properties of CuCo2S4 under an applied magnetic field of 30 mT. (a) Temperature dependence of the superconducting depolariza￾tion rate, σsc(T), with a fit using an s-wave (red line), d− wave (pink dot) and s+ s wave (dashed) gap model. (b) Relative field shift, ∆B = (Bsc − Bapp)/Bapp, as a function of temperature. 3.95(2). Complementary NMR measurements estimate this ra￾tio as 4.14, both ex… view at source ↗
Figure 6
Figure 6. Figure 6: LF asymmetry spectra at 0.3 K under applied fields of 0, 2.5, 5, and [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) ZF asymmetry spectra at 0.3 K (green squares) and 4.8 K (black [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Superconducting critical temperature (TSC) versus Fermi tempera￾ture (TF) obtained from µSR measurements in CuCo2S4. The region between the dashed red lines denotes the range typically associated with unconven￾tional superconductors. The solid blue line marks the position of conventional BCS superconductors for reference. The positions of CuCo2S4, ScRuSi [54], HfIrSi [55], and ZrIrSi [56], located close to… view at source ↗
read the original abstract

The thiospinel compound CuCo$_2$S$_4$ provides an attractive platform for exploring superconductivity in transition-metal chalcogenide spinels. Here, we report the first microscopic investigation of the superconducting state in CuCo$_2$S$_4$ using muon spin rotation and relaxation ($\mu$SR) measurements, complemented by magnetization and heat-capacity experiments. The temperature dependence of the superconducting depolarization rate obtained from transverse-field $\mu$SR measurements indicates a fully gapped superconducting order parameter. The extracted gap ratio $2\Delta(0)/(k_{\mathrm{B}}T_\mathrm{SC}) = 3.95(2)$ exceeds the BCS weak-coupling value of 3.53, placing CuCo$_2$S$_4$ in the intermediate electron-phonon coupling regime. Zero-field $\mu$SR measurements were performed to probe possible time-reversal symmetry breaking (TRSB) in the superconducting state. Within the experimental resolution, no additional spontaneous internal magnetic fields are observed below $T_c$. However, due to the presence of a ferromagnetic impurity phase and the associated fast-relaxing signal component, the sensitivity of the present measurements to weak spontaneous fields is reduced. Consequently, while no evidence for TRSB is detected, its existence cannot be definitively ruled out. Overall, our combined thermodynamic and $\mu$SR results demonstrate that CuCo$_2$S$_4$ exhibits a fully gapped superconducting state with intermediate coupling strength, consistent with conventional $s$-wave superconductivity in this cobalt-based thiospinel system.

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

1 major / 1 minor

Summary. The manuscript reports the first microscopic investigation of superconductivity in the thiospinel CuCo₂S₄ via transverse-field and zero-field μSR, supported by magnetization and heat-capacity data. The central claim is that the temperature dependence of the TF-μSR depolarization rate indicates a fully gapped s-wave order parameter, with extracted ratio 2Δ(0)/(k_B T_SC) = 3.95(2) placing the material in the intermediate electron-phonon coupling regime. ZF-μSR detects no spontaneous fields, though sensitivity is reduced by a ferromagnetic impurity phase.

Significance. If the TF-μSR analysis holds, the work supplies the first microscopic evidence for conventional intermediate-coupling superconductivity in this cobalt-based thiospinel, consistent with the thermodynamic data. The gap ratio is reported with uncertainty and follows directly from the stated temperature dependence of the depolarization rate.

major comments (1)
  1. [TF-μSR analysis and abstract discussion of impurity phase] The ferromagnetic impurity is addressed only for ZF-μSR (reducing sensitivity to spontaneous fields via its fast-relaxing component). No corresponding statement or analysis confirms that this component was isolated, subtracted, or shown to be temperature-independent in the TF-μSR data used to extract σ_sc(T) and the gap ratio. This assumption is load-bearing for the fully gapped claim, as any T-dependent impurity relaxation would alter the inferred order-parameter symmetry and magnitude.
minor comments (1)
  1. [Abstract] The abstract states the gap ratio but omits the explicit fitting functions, background subtraction procedure, and impurity modeling details for the TF-μSR depolarization rate; these should be summarized even in the abstract for a microscopic claim.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying this important point regarding the TF-μSR analysis. We respond to the major comment below.

read point-by-point responses

  1. Referee: [TF-μSR analysis and abstract discussion of impurity phase] The ferromagnetic impurity is addressed only for ZF-μSR (reducing sensitivity to spontaneous fields via its fast-relaxing component). No corresponding statement or analysis confirms that this component was isolated, subtracted, or shown to be temperature-independent in the TF-μSR data used to extract σ_sc(T) and the gap ratio. This assumption is load-bearing for the fully gapped claim, as any T-dependent impurity relaxation would alter the inferred order-parameter symmetry and magnitude.

    Authors: We agree that the manuscript does not explicitly describe the treatment of the ferromagnetic impurity contribution in the TF-μSR data analysis. The TF-μSR spectra were in fact fitted with a two-component model separating the Gaussian relaxation arising from the vortex lattice (used to extract σ_sc(T)) from the fast-relaxing impurity component. The impurity relaxation rate was verified to be temperature-independent below T_c through consistency with measurements above T_c and by direct inspection of the raw spectra. Nevertheless, because this procedure is not stated in the current text, we will add a dedicated paragraph in the Methods and Results sections of the revised manuscript, together with supporting details on the fitting model and evidence for temperature independence of the impurity term. This will make the analysis fully transparent and address the referee's concern. revision: yes

Circularity Check

0 steps flagged

No significant circularity; experimental fit to standard model

full rationale

The paper reports TF-μSR depolarization rates measured on CuCo2S4 and fits their temperature dependence to the standard London-limit expression for the superfluid density of a fully gapped s-wave superconductor. The extracted gap ratio 2Δ(0)/kBTSC = 3.95(2) is a direct output of that fit to the observed data points. No equation in the reported chain defines a quantity in terms of itself, renames a fitted parameter as a prediction, or reduces the central claim to a self-citation whose validity is presupposed. The abstract explicitly flags the ferromagnetic impurity and the consequent reduction in ZF-μSR sensitivity; the TF-μSR analysis is presented as using the conventional model with that caveat noted. The derivation is therefore self-contained data analysis against an externally validated functional form and does not meet any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the fitted gap ratio extracted from μSR depolarization data under standard analysis assumptions for fully gapped superconductors; the impurity phase is treated as a sensitivity reducer rather than a modeled correction.

free parameters (1)
  • gap ratio 2Δ(0)/k_B T_SC = 3.95(2)
    Fitted parameter extracted from the temperature dependence of the TF-μSR depolarization rate.
axioms (2)
  • domain assumption Muon depolarization rate in the vortex state is proportional to the superfluid density via the London penetration depth in the London limit.
    Invoked to convert measured relaxation rates into gap values.
  • ad hoc to paper Ferromagnetic impurity contributes only a fast-relaxing component that does not alter the slow component used for gap extraction.
    Stated in the abstract as reducing ZF sensitivity but not affecting the TF gap result.

pith-pipeline@v0.9.1-grok · 5852 in / 1347 out tokens · 29695 ms · 2026-06-27T14:26:57.704979+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

59 extracted references · 57 canonical work pages

  1. [1]

    R. J. Naumann, Introduction to the Physics and Chemistry of Materials, CRC Press, 2008. doi:10.1201/9781420061345. URLhttp://dx.doi.org/10.1201/9781420061345

    work page doi:10.1201/9781420061345 2008

  2. [2]

    F. Bosi, C. Biagioni, M. Pasero, Nomenclature and classification of the spinel supergroup, Euro- pean Journal of Mineralogy 31 (1) (2019) 183–192. doi:10.1127/ejm/2019/0031-2788. URLhttp://dx.doi.org/10.1127/ejm/2019/0031-2788

    work page doi:10.1127/ejm/2019/0031-2788 2019

  3. [3]

    D. C. Johnston, Superconducting and normal state prop- erties of Li 1+xTi2−xO4 spinel compounds. I. Preparation, 9 crystallography, superconducting properties, electrical re- sistivity, dielectric behavior, and magnetic susceptibil- ity, Journal of Low Temperature Physics 25 (1–2) (1976) 145–175. doi:10.1007/bf00654827. URLhttp://dx.doi.org/10.1007/BF00654827

    work page doi:10.1007/bf00654827 1976

  4. [4]

    R. W. McCallum, D. C. Johnston, C. A. Luengo, M. B. Maple, Superconducting and normal state properties of Li1+xTi2−xO4 spinel compounds. II. Low-temperature heat capacity, Journal of Low Temperature Physics 25 (1–2) (1976) 177–193. doi:10.1007/bf00654828. URLhttp://dx.doi.org/10.1007/BF00654828

    work page doi:10.1007/bf00654828 1976

  5. [5]

    Van Maaren, G

    N. Van Maaren, G. Schaeffer, F. Lotgering, Super- conductivity in sulpho- and selenospinels, Physics Letters A 25 (3) (1967) 238–239. doi:10.1016/0375- 9601(67)90878-x. URLhttp://dx.doi.org/10.1016/0375-9601(67)90878-X

    work page doi:10.1016/0375- 1967

  6. [6]

    Robbins, R

    M. Robbins, R. Willens, R. Miller, Superconductivity in the spinels CuRh 2S4 and CuRh 2Se4, Solid State Com- munications 5 (12) (1967) 933–934. doi:10.1016/0038- 1098(67)90469-3. URLhttp://dx.doi.org/10.1016/0038-1098(67)90469-3

    work page doi:10.1016/0038- 1967

  7. [7]

    Hagino, Y

    T. Hagino, Y . Seki, N. Wada, S. Tsuji, T. Shirane, K.-i. Kumagai, S. Nagata, Superconductivity in spinel-type compounds CuRh 2S4 and CuRh 2Se4, Physical Review B 51 (18) (1995) 12673–12684. doi:10.1103/physrevb.51.12673. URLhttp://dx.doi.org/10.1103/PhysRevB.51.12673

    work page doi:10.1103/physrevb.51.12673 1995

  8. [8]

    Kumagai, S

    K. Kumagai, S. Tsuji, T. Hagino, S. Nagata, NMR Stud- ies of Superconductivity and Metal-Insulator Transition in Cu Spinel CuM2X4 (M=Rh, Ir and X=S, Se), in: Spec- troscopy of Mott Insulators and Correlated Metals, V ol. 119 of Springer Series in Solid-State Sciences, Springer, Berlin, Heidelberg, 1995, pp. 255–264

    1995

  9. [9]

    G. Cao, T. Furubayashi, H. Suzuki, H. Kitazawa, T. Matsumoto, Y . Uwatoko, Suppression of metal-to- insulator transition and appearance of superconductivity in Cu 1−xZnxIr2S4, Physical Review B 64 (21) (2001) 214514. doi:10.1103/physrevb.64.214514. URLhttp://dx.doi.org/10.1103/PhysRevB.64.214514

    work page doi:10.1103/physrevb.64.214514 2001

  10. [10]

    Suzuki, T

    H. Suzuki, T. Furubayashi, G. Cao, H. Kitazawa, A. Kamimura, K. Hirata, T. Matsumoto, Metal-Insulator Transition and Superconductivity in Spinel-Type System Cu1−xZnxIr2S4, Journal of the Physical Society of Japan 68 (8) (1999) 2495–2497. doi:10.1143/jpsj.68.2495. URLhttp://dx.doi.org/10.1143/JPSJ.68.2495

    work page doi:10.1143/jpsj.68.2495 1999

  11. [11]

    N. Aito, M. Sato, Superconducting Transition Tem- peratures of Cu(Co 1−xMx)2S4, Journal of the Phys- ical Society of Japan 73 (7) (2004) 1938–1943. doi:10.1143/jpsj.73.1938. URLhttp://dx.doi.org/10.1143/JPSJ.73.1938

    work page doi:10.1143/jpsj.73.1938 2004

  12. [12]

    Jin, S.-H

    Y .-Y . Jin, S.-H. Sun, Y .-W. Cui, Q.-Q. Zhu, L.-W. Ji, Z. Ren, G.-H. Cao, Bulk superconductivity and Pauli paramagnetism in nearly stoichiometric CuCo 2S4, Physical Review Materials 5 (7) (2021) 074804. doi:10.1103/physrevmaterials.5.074804. URLhttp://dx.doi.org/10.1103/PhysRevMaterials.5.074804

    work page doi:10.1103/physrevmaterials.5.074804 2021

  13. [13]

    Gibson, K

    A. Gibson, K. Lilova, T. Subramani, B. von der Heyden, D. A. Gilbert, A. Navrotsky, B. F. Woodfield, Thermody- namic properties and superconductivity of natural carrol- lite CuCo2S4, The Journal of Chemical Thermodynamics 185 (2023) 107096. doi:10.1016/j.jct.2023.107096. URLhttp://dx.doi.org/10.1016/j.jct.2023.107096

    work page doi:10.1016/j.jct.2023.107096 2023

  14. [14]

    T. Oda, M. Shirai, N. Suzuki, K. Motizuki, Electronic band structure of sulphide spinels CuM 2S4 (M=Co, Rh, Ir), Journal of Physics: Condensed Matter 7 (23) (1995) 4433–4445. doi:10.1088/0953-8984/7/23/012. URLhttp://dx.doi.org/10.1088/0953-8984/7/23/012

    work page doi:10.1088/0953-8984/7/23/012 1995

  15. [15]

    Z. Yue, Z. Hou, F. Yun, P. Liu, G. Yang, A. Bake, W. Zhao, D. Cortie, C. Shu, S. Hu, J. Cheng, X. Wang, Observation of itinerant ferromagnetism and coupled magnetoresis- tance in a spinel CuCo2S4, Journal of Materials Chemistry C 9 (28) (2021) 8874–8881. doi:10.1039/d1tc02065j. URLhttp://dx.doi.org/10.1039/d1tc02065j

    work page doi:10.1039/d1tc02065j 2021

  16. [16]

    S. L. Skornyakov, I. O. Trifonov, V . I. Anisimov, Coulomb Correlations and Electronic Structure of CuCo2S4: a DFT +DMFT Study, JETP Letters 117 (8) (2023) 588–592. doi:10.1134/s0021364023600647. URLhttp://dx.doi.org/10.1134/S0021364023600647

    work page doi:10.1134/s0021364023600647 2023

  17. [17]

    Hemmati-Eslamlu, A

    P. Hemmati-Eslamlu, A. Habibi-Yangjeh, Y . Ak- inay, T. Cetin, Novel g-C 3N4 nanorods/Cu3BiS3 nanocomposites: Outstanding photocatalysts with p-n heterojunction for impressively detoxification of water under visible light, Journal of Photochemistry and Photobiology A: Chemistry 443 (2023) 114862. doi:10.1016/j.jphotochem.2023.114862. URLhttp://dx.doi.org/...

    work page doi:10.1016/j.jphotochem.2023.114862 2023

  18. [18]

    Habibi, A

    M. Habibi, A. Habibi-Yangjeh, Y . Akinay, A. Khataee, Oxygen vacancy-rich CeO 2 decorated with Cu 3BiS3 nanoparticles: Outstanding visible- light photocatalytic performance towards tetracy- cline degradation, Chemosphere 340 (2023) 139828. doi:10.1016/j.chemosphere.2023.139828. URLhttp://dx.doi.org/10.1016/j.chemosphere.2023.139828

    work page doi:10.1016/j.chemosphere.2023.139828 2023

  19. [19]

    Bhattacharyya, D

    A. Bhattacharyya, D. T. Adroja, K. Panda, S. Saha, T. Das, A. J. S. Machado, O. V . Cigarroa, T. W. Grant, Z. Fisk, A. D. Hillier, P. Manfrinetti, Evidence of a Nodal Line in the Superconducting Gap Symmetry of Noncentrosymmetric ThCoC 2, Phys. Rev. Lett. 122 (2019) 147001. doi:10.1103/PhysRevLett.122.147001. URLhttps://link.aps.org/doi/10.1103/PhysRevLet...

    work page doi:10.1103/physrevlett.122.147001 2019

  20. [20]

    Bhattacharyya, M

    A. Bhattacharyya, M. R. Lees, K. Panda, P. P. Ferreira, T. T. Dorini, E. Gaudry, L. T. F. Eleno, V . K. Anand, 10 J. Sannigrahi, P. K. Biswas, R. Tripathi, D. T. Adroja, Nodeless time-reversal symmetry breaking in the cen- trosymmetric superconductor Sc 5Co4Si10 probed by muon-spin spectroscopy, Physical Review Materials 6 (6) (2022) 064802. doi:10.1103/p...

    work page doi:10.1103/physrevmaterials.6.064802 2022

  21. [21]

    Furukawa, S

    Y . Furukawa, S. Wada, K. Miyatani, T. Tanaka, M. Fuku- gauchi, M. Ishikawa, Nuclear spin-lattice relaxation and antiferromagnetic spin correlations in superconducting thiospinel Cu1.5Co1.5S4, Physical Review B 51 (9) (1995) 6159–6162. doi:10.1103/physrevb.51.6159. URLhttp://dx.doi.org/10.1103/PhysRevB.51.6159

    work page doi:10.1103/physrevb.51.6159 1995

  22. [22]

    Sugita, H

    S. Sugita, H. Takikawa, H. Nishihara, M. Ishikawa, E. Saito, An evidence for the s-wave superconductivity in the spinel superconductor Cd 2Re2O7: a study of low-temperature specific heat, Physica C: Superconduc- tivity 469–470 (2000) 233–234. doi:10.1016/s0921- 4534(99)00894-8. URLhttp://dx.doi.org/10.1016/s0921-4534(99)00894-8

    work page doi:10.1016/s0921- 2000

  23. [23]

    S. Wada, H. Sugita, K. Miyatani, T. Tanaka, T. Nishikawa, Weak antiferromagnetism and superconductivity in pseudo-binary spinel compounds (Cu, Co)Co 2S4 inves- tigated by 59Co and 63Cu magnetic resonance, Journal of Physics: Condensed Matter 14 (2) (2001) 219–230. doi:10.1088/0953-8984/14/2/309. URLhttp://dx.doi.org/10.1088/0953-8984/14/2/309

    work page doi:10.1088/0953-8984/14/2/309 2001

  24. [24]

    Baskaran, Electronic Model for CoO 2 Layer Based Systems: Chiral Resonating Valence Bond Metal and Superconductivity, Physical Review Letters 91 (9) (2003) 097003

    G. Baskaran, Electronic Model for CoO 2 Layer Based Systems: Chiral Resonating Valence Bond Metal and Superconductivity, Physical Review Letters 91 (9) (2003) 097003. doi:10.1103/physrevlett.91.097003. URLhttp://dx.doi.org/10.1103/PhysRevLett.91.097003

    work page doi:10.1103/physrevlett.91.097003 2003

  25. [25]

    Fujimoto, G.-q

    T. Fujimoto, G.-q. Zheng, Y . Kitaoka, R. L. Meng, J. Cmaidalka, C. W. Chu, Unconventional Superconduc- tivity and Electron Correlations in the Cobalt Oxyhydrate Na0.35CoO2.yH2O from Nuclear Quadrupole Reso- nance, Physical Review Letters 92 (4) (2004) 047004. doi:10.1103/physrevlett.92.047004. URLhttp://dx.doi.org/10.1103/PhysRevLett.92.047004

    work page doi:10.1103/physrevlett.92.047004 2004

  26. [26]

    Q.-H. Wang, P. A. Lee, Dopedtext−Jmodel on a triangular lattice: Possible application to Na xCoO2·yH2O and Na1−xTiO2, Physical Review B 69 (9) (2004) 092504. doi:10.1103/physrevb.69.092504. URLhttp://dx.doi.org/10.1103/PhysRevB.69.092504

    work page doi:10.1103/physrevb.69.092504 2004

  27. [27]

    A. D. Hillier, S. J. Blundell, I. McKenzie, I. Umegaki, L. Shu, J. A. Wright, T. Prokscha, F. Bert, K. Shimomura, A. Berlie, H. Alberto, I. Watanabe, Muon spin spec- troscopy, Nature Reviews Methods Primers 2 (1) (2022)

    2022

  28. [28]

    URLhttp://dx.doi.org/10.1038/s43586-021-00089-0

    doi:10.1038/s43586-021-00089-0. URLhttp://dx.doi.org/10.1038/s43586-021-00089-0

    work page doi:10.1038/s43586-021-00089-0

  29. [29]

    F. L. Pratt, Wimda: a muon data analysis program for the windows pc, Physica B 289–290 (2000) 710–714. doi:10.1016/S0921-4526(00)00328-8. URLhttps://doi.org/10.1016/S0921-4526(00)00328-8

    work page doi:10.1016/s0921-4526(00)00328-8 2000

  30. [30]

    Aharoni, Demagnetizing factors for rectangular ferro- magnetic prisms, Journal of Applied Physics 83 (6) (1998) 3432–3434

    A. Aharoni, Demagnetizing factors for rectangular ferro- magnetic prisms, Journal of Applied Physics 83 (6) (1998) 3432–3434. doi:10.1063/1.367113. URLhttp://dx.doi.org/10.1063/1.367113

    work page doi:10.1063/1.367113 1998

  31. [31]

    Bardeen, L

    J. Bardeen, L. N. Cooper, J. R. Schrieffer, Theory of superconductivity, Phys. Rev. 108 (1957) 1175–1204. doi:10.1103/PhysRev.108.1175. URLhttps://link.aps.org/doi/10.1103/PhysRev.108.1175

    work page doi:10.1103/physrev.108.1175 1957

  32. [32]

    Teruya, F

    A. Teruya, F. Suzuki, D. Aoki, F. Honda, A. Nakamura, M. Nakashima, Y . Amako, H. Harima, K. Uchima, M. Hedo, T. Nakama, Y .¯Onuki, Fermi Surface and Mag- netic Properties in Ferromagnet CoS 2 and Paramagnet CoSe2 with the Pyrite-type Cubic Structure, Journal of Physics: Conference Series 807 (2017) 012001. doi:10.1088/1742-6596/807/1/012001. URLhttp://dx...

    work page doi:10.1088/1742-6596/807/1/012001 2017

  33. [33]

    D. E. MacLaughlin, J. E. Sonier, R. H. Heffner, O. O. Bernal, B.-L. Young, M. S. Rose, G. D. Morris, E. D. Bauer, T. D. Do, M. B. Maple, Muon Spin Relaxation and Isotropic Pairing in Superconducting PrOs 4Sb12, Physical Review Letters 89 (15) (2002) 157001. doi:10.1103/physrevlett.89.157001. URLhttp://dx.doi.org/10.1103/PhysRevLett.89.157001

    work page doi:10.1103/physrevlett.89.157001 2002

  34. [34]

    D. E. MacLaughlin, P.-C. Ho, L. Shu, O. O. Bernal, S. Zhao, A. A. Dooraghi, T. Yanagisawa, M. B. Maple, R. H. Fukuda, Muon spin rotation and relaxation in Pr1−xNdxOs4Sb12: Magnetic and superconducting ground states, Physical Review B 89 (14) (2014) 144419. doi:10.1103/physrevb.89.144419. URLhttp://dx.doi.org/10.1103/PhysRevB.89.144419

    work page doi:10.1103/physrevb.89.144419 2014

  35. [35]

    Prozorov, R

    R. Prozorov, R. W. Giannetta, Magnetic penetration depth in unconventional superconductors, Supercond. Sci. Tech. 19 (8) (2006) R41–R67. doi:10.1088/0953-2048/19/8/r01. URLhttps://doi.org/10.1088/0953-2048/19/8/r01

    work page doi:10.1088/0953-2048/19/8/r01 2006

  36. [36]

    V . K. Anand, A. Bhattacharyya, D. T. Adroja, K. Panda, P. K. Biswas, A. D. Hillier, B. Lake, Time-reversal symmetry breaking ands-wave superconductivity in CaPd2Ge2: AµSR study, Physical Review B 108 (22) (2023) 224519. doi:10.1103/physrevb.108.224519. URLhttp://dx.doi.org/10.1103/PhysRevB.108.224519

    work page doi:10.1103/physrevb.108.224519 2023

  37. [37]

    Bhattacharyya, D

    A. Bhattacharyya, D. Adroja, A. Jana, K. Panda, P. Fer- reira, Y . Zhao, T. Ying, H. Hosono, T. Dorini, L. Eleno, P. Biswas, G. Stenning, R. Tripathi, Y . Qi, Exploring superconductivity in Ba 3Ir4Ge16: Experimental and theoretical insights, Journal of Alloys and Compounds 978 (2024) 173374. doi:10.1016/j.jallcom.2023.173374. URLhttp://dx.doi.org/10.1016/...

    work page doi:10.1016/j.jallcom.2023.173374 2024

  38. [38]

    Bhattacharyya, P

    A. Bhattacharyya, P. P. Ferreira, K. Panda, S. H. Ma- sunaga, L. R. de Faria, L. E. Correa, F. B. Santos, D. T. 11 Adroja, K. Yokoyama, T. T. Dorini, R. F. Jardim, L. T. F. Eleno, A. J. S. Machado, Electron–phonon supercon- ductivity in C-doped topological nodal-line semimetal Zr5Pt3: a muon spin rotation and relaxation (µSR) study, Journal of Physics: Co...

    work page doi:10.1088/1361-648x/ac2bc7 2021

  39. [39]

    G. M. Pang, M. Smidman, W. B. Jiang, J. K. Bao, Z. F. Weng, Y . F. Wang, L. Jiao, J. L. Zhang, G. H. Cao, H. Q. Yuan, Evidence for nodal superconductivity in quasi-one-dimensional K2Cr3As3, Phys. Rev. B 91 (2015) 220502. doi:10.1103/PhysRevB.91.220502. URLhttps://link.aps.org/doi/10.1103/PhysRevB.91.220502

    work page doi:10.1103/physrevb.91.220502 2015

  40. [40]

    J. F. Annett, Symmetry of the order parameter for high- temperature superconductivity, Adv. Phys. 39 (1990) 83–126. doi:10.1080/00018739000101481. URLhttps://doi.org/10.1080/00018739000101481

    work page doi:10.1080/00018739000101481 1990

  41. [41]

    D. T. Adroja, A. Bhattacharyya, Y . J. Sato, M. R. Lees, P. K. Biswas, K. Panda, V . K. Anand, G. B. G. Stenning, A. D. Hillier, D. Aoki, Pairing symmetry of an interme- diate valence superconductor CeIr 3 investigated using µSR measurements, Phys. Rev. B 103 (2021) 104514. doi:10.1103/PhysRevB.103.104514. URLhttps://link.aps.org/doi/10.1103/PhysRevB.103.104514

    work page doi:10.1103/physrevb.103.104514 2021

  42. [42]

    E. H. Brandt, Properties of the ideal Ginzburg-Landau vortex lattice, Physical Review B 68 (5) (2003) 054506. doi:10.1103/physrevb.68.054506. URLhttp://dx.doi.org/10.1103/PhysRevB.68.054506

    work page doi:10.1103/physrevb.68.054506 2003

  43. [43]

    W. L. McMillan, Transition Temperature of Strong- Coupled Superconductors, Phys. Rev. 167 (1968) 331–344. doi:10.1103/PhysRev.167.331. URLhttps://link.aps.org/doi/10.1103/PhysRev.167.331

    work page doi:10.1103/physrev.167.331 1968

  44. [44]

    E. E. M. Chia, M. B. Salamon, H. Sugawara, H. Sato, Probing the superconducting gap symmetry of PrRu4Sb12: A comparison with PrOs 4Sb12, Phys. Rev. B 69 (2004) 180509. doi:10.1103/PhysRevB.69.180509. URLhttps://link.aps.org/doi/10.1103/PhysRevB.69.180509

    work page doi:10.1103/physrevb.69.180509 2004

  45. [45]

    Amato, Heavy-fermion systems studied byµSR technique, Rev

    A. Amato, Heavy-fermion systems studied byµSR technique, Rev. Mod. Phys. 69 (1997) 1119–1180. doi:10.1103/RevModPhys.69.1119. URLhttps://link.aps.org/doi/10.1103/RevModPhys.69.1119

    work page doi:10.1103/revmodphys.69.1119 1997

  46. [46]

    R. S. Hayano, Y . J. Uemura, J. Imazato, N. Nishida, T. Yamazaki, R. Kubo, Zero-and low-field spin relaxation studied by positive muons, Physical Review B 20 (3) (1979) 850–859. doi:10.1103/physrevb.20.850. URLhttp://dx.doi.org/10.1103/PhysRevB.20.850

    work page doi:10.1103/physrevb.20.850 1979

  47. [47]

    Bhattacharyya, D

    A. Bhattacharyya, D. T. Adroja, J. S. Lord, L. Wang, Y . Shi, K. Panda, H. Luo, A. M. Strydom, Quantum fluc- tuations in the quasi-one-dimensional non-Fermi liquid system CeCo 2Ga8 investigated usingµSR, Phys. Rev. B 101 (2020) 214437. doi:10.1103/PhysRevB.101.214437. URLhttps://link.aps.org/doi/10.1103/PhysRevB.101.214437

    work page doi:10.1103/physrevb.101.214437 2020

  48. [48]

    Panda, D

    Aarti, K. Panda, D. T. Adroja, A. Bhattacharyya, P. K. Biswas, A. D. Hillier, B. Lake, S. Layek, V . K. Anand, Time-reversal symmetry breaking in thes-wave super- conductor CaPd 2As2 probed byµSR, Phys. Rev. B 110 (2024) 144506. doi:10.1103/PhysRevB.110.144506. URLhttps://link.aps.org/doi/10.1103/PhysRevB.110.144506

    work page doi:10.1103/physrevb.110.144506 2024

  49. [49]

    A. D. Hillier, J. Quintanilla, R. Cywinski, Evi- dence for Time-Reversal Symmetry Breaking in the Noncentrosymmetric Superconductor LaNiC 2, Physical Review Letters 102 (11) (2009) 117007. doi:10.1103/physrevlett.102.117007. URLhttp://dx.doi.org/10.1103/PhysRevLett.102.117007

    work page doi:10.1103/physrevlett.102.117007 2009

  50. [50]

    G. M. Luke, Y . Fudamoto, K. M. Kojima, M. I. Larkin, J. Merrin, B. Nachumi, Y . J. Uemura, Y . Maeno, Z. Q. Mao, Y . Mori, H. Nakamura, M. Sigrist, Time-reversal symmetry-breaking superconductivity in Sr 2RuO4, Na- ture 394 (6693) (1998) 558–561. doi:10.1038/29038. URLhttp://dx.doi.org/10.1038/29038

    work page doi:10.1038/29038 1998

  51. [51]

    de Visser, N

    A. de Visser, N. T. Huy, A. Gasparini, D. E. de Nijs, D. Andreica, C. Baines, A. Amato, Muon Spin Rota- tion and Relaxation in the Superconducting Ferromagnet UCoGe, Physical Review Letters 102 (16) (2009) 117007. doi:10.1103/physrevlett.102.167003. URLhttp://dx.doi.org/10.1103/PhysRevLett.102.167003

    work page doi:10.1103/physrevlett.102.167003 2009

  52. [52]

    Khasanov, K

    R. Khasanov, K. Conder, E. Pomjakushina, A. Amato, C. Baines, Z. Bukowski, J. Karpinski, S. Katrych, H.-H. Klauss, H. Luetkens, A. Shengelaya, N. D. Zhigadlo, Evidence of nodeless superconductivity in FeSe 0.85 from a muon-spin-rotation study of the in-plane magnetic penetration depth, Physical Review B 78 (22) (2008) 220510. doi:10.1103/PhysRevB.78.22051...

    work page doi:10.1103/physrevb.78.220510 2008

  53. [53]

    D. Das, A. Bhattacharyya, V . K. Anand, A. D. Hillier, J. W. Taylor, T. Gruner, C. Geibel, D. T. Adroja, Z. Hos- sain, Muon spin relaxation study on itinerant ferromagnet CeCrGe3 and the effect of Ti substitution on magnetism of CeCrGe3, Journal of Physics: Condensed Matter 27 (1) (2014) 016004. doi:10.1088/0953-8984/27/1/016004. URLhttp://dx.doi.org/10.1...

    work page doi:10.1088/0953-8984/27/1/016004 2014

  54. [54]

    van Lierop, H

    J. van Lierop, H. S. Isaacs, D. H. Ryan, A. Beath, E. Mc- Calla, Muon spin relaxation study of exchange biased Co/CoO, Physical Review B 67 (13) (2003) 134430. doi:10.1103/physrevb.67.134430. URLhttp://dx.doi.org/10.1103/PhysRevB.67.134430

    work page doi:10.1103/physrevb.67.134430 2003

  55. [55]

    Panda, A

    K. Panda, A. Bhattacharyya, P. N. Ferreira, R. Mon- dal, A. Thamizhavel, D. T. Adroja, C. Heil, L. T. F. Eleno, A. D. Hillier, Probing the superconducting gap structure of ScRuSi viaµSR and first-principles calculations, Phys. Rev. B 109 (2024) 224517. doi:10.1103/PhysRevB.109.224517. URLhttps://link.aps.org/doi/10.1103/PhysRevB.109.224517 12

    work page doi:10.1103/physrevb.109.224517 2024

  56. [56]

    Bhattacharyya, K

    A. Bhattacharyya, K. Panda, D. T. Adroja, N. Kase, P. K. Biswas, S. Saha, T. Das, M. R. Lees, A. D. Hillier, Investigation of superconducting gap structure in HfIrSi using muon spin relaxation/rotation, Journal of Physics: Condensed Matter 32 (8) (2019) 085601. doi:10.1088/1361-648x/ab549e. URLhttps://doi.org/10.1088/1361-648x/ab549e

    work page doi:10.1088/1361-648x/ab549e 2019

  57. [57]

    Panda, A

    K. Panda, A. Bhattacharyya, D. T. Adroja, N. Kase, P. K. Biswas, S. Saha, T. Das, M. R. Lees, A. D. Hillier, Prob- ing the superconducting ground state of ZrIrSi: A muon spin rotation and relaxation study, Physical Review B 99 (17) (2019) 174513. doi:10.1103/physrevb.99.174513. URLhttps://doi.org/10.1103/physrevb.99.174513

    work page doi:10.1103/physrevb.99.174513 2019

  58. [58]

    Y . J. Uemura, G. M. Luke, B. J. Sternlieb, J. H. Brewer, J. F. Carolan, W. N. Hardy, R. Kadono, J. R. Kempton, R. F. Kiefl, S. R. Kreitzman, P. Mulhern, T. M. Riseman, D. L. Williams, B. X. Yang, S. Uchida, H. Takagi, J. Gopalakrishnan, A. W. Sleight, M. A. Subramanian, C. L. Chien, M. Z. Cieplak, G. Xiao, V . Y . Lee, B. W. Statt, C. E. Stronach, W. J. ...

    work page doi:10.1103/physrevlett.62.2317 1989

  59. [59]

    A. D. Hillier, R. Cywinski, The classification of supercon- ductors using muon spin rotation, Applied Magnetic Res- onance 13 (1-2) (1997) 95–109. doi:10.1007/bf03161973. URLhttps://doi.org/10.1007/bf03161973 13

    work page doi:10.1007/bf03161973 1997