# Magnetic substitution and superconductivity

Separate carrier, structural, scattering and exchange effects in magnetic substitutions, with dilute alloys, rare-earth borocarbides and reentrant nickelate evidence.

## Scope

Magnetic substitution can change carrier balance, crystal structure, potential scattering, spin-flip scattering and exchange fields at the same time. These effects are distinguishable experimental questions, not mutually exclusive channels. A falling superconducting transition temperature does not uniquely identify magnetic pair breaking, and the presence of a magnetic element does not establish magnetically mediated pairing. Compare actual composition, valence, phase purity and preparation before treating concentration as a single physical control. [R3](#ref-source-8d0e592da8ec9c7b) [R4](#ref-source-23c62b46f5681d83) [R5](#ref-source-9ff1d5edeb007a39) [R11](#ref-source-3504ee9027165d0a)

Dilute paramagnetic impurities, an ordered rare-earth sublattice and a concentrated magnetic film are different physical regimes. Balatsky et al.'s review distinguishes dynamic impurity spins from the classical-spin limit. Its ensemble treatment neglects interactions between impurity spins and interference between different scatterers. Those assumptions cannot simply be carried over to an ordered magnetic lattice. The original AG paper remains a historical citation here; its full derivation has not been checked.

For a claim of magnetic–superconducting coexistence, separate three questions:

1. **Same sample?** Check composition, phase purity, field, temperature and the volume sampled by each probe. Two bulk signals alone leave spatial separation as a possibility.
2. **Coupled orders?** Seek a response of one ordered state to the other. In Yaron's ErNi2B2C experiment, the changing vortex orientation was also consistent with transverse magnetization. This supports a coupling-based argument for microscopic coexistence, beyond coincident transition anomalies.
3. **Which spatial scale?** Report what the measurement resolves. The authors retain longer-scale vortex-orientation variation as an explanation of rocking-curve broadening. Broadening alone does not identify microscopic pinning. Their experiment is not an atom-by-atom map or a calibrated superconducting volume-fraction measurement.

These are editorial criteria for comparing evidence, not a new model fit. Neither a magnetic element nor coexistence by itself establishes magnetic pairing, triplet pairing or a universal impurity threshold. [R1](#ref-source-daf8f301de81a726) [R2](#ref-source-3a528aeee1b7cf04) [R7](#ref-source-e4fdbfe063c34217) [R8](#ref-source-6666556b639390d7)

## Mathematical assumptions

For dilute, uncorrelated weak magnetic scattering in an isotropic singlet host, define a pair-breaking energy $\Gamma$ through $\ln(T_{c0}/T_c)=\psi[1/2+\Gamma/(2\pi k_BT_c)]-\psi(1/2)$. Here $T_{c0}$ is the corresponding clean-host transition, not necessarily the transition of the unsubstituted parent if substitution also changes its bands or interaction. With $g=\Gamma/(k_BT_{c0})$ and $t=T_c/T_{c0}$, this convention gives $dt/dg=-\pi/4$ initially and $g_c=\pi e^{-\gamma_E}/2\simeq0.882$. Scattering-rate conventions require explicit factors of $\hbar$; neither atomic fraction nor residual resistivity can be inserted directly as $\Gamma$. The equation convention has a scoped review-paper check, while the original AG full text remains unaudited. [R1](#ref-source-daf8f301de81a726) [R2](#ref-source-3a528aeee1b7cf04) [R4](#ref-source-23c62b46f5681d83)

An independent inversion illustrates the ambiguity. In units with $k_B=1$, prescribe an observed curve $T_c=1-0.6c$, where $c$ is a synthetic dimensionless control. Both a fixed clean-host scale $T_{c0}=1$ and a changing scale $T_{c0}=1-0.2c$ admit different positive $\Gamma(c)$ values that reproduce the same transitions. Five checked points demonstrate non-uniqueness; they are not alloy fits or concentration calibrations. Additional composition, band, magnetic and scattering measurements are needed to choose between such explanations. [R2](#ref-source-3a528aeee1b7cf04) [R3](#ref-source-8d0e592da8ec9c7b) [R4](#ref-source-23c62b46f5681d83)

For a free Eu2+ ion with $S=7/2$ and $g=2$, the saturated moment is $gS\mu_B=7\mu_B$, whereas the Curie effective moment is $g\sqrt{S(S+1)}\mu_B\simeq7.94\mu_B$. Neither specifies the sign or strength of the exchange field acting on conduction electrons. In a collinear compensation illustration, $B_{\mathrm{eff}}=B_{\mathrm{ext}}+B_{\mathrm{ex}}$ and opposite signed contributions can reduce Zeeman splitting. This does not eliminate the orbital action of the applied field. Local-moment size, exchange energy and magnetic induction have different units and roles. [R9](#ref-source-849f7f4f675464de) [R11](#ref-source-3504ee9027165d0a)

## Experimental criteria

Sugawara and Eguchi measured transition temperatures and critical fields magnetically in dilute La–Ce and La–Gd alloys. Their original abstract reports deviations from the AG Born-approximation result that depend on the exchange sign, interpreting them as evidence of Kondo effects. It also describes behavior characteristic of inhomogeneous type-II superconductors. This is a historical test of the theory's limits, not permission to assign one universal critical impurity fraction or transition-temperature slope to magnetic substitutions. [R5](#ref-source-9ff1d5edeb007a39)

Anderson's robustness argument for nonmagnetic disorder applies when appropriate time-reversed states, an essentially unchanged pairing interaction and density of states, and extended electronic states remain available. It is not immunity to arbitrary chemical substitution. Prozorov's controlled electron-irradiation study of a ruthenium-substituted iron arsenide illustrates why intra- and interband scattering, annealing and sample continuity matter. Nonmagnetic disorder can suppress sign-changing pairing, so comparing magnetic and nonmagnetic substitutions alone does not supply an independent singlet verdict. [R3](#ref-source-8d0e592da8ec9c7b) [R4](#ref-source-23c62b46f5681d83)

Cava established superconductivity in the LnNi2B2C family, including magnetic rare-earth members. Cho's cited paper then studied single-crystal ErNi2B2C specifically: transport and magnetization show a superconducting transition around 10.5 K, while the magnetic transition lies near 6 K. Its heat-capacity estimate is $5.85\pm0.15$ K. These are distinct probe-specific scales. The paper is not a systematic survey of all rare-earth ions, and changing the rare earth also changes crystal fields, structure and exchange. No universal free-ion-moment ranking follows. [R6](#ref-source-4a5af9d54dea74ba) [R7](#ref-source-e4fdbfe063c34217)

Yaron's small-angle neutron study provides a more direct coupling test. On a boron-11-enriched ErNi2B2C crystal, superconducting vortex diffraction and magnetic diffraction establish their relative orientations. Figure 1's vortex pattern is measured at 1.6 K and 4 kOe with field near the c axis; the magnetic comparison uses zero field and a different neutron wavelength. The measured vortex lines rotate away from the applied field as temperature falls, and their rocking curves broaden. These observations support microscopic coexistence through interaction between magnetic order and the vortex structure, rather than merely coincident bulk anomalies. [R8](#ref-source-6666556b639390d7)

The geometry matters: the applied field in that experiment was already tilted about 1.6 degrees from the c axis. The additional vortex rotation begins around 4 K and can approach one degree, whereas antiferromagnetic ordering occurs near 6 K. These temperatures should not be equated. The authors also consider long-distance orientation variation as an alternative contribution to rocking-curve broadening; width alone is not a unique measure of microscopic pinning or a demonstration of triplet pairing. [R8](#ref-source-6666556b639390d7)

Meul's Eu–Sn molybdenum chalcogenide work reports magnetic-field-induced superconductivity interpreted through exchange compensation. The checked original abstract supports that historical connection, but does not establish every numerical endpoint or the precise alloy composition used in earlier summaries. A compensation claim in another material needs its own signed exchange estimate, local-moment response, angle dependence and orbital constraints. Large upper critical fields or field-enhanced resistance drops alone are insufficient. [R9](#ref-source-849f7f4f675464de) [R10](#ref-source-d564bee026e788c7)

Yang's 2026 Sm/Ca/Eu infinite-layer nickelate study involves rare-earth substitution, fixed nominal Ca content and film reduction. In the checked later author version, SCE0.34 regains zero resistance at 2 K beyond 6.23 T; SCE0.32 does so at 3 K by 13.04 T. The inherited SCE0.36 / 0.3 K / 45 T tuple is not verified by the selected later-author-version panels: Extended Data Figure 9 labels SCE0.36 at 4.2 K and SCE0.40 at 0.3 K. It is withheld pending version and sample reconciliation. These are different samples and measurement temperatures, not a single transition curve. Compensation-like explanations remain under discussion; neither established uniform ferromagnetism nor triplet pairing follows from the reported reentrance alone. [R11](#ref-source-3504ee9027165d0a)

## Limits and disputes

The same substitution series may move a clean-host pairing scale, alter scattering and create an exchange contribution. An AG-looking fit cannot separate these without additional constraints. Conversely, a departure from simple AG behavior does not automatically prove unconventional pairing or exchange compensation. Complete scientific acceptance remains open: original AG and several classic full texts, final-version comparisons, calibration details and raw-data reanalysis remain unfinished. The numerical exercises check restricted inference and units, not a complete magnetic-alloy theory. [R1](#ref-source-daf8f301de81a726) [R2](#ref-source-3a528aeee1b7cf04) [R5](#ref-source-9ff1d5edeb007a39) [R7](#ref-source-e4fdbfe063c34217) [R10](#ref-source-d564bee026e788c7) [R11](#ref-source-3504ee9027165d0a)

## Discovery implications

Track chemical composition and valence alongside diffraction, magnetic response, transport and thermodynamics. Preserve the distinction between dilute moments, ordered sublattices and possible glassy or inhomogeneous behavior. Keep onset, midpoint, measured-zero, ordering and measurement temperatures separate. For compensation, constrain the electronic exchange field and its uncertainty independently; for coexistence, seek a probe of coupling or spatial overlap. Use those measurements to distinguish explanations before extrapolating a concentration trend to a new material. [R4](#ref-source-23c62b46f5681d83) [R5](#ref-source-9ff1d5edeb007a39) [R7](#ref-source-e4fdbfe063c34217) [R8](#ref-source-6666556b639390d7) [R11](#ref-source-3504ee9027165d0a)

## Related topics

[Disorder and impurities](/scwiki/disorder-and-impurities), [Chemical substitution](/scwiki/chemical-doping), [Magnetism and superconductivity](/scwiki/ferromagnetism-and-superconductivity), [Exchange compensation](/scwiki/jaccarino-peter-effect), and [Reentrant superconductivity](/scwiki/reentrant-superconductivity).

## Material cases

Values describe individual reports, not a ranking. Unknown means the checked source did not supply the field at this review scope.

| Material and sample | Reported temperature | Criterion | Probe | Pressure | State | Evidence |
|---|---|---|---|---|---|---|
| ErNi2B2C (aliases: erbium nickel borocarbide); Yaron1996 boron11-enriched single crystal,Figure1 vortex diffraction at4kOe near c axis | 1.6 K; SANS measurement temperature, not superconducting transition. Magnetic comparison at zero field uses a different neutron wavelength. | measurement; vortex-diffraction | Small-angle neutron scattering | ambient; unknown GPa | unknown | experiment; [source](#ref-source-6666556b639390d7) |
| Sm0.61Ca0.05Eu0.34NiO2 (aliases: SCE0.34, Eu-doped Sm Ca nickelate); Yang2026 SCE0.34 film; reentrant zero resistance beyond6.23T at2K | 2 K; Fixed-temperature field sweep, not Tc or a universal composition/field relation. | measurement; field-sweep-zero-resistance | Film magnetotransport | ambient; unknown GPa | unknown | experiment; [source](#ref-source-3504ee9027165d0a) |

## Sources

### Ref source-daf8f301de81a726

[R1] Contribution to the theory of superconducting alloys with paramagnetic impurities (1961). [Source publication](https://www.itp.ac.ru/en/persons/abrikosov-alexey-alekseevich/). Publication: journal-article. Check: historical-bibliographic-anchor-only. Checked: 2026-10-18. Soviet Physics JETP12,1243–1253; Russian original39,1781–1796(1960). No DOI asserted. Attempted archive PDFs404; original full text not retrieved. Displayed convention checked separately in Balatsky author manuscript and bounded local calculations.
### Ref source-3a528aeee1b7cf04

[R2] Impurity-induced states in conventional and unconventional superconductors (2006). [DOI 10.1103/RevModPhys.78.373](https://doi.org/10.1103/RevModPhys.78.373). Publication: journal-article. Check: selected-author-equation-conventions. Checked: 2026-10-20. Authorv1 submitted11November2004; selected sectionsVI andXIV,pp13–14 and40–41 read. p14 Eq6.8–6.15 and p40 Eq14.12–14.13 visually checked. This is a review, not a substitute for the unavailable original AG/Shiba derivations. Final-version comparison remains open. Additional selected pp. 11 and 39–40 read; pp. 11 and 39 visually inspected. Spin dynamics, classical-spin limit and neglected inter-impurity interactions/interference define model limits. This review is not independent primary experimental evidence.
### Ref source-8d0e592da8ec9c7b

[R3] Theory of dirty superconductors (1959). [DOI 10.1016/0022-3697(59)90036-8](https://doi.org/10.1016/0022-3697(59)90036-8). Publication: journal-article. Check: selected-original-scan-reread. Checked: 2026-10-18. Original journal pp26 and29 visually re-read: exact time-reversed states, chemical changes/DOS and anisotropy. Complete derivation and localization corrections not independently reviewed.
### Ref source-23c62b46f5681d83

[R4] Effect of electron irradiation on superconductivity in single crystals of Ba(Fe1-xRux)2As2 (x=0.24) (2014). [DOI 10.1103/PhysRevX.4.041032](https://doi.org/10.1103/PhysRevX.4.041032). Publication: journal-article. Check: selected-author-methods-and-figures. Checked: 2026-10-18. Authorv1 dated13May2014; selectedpp1–4 methods,annealing,Figs1–3 andmultiband discussion read; p3 Figs1–2 visually checked. Tc0 methods17.8K versus transportfigure17.85K retained; exact operational threshold not established. Final APS PDF403; completefinalcomparison/rawdata remain open.
### Ref source-9ff1d5edeb007a39

[R5] Paramagnetic Impurity Effect in Dilute Superconducting La-Alloys (1967). [DOI 10.1143/JPSJ.23.965](https://doi.org/10.1143/JPSJ.23.965). Publication: journal-article. Check: publisher-original-abstract-and-date. Checked: 2026-10-19. Published 5 November 1967, not the 2007 digital release. Magnetic-method La–Ce/La–Gd transitions and critical fields; deviations from AG Born approximation depend on exchange sign, interpreted as Kondo physics. Inhomogeneous type-II behavior reported. Full methods and concentration calibration not read.
### Ref source-4a5af9d54dea74ba

[R6] Superconductivity in the quaternary intermetallic compounds LnNi2B2C (1994). [DOI 10.1038/367252a0](https://doi.org/10.1038/367252a0). Publication: journal-article. Check: indexed-publisher-original-abstract. Checked: 2026-10-19. Published 20 January 1994. Ln=Y,Tm,Er,Ho,Lu family established. Distinguishes unidentified superconducting phase in earlier Y–Pd–B–C work from identified LnNi2B2C compounds. No full methods or per-member numerical criteria checked.
### Ref source-e4fdbfe063c34217

[R7] Magnetism and superconductivity in single-crystal ErNi2B2C (1995). [DOI 10.1103/PhysRevB.52.3684](https://doi.org/10.1103/PhysRevB.52.3684). Publication: journal-article. Check: publisher-original-abstract-and-material-scope. Checked: 2026-10-19. Published 1 August 1995. Cho et al. study ErNi2B2C, not a complete rare-earth series. Transport/magnetization transition10.5K; heat-capacity magnetic anomaly5.85±0.15K versus6K magnetic/transport scale. Numerical superconducting operational threshold and full methods not read.
### Ref source-6666556b639390d7

[R8] Microscopic coexistence of magnetism and superconductivity in ErNi2B2C (1996). [DOI 10.1038/382236a0](https://doi.org/10.1038/382236a0). Publication: journal-article. Check: selected-final-SANS-methods-and-figures. Checked: 2026-10-20. Yaron et al.,18July1996. Selected journal pp236–238 methods/results; pp237–238 Figures1–3 visually checked. Boron11 crystal, field near c/incident beam,4kOe and1.6K Figure1; magnetic peaks measured at zero field with a separate neutron wavelength. Field tilted1.6degrees from c; vortex rotation develops near4K and can reach1degree. Rocking-curve width may reflect long-scale orientation variations, not uniquely microscopic pinning. Complete raw-data/reflection fit and phase-diagram reconstruction open. Final pp. 237–238 re-read and visually checked: transverse magnetization agrees with the inferred vortex rotation; longer-scale orientation variation remains an alternative to microscopic pinning. No calibrated coexistence volume fraction or real-space atomic map extracted.
### Ref source-849f7f4f675464de

[R9] Ultra-High-Field Superconductivity (1962). [DOI 10.1103/PhysRevLett.9.290](https://doi.org/10.1103/PhysRevLett.9.290). Publication: journal-article. Check: publisher-identity-only. Checked: 2026-10-18. Published1October1962. Original identity verified; full text unavailable. Independent field-budget illustration is not a reproduction of the original derivation.
### Ref source-d564bee026e788c7

[R10] Observation of Magnetic-Field-Induced Superconductivity (1984). [DOI 10.1103/PhysRevLett.53.497](https://doi.org/10.1103/PhysRevLett.53.497). Publication: journal-article. Check: original-publisher-abstract. Checked: 2026-10-18. Published30July1984. Original abstract confirms Eu-Sn molybdenum chalcogenide family and compensation interpretation. Exact composition, curves and full methods not checked.
### Ref source-3504ee9027165d0a

[R11] Field re-entrant superconductivity in Eu-doped infinite-layer nickelates (2026). [DOI 10.1038/s41586-026-10547-y](https://doi.org/10.1038/s41586-026-10547-y). Publication: journal-article. Check: selected-author-text-and-figures. Checked: 2026-10-18. Published23April2026; read authorv3 dated25April2026, selectedpp2–8, captionsp12, methodsp13–14; Fig2p19/Fig3p20 visually checked. Full final equivalence, calibration and all raw data remain open.

## Claim evidence and conditions

### scwiki-d15-claim-scope-1

Magnetic substitution can change carrier balance, crystal structure, potential scattering, spin-flip scattering and exchange fields at the same time. These effects are distinguishable experimental questions, not mutually exclusive channels. A falling superconducting transition temperature does not uniquely identify magnetic pair breaking, and the presence of a magnetic element does not establish magnetically mediated pairing. Compare actual composition, valence, phase purity and preparation before treating concentration as a single physical control.

Evidence: hypothesis. Sources: source-8d0e592da8ec9c7b, source-23c62b46f5681d83, source-9ff1d5edeb007a39, source-3504ee9027165d0a.

Conditions: Preserve composition, valence, sample, field direction, probe and temperature type; scattering energy is not nominal concentration.

Verification scope: Named primary passages/figures and restricted inference checks; full scientific acceptance remains open.

### scwiki-d15-claim-scope-2

Dilute paramagnetic impurities, an ordered rare-earth sublattice and a concentrated magnetic film are different physical regimes. Balatsky et al.'s review distinguishes dynamic impurity spins from the classical-spin limit. Its ensemble treatment neglects interactions between impurity spins and interference between different scatterers. Those assumptions cannot simply be carried over to an ordered magnetic lattice. The original AG paper remains a historical citation here; its full derivation has not been checked.

For a claim of magnetic–superconducting coexistence, separate three questions:

1. **Same sample?** Check composition, phase purity, field, temperature and the volume sampled by each probe. Two bulk signals alone leave spatial separation as a possibility.
2. **Coupled orders?** Seek a response of one ordered state to the other. In Yaron's ErNi2B2C experiment, the changing vortex orientation was also consistent with transverse magnetization. This supports a coupling-based argument for microscopic coexistence, beyond coincident transition anomalies.
3. **Which spatial scale?** Report what the measurement resolves. The authors retain longer-scale vortex-orientation variation as an explanation of rocking-curve broadening. Broadening alone does not identify microscopic pinning. Their experiment is not an atom-by-atom map or a calibrated superconducting volume-fraction measurement.

These are editorial criteria for comparing evidence, not a new model fit. Neither a magnetic element nor coexistence by itself establishes magnetic pairing, triplet pairing or a universal impurity threshold.

Evidence: editorial-analysis. Sources: source-daf8f301de81a726, source-3a528aeee1b7cf04, source-e4fdbfe063c34217, source-6666556b639390d7.

Source relationship: context-for-editorial-analysis. Editorial comparison of impurity-model assumptions and the original ErNi2B2C coupling experiment. Balatsky author v1 pp. 11 and 39–40 provide review context; Yaron final pp. 237–238 provide measured vortex/magnetization evidence and the length-scale caveat. The original AG derivation and full Cho paper remain unchecked.

Conditions: Distinguish isolated or uncorrelated impurity spins from an ordered sublattice. Match sample, field, temperature, probe volume and spatial resolution before inferring coexistence. Coupling evidence is not a measured universal volume fraction or pairing symmetry.

Verification scope: Selected review pages and original Yaron final pp. 236–238; four selected source pages visually inspected this round. No raw neutron-data fit, complete microscopic model, calibrated volume fraction or independent scientific review.

### scwiki-d15-claim-mathematical-assumptions-1

For dilute, uncorrelated weak magnetic scattering in an isotropic singlet host, define a pair-breaking energy $\Gamma$ through $\ln(T_{c0}/T_c)=\psi[1/2+\Gamma/(2\pi k_BT_c)]-\psi(1/2)$. Here $T_{c0}$ is the corresponding clean-host transition, not necessarily the transition of the unsubstituted parent if substitution also changes its bands or interaction. With $g=\Gamma/(k_BT_{c0})$ and $t=T_c/T_{c0}$, this convention gives $dt/dg=-\pi/4$ initially and $g_c=\pi e^{-\gamma_E}/2\simeq0.882$. Scattering-rate conventions require explicit factors of $\hbar$; neither atomic fraction nor residual resistivity can be inserted directly as $\Gamma$. The equation convention has a scoped review-paper check, while the original AG full text remains unaudited.

Evidence: theory. Sources: source-daf8f301de81a726, source-3a528aeee1b7cf04, source-23c62b46f5681d83.

Conditions: Preserve composition, valence, sample, field direction, probe and temperature type; scattering energy is not nominal concentration.

Verification scope: Named primary passages/figures and restricted inference checks; full scientific acceptance remains open.

### scwiki-d15-claim-mathematical-assumptions-2

An independent inversion illustrates the ambiguity. In units with $k_B=1$, prescribe an observed curve $T_c=1-0.6c$, where $c$ is a synthetic dimensionless control. Both a fixed clean-host scale $T_{c0}=1$ and a changing scale $T_{c0}=1-0.2c$ admit different positive $\Gamma(c)$ values that reproduce the same transitions. Five checked points demonstrate non-uniqueness; they are not alloy fits or concentration calibrations. Additional composition, band, magnetic and scattering measurements are needed to choose between such explanations.

Evidence: theory. Sources: source-3a528aeee1b7cf04, source-8d0e592da8ec9c7b, source-23c62b46f5681d83.

Conditions: Preserve composition, valence, sample, field direction, probe and temperature type; scattering energy is not nominal concentration.

Verification scope: Named primary passages/figures and restricted inference checks; full scientific acceptance remains open.

### scwiki-d15-claim-mathematical-assumptions-3

For a free Eu2+ ion with $S=7/2$ and $g=2$, the saturated moment is $gS\mu_B=7\mu_B$, whereas the Curie effective moment is $g\sqrt{S(S+1)}\mu_B\simeq7.94\mu_B$. Neither specifies the sign or strength of the exchange field acting on conduction electrons. In a collinear compensation illustration, $B_{\mathrm{eff}}=B_{\mathrm{ext}}+B_{\mathrm{ex}}$ and opposite signed contributions can reduce Zeeman splitting. This does not eliminate the orbital action of the applied field. Local-moment size, exchange energy and magnetic induction have different units and roles.

Evidence: theory. Sources: source-849f7f4f675464de, source-3504ee9027165d0a.

Conditions: Preserve composition, valence, sample, field direction, probe and temperature type; scattering energy is not nominal concentration.

Verification scope: Named primary passages/figures and restricted inference checks; full scientific acceptance remains open.

### scwiki-d15-claim-experimental-criteria-1

Sugawara and Eguchi measured transition temperatures and critical fields magnetically in dilute La–Ce and La–Gd alloys. Their original abstract reports deviations from the AG Born-approximation result that depend on the exchange sign, interpreting them as evidence of Kondo effects. It also describes behavior characteristic of inhomogeneous type-II superconductors. This is a historical test of the theory's limits, not permission to assign one universal critical impurity fraction or transition-temperature slope to magnetic substitutions.

Evidence: experiment. Sources: source-9ff1d5edeb007a39.

Conditions: Preserve composition, valence, sample, field direction, probe and temperature type; scattering energy is not nominal concentration.

Verification scope: Named primary passages/figures and restricted inference checks; full scientific acceptance remains open.

### scwiki-d15-claim-experimental-criteria-2

Anderson's robustness argument for nonmagnetic disorder applies when appropriate time-reversed states, an essentially unchanged pairing interaction and density of states, and extended electronic states remain available. It is not immunity to arbitrary chemical substitution. Prozorov's controlled electron-irradiation study of a ruthenium-substituted iron arsenide illustrates why intra- and interband scattering, annealing and sample continuity matter. Nonmagnetic disorder can suppress sign-changing pairing, so comparing magnetic and nonmagnetic substitutions alone does not supply an independent singlet verdict.

Evidence: experiment. Sources: source-8d0e592da8ec9c7b, source-23c62b46f5681d83.

Conditions: Preserve composition, valence, sample, field direction, probe and temperature type; scattering energy is not nominal concentration.

Verification scope: Named primary passages/figures and restricted inference checks; full scientific acceptance remains open.

### scwiki-d15-claim-experimental-criteria-3

Cava established superconductivity in the LnNi2B2C family, including magnetic rare-earth members. Cho's cited paper then studied single-crystal ErNi2B2C specifically: transport and magnetization show a superconducting transition around 10.5 K, while the magnetic transition lies near 6 K. Its heat-capacity estimate is $5.85\pm0.15$ K. These are distinct probe-specific scales. The paper is not a systematic survey of all rare-earth ions, and changing the rare earth also changes crystal fields, structure and exchange. No universal free-ion-moment ranking follows.

Evidence: experiment. Sources: source-4a5af9d54dea74ba, source-e4fdbfe063c34217.

Conditions: Preserve composition, valence, sample, field direction, probe and temperature type; scattering energy is not nominal concentration.

Verification scope: Named primary passages/figures and restricted inference checks; full scientific acceptance remains open.

### scwiki-d15-claim-experimental-criteria-4

Yaron's small-angle neutron study provides a more direct coupling test. On a boron-11-enriched ErNi2B2C crystal, superconducting vortex diffraction and magnetic diffraction establish their relative orientations. Figure 1's vortex pattern is measured at 1.6 K and 4 kOe with field near the c axis; the magnetic comparison uses zero field and a different neutron wavelength. The measured vortex lines rotate away from the applied field as temperature falls, and their rocking curves broaden. These observations support microscopic coexistence through interaction between magnetic order and the vortex structure, rather than merely coincident bulk anomalies.

Evidence: experiment. Sources: source-6666556b639390d7.

Conditions: Preserve composition, valence, sample, field direction, probe and temperature type; scattering energy is not nominal concentration.

Verification scope: Named primary passages/figures and restricted inference checks; full scientific acceptance remains open.

### scwiki-d15-claim-experimental-criteria-5

The geometry matters: the applied field in that experiment was already tilted about 1.6 degrees from the c axis. The additional vortex rotation begins around 4 K and can approach one degree, whereas antiferromagnetic ordering occurs near 6 K. These temperatures should not be equated. The authors also consider long-distance orientation variation as an alternative contribution to rocking-curve broadening; width alone is not a unique measure of microscopic pinning or a demonstration of triplet pairing.

Evidence: experiment. Sources: source-6666556b639390d7.

Conditions: Preserve composition, valence, sample, field direction, probe and temperature type; scattering energy is not nominal concentration.

Verification scope: Named primary passages/figures and restricted inference checks; full scientific acceptance remains open.

### scwiki-d15-claim-experimental-criteria-6

Meul's Eu–Sn molybdenum chalcogenide work reports magnetic-field-induced superconductivity interpreted through exchange compensation. The checked original abstract supports that historical connection, but does not establish every numerical endpoint or the precise alloy composition used in earlier summaries. A compensation claim in another material needs its own signed exchange estimate, local-moment response, angle dependence and orbital constraints. Large upper critical fields or field-enhanced resistance drops alone are insufficient.

Evidence: experiment. Sources: source-849f7f4f675464de, source-d564bee026e788c7.

Conditions: Preserve composition, valence, sample, field direction, probe and temperature type; scattering energy is not nominal concentration.

Verification scope: Named primary passages/figures and restricted inference checks; full scientific acceptance remains open.

### scwiki-d15-claim-experimental-criteria-7

Yang's 2026 Sm/Ca/Eu infinite-layer nickelate study involves rare-earth substitution, fixed nominal Ca content and film reduction. In the checked later author version, SCE0.34 regains zero resistance at 2 K beyond 6.23 T; SCE0.32 does so at 3 K by 13.04 T. The inherited SCE0.36 / 0.3 K / 45 T tuple is not verified by the selected later-author-version panels: Extended Data Figure 9 labels SCE0.36 at 4.2 K and SCE0.40 at 0.3 K. It is withheld pending version and sample reconciliation. These are different samples and measurement temperatures, not a single transition curve. Compensation-like explanations remain under discussion; neither established uniform ferromagnetism nor triplet pairing follows from the reported reentrance alone.

Evidence: experiment. Sources: source-3504ee9027165d0a.

Conditions: Preserve composition, valence, sample, field direction, probe and temperature type; scattering energy is not nominal concentration.

Verification scope: Named primary passages/figures and restricted inference checks; full scientific acceptance remains open.

### scwiki-d15-claim-limits-and-disputes-1

The same substitution series may move a clean-host pairing scale, alter scattering and create an exchange contribution. An AG-looking fit cannot separate these without additional constraints. Conversely, a departure from simple AG behavior does not automatically prove unconventional pairing or exchange compensation. Complete scientific acceptance remains open: original AG and several classic full texts, final-version comparisons, calibration details and raw-data reanalysis remain unfinished. The numerical exercises check restricted inference and units, not a complete magnetic-alloy theory.

Evidence: hypothesis. Sources: source-daf8f301de81a726, source-3a528aeee1b7cf04, source-9ff1d5edeb007a39, source-e4fdbfe063c34217, source-d564bee026e788c7, source-3504ee9027165d0a.

Conditions: Preserve composition, valence, sample, field direction, probe and temperature type; scattering energy is not nominal concentration.

Verification scope: Named primary passages/figures and restricted inference checks; full scientific acceptance remains open.

### scwiki-d15-claim-discovery-implications-1

Track chemical composition and valence alongside diffraction, magnetic response, transport and thermodynamics. Preserve the distinction between dilute moments, ordered sublattices and possible glassy or inhomogeneous behavior. Keep onset, midpoint, measured-zero, ordering and measurement temperatures separate. For compensation, constrain the electronic exchange field and its uncertainty independently; for coexistence, seek a probe of coupling or spatial overlap. Use those measurements to distinguish explanations before extrapolating a concentration trend to a new material.

Evidence: hypothesis. Sources: source-23c62b46f5681d83, source-9ff1d5edeb007a39, source-e4fdbfe063c34217, source-6666556b639390d7, source-3504ee9027165d0a.

Conditions: Preserve composition, valence, sample, field direction, probe and temperature type; scattering energy is not nominal concentration.

Verification scope: Named primary passages/figures and restricted inference checks; full scientific acceptance remains open.

## Revision and review

Article ID: scwiki-d15. Revision: ba44b2099834049df4b1. Updated: 2026-10-19T17:49:19.830223+00:00.

Review scope: Selected Yaron final methods and Figures1–3; Sugawara,Cava,Cho original abstracts; inherited E7/G5 evidence scopes; five matched-transition counterexamples and free-ion moment distinction. Yang v3 selected passages and Figures 2, 3, Extended Data 9 checked; inherited 45 T tuple withheld. Follow-up: impurity-ensemble assumptions and coexistence evidence organized by sample, coupling and length scale; explicit editorial-analysis role.

- Complete scientific acceptance remains open.
- Original AG and several classic full texts remain unaudited; review-paper equation conventions are identified separately.
- Final-version, concentration calibration, raw-data and film magnetic-order acceptance remain open.
- Synthetic transition inversions do not reproduce any alloy or determine a material mechanism.

Source: [D_material_families/D15_magnetic_doping.md](https://github.com/JackZH26/jzis-superconductivity/blob/0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf/D_material_families/D15_magnetic_doping.md), commit 0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf, SHA-256 01fe5565239482cc994114a6ff1bba4bfac1093006441b75d70130723167bbaa.