# Magnetic field: pair breaking, phase boundaries and re-entrant states

Separate orbital and Zeeman references from measured field-angle phase boundaries, and distinguish finite-momentum candidates from direct evidence.

## Scope

Magnetic field is both a control parameter and a probe of superconductivity. Orbital currents, Zeeman splitting, vortex motion and changes in the magnetic background can produce different boundaries. A resistive onset, loss of zero resistance, heat-capacity anomaly and magnetic transition need not coincide. Retain temperature, crystal orientation, sample history, sweep direction and pulse conditions when comparing field scales. [R1](#ref-source-7ba854cc57960377) [R5](#ref-source-a626e7fcb17b94fa) [R7](#ref-source-0c4d7cebb12a0d5b)

This article uses $B$ in tesla for the field scale; experimental papers often label that axis $H$ while reporting tesla, meaning an applied $\mu_0H$ scale. Converting an applied field to local induction requires the magnetization and demagnetizing geometry. Neither an unusually large upper critical field nor field-induced superconductivity alone identifies a pairing symmetry. [R2](#ref-source-16926b3817cff55d) [R7](#ref-source-0c4d7cebb12a0d5b) [R10](#ref-source-b717fb1db41e9f29)

## Mathematical assumptions

For a weak-coupling singlet reference with Zeeman levels shifted by $\pm g\mu_B B/2$, zero residual superconducting spin susceptibility and no orbital cost, condensation-energy balance gives $B_P=\sqrt{2}\Delta_0/(g\mu_B)$. Using $\Delta_0=\pi e^{-\gamma_E}k_BT_c$ and $g=2$ gives about $1.86\,T_c$ tesla when $T_c$ is in kelvin. This is a conditional reference, not a universal upper bound. Spin-orbit coupling, anisotropic spin response and strong coupling change the comparison. Clogston's historical identity is retained; its complete original derivation was not retrieved here. [R9](#ref-source-d32df19524b2a1c8) [R10](#ref-source-b717fb1db41e9f29)

A second restricted reference is the dirty, single-band, purely orbital result $B_{c2}^{\rm orb}(0)\simeq0.693\,T_c|dB_{c2}/dT|_{T_c}$. Gurevich's final paper recovers it when the two diffusivities are equal. The near-transition slope must refer to the same field orientation and criterion being extrapolated. Its Eq. (31) defines $U(x)=\psi(1/2+x)-\psi(1/2)$, satisfying $U(0)=0$. The early author v1 prints a plus sign at that location; use the final definition. For clarity, let $t=T/T_c$, $s=|dB_{c2}/dT|_{T_c}$ and $b=B_{c2}/(T_cs)$. The restricted equation is $\ln t+U(2b/(\pi^2t))=0$. Its limits are $b\simeq1-t$ near $t=1$ and $b(0)=\pi^2e^{-\gamma_E}/8\simeq0.6927$. Our local solution gives $b(0.5)\simeq0.4505$, checked against an independent integral representation. These are dimensionless model values, not measured tesla. Unequal diffusivities produce different curves. This calculation does not validate a full WHH fit with Zeeman and spin-orbit terms, or a multiband fit to a particular material. [R1](#ref-source-7ba854cc57960377) [R2](#ref-source-16926b3817cff55d)

The Maki parameter compares those reference scales, $\alpha_M=\sqrt{2}B_{c2}^{\rm orb}(0)/B_P$; it is not by itself an FFLO detection criterion. In a parabolic band with small splitting, the Fermi-wavevector mismatch is $\delta k\simeq g\mu_B B/(\hbar v_F)$. The inherited expression contains an extra factor of two under the stated Zeeman convention. This kinematic estimate does not solve for the optimum finite-momentum pair wavevector or establish the stability of a Fulde–Ferrell–Larkin–Ovchinnikov state. Disorder, orbital effects, dimensionality and competing orders matter. Bianchi's author v1 writes its parameter as $H_{c2}^{0}/H_P$, without the $\sqrt{2}$ used in this page's definition; a numerical threshold must not be moved between those conventions without reconciliation. This identifies a source-convention difference, not a verified correction to the final paper. [R3](#ref-source-a1695d99aaf064c8) [R5](#ref-source-a626e7fcb17b94fa)

## Experimental criteria

Petrovic's discovery report describes zero resistance and full diamagnetic shielding at approximately 2.3 K in CeCoIn5. Its field–temperature paragraph compares specific heat with zero resistance for field along the c-axis. That zero-field transition is distinct from lower-temperature anomalies inside the superconducting phase. The same report finds an upper-critical-field anisotropy of at least two from additional transverse-field transport measurements, so one orientation cannot stand in for every field direction. It also cautions that a temperature-dependent normal-state heat-capacity coefficient complicates a simple weak-versus-strong-coupling inference from the jump size. [R4](#ref-source-5962cf8038597944)

Bianchi's selected author-manuscript passages describe heat-pulse and temperature-decay calorimetry, including subtraction of the In/Co nuclear Schottky contribution. Figure 1 uses different vertical quantities in its panels: $(C-C_{\rm Sch})/T$ and $C$, with a $C/T$ inset. Equal-entropy construction concerns the integral of $C/T$, not equal areas under an unconverted $C$ curve. At high in-plane fields the report finds a first-order upper boundary and an internal anomaly around 0.3 K. These are not new zero-field transition temperatures. Figure 3c reports entropy gain starting at 0.13 K, not absolute entropy measured down to zero. The first-order-boundary evidence includes heating/cooling hysteresis in the [100] scans at 11.2 and 11.4 T; the 1.1 ± 0.1 K order-change temperature refers to [110]. These orientations and thermal paths must accompany the values. Its final title explicitly says “Possible” FFLO state; calorimetry does not directly measure pair momentum. [R5](#ref-source-a626e7fcb17b94fa)

The later Kenzelmann neutron-scattering report finds magnetic order coupled to superconductivity in this high-field region. Its symmetry interpretation suggests a modulated superconducting state, while the observed magnetic order does not alone reconstruct the spatial pair field. This article checked that paper's original abstract, not its complete neutron methods or supplementary analysis. [R6](#ref-source-fda01ade7737b638)

Lewin's UTe2 experiments combine pulsed-field resistance and proximity-detector-oscillator measurements. Typical pulses reached 60 T or, in a different magnet, 73 T; the common measurement temperature was about 0.63 K. The high-field zero-resistance region depends strongly on both field angles. The oscillator frequency is a conductivity-sensitive proxy, and a comparison at 2.09 K without the superconducting feature is a normal-state measurement, not a 2.09 K transition determination. Four specimens contribute resistance or oscillator data, and the authors discuss sample dependence and possible field-induced heating. The angular map is symmetrized for visualization. At the source's $\theta_{bc}=8^\circ$ setting the oscillator feature persists to the 73 T magnet ceiling; continuation above that ceiling is inferred from its trend, not directly measured. In the ab plane, non-observation within the available field window does not exclude a higher-field onset. A measured field extent is not necessarily an observed upper critical field. [R7](#ref-source-0c4d7cebb12a0d5b)

Zambra's April 2026 study measures magnetotropic response at 4 K, where the superconducting phases are suppressed. Its Figure 1 separately reproduces a 300 mK superconducting phase diagram and 1.4 K magnetization from earlier work. These temperatures must not be merged into a claim of superconductivity at 4 K. “Transverse” refers to response perpendicular to the static field, not automatically an off-diagonal susceptibility element. The final article number is 3742, correcting the inherited 3814. [R8](#ref-source-15cfc4a2f9587af0)


Use this guide to keep the provenance of each number visible when comparing field-dependent results.

| Evidence and source | Temperature or construction | What the value does not establish |
|---|---|---|
| Petrovic CeCoIn5 [R4](#ref-source-5962cf8038597944) | Approximately 2.3 K zero resistance and shielding; c-axis field comparison | A universal, orientation-independent upper critical field |
| Bianchi CeCoIn5 [R5](#ref-source-a626e7fcb17b94fa) | About 0.3 K internal anomaly; 1.1 ± 0.1 K order-change scale for [110] | Two additional zero-field transition temperatures or direct pair momentum |
| Bianchi entropy comparison [R5](#ref-source-a626e7fcb17b94fa) | Integral of C/T referenced to 0.13 K | Absolute entropy or equal-area construction on raw C |
| Lewin UTe2 [R7](#ref-source-0c4d7cebb12a0d5b) | 0.63 K typical measurement / 0.64 K PDO example; 2.09 K normal comparison | A Tc determined from the temperature held during a field pulse |
| Zambra UTe2 [R8](#ref-source-15cfc4a2f9587af0) | 4 K response; separate borrowed 300 mK phase diagram and 1.4 K magnetization | Superconductivity established at 4 K |

## Limits and disputes

Magnetotropic susceptibility, an angular derivative of torque measured through a cantilever frequency shift, probes a different response from longitudinal magnetization. Zambra's long-wavelength result supports an inference of enhanced transverse ferromagnetic fluctuations; it does not measure a complete frequency-dependent pairing interaction. Values below 15 T in one normalized color map were set to zero to suppress amplified noise, rather than demonstrating a physically vanishing susceptibility. Alignment and calibration details remain relevant to comparisons with phase boundaries. [R8](#ref-source-15cfc4a2f9587af0)

Keep measured phenomena separate from candidate explanations. A heat-capacity anomaly, magnetic Q phase and proposed FFLO modulation are distinct statements. Likewise, the multicomponent triplet model discussed for the UTe2 field-angle halo is an interpretation, not a direct determination of topology. Selected original passages and figures were checked here; remaining final-version comparisons, full supplements, raw-data reproduction and complete scientific acceptance remain open. [R5](#ref-source-a626e7fcb17b94fa) [R6](#ref-source-fda01ade7737b638) [R7](#ref-source-0c4d7cebb12a0d5b)

## Discovery implications

Construct a field–temperature–angle map with explicit criteria and uncertainties. Compare transport with thermodynamic or magnetic probes where possible, retain pulsed-field heating and alignment controls, and distinguish re-entrant regions from a simple monotonic critical field. The local equation checks verify declared Zeeman conventions, an orbital asymptote and an illustrative entropy construction. They do not establish a new superconducting phase, fit an experimental boundary or certify a universal pairing mechanism. [R1](#ref-source-7ba854cc57960377) [R5](#ref-source-a626e7fcb17b94fa) [R7](#ref-source-0c4d7cebb12a0d5b) [R8](#ref-source-15cfc4a2f9587af0)

## Related topics

Compare [critical fields](/scwiki/critical-fields), [pair-density waves](/scwiki/pair-density-wave), [heavy-fermion superconductors](/scwiki/heavy-fermion-superconductors), [electrostatic gating](/scwiki/electrostatic-gating) and [strain tuning](/scwiki/strain).

## 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 |
|---|---|---|---|---|---|---|
| CeCoIn5 (aliases: heavy fermion, heavy fermions); Petrovic zero-field discovery sample | 2.3 K; Approximate zero-resistance/full-shielding scale, distinct from high-field internal anomalies. Thermodynamic equilibrium is not established by this scoped source review. | transition; zero-resistance | Resistivity with accompanying diamagnetic shielding | ambient; unknown GPa | unknown | experiment; [source](#ref-source-5962cf8038597944) |
| CeCoIn5 (aliases: heavy fermion, heavy fermions); Bianchi high in-plane field internal anomaly | 0.3 K; Approximate internal superconducting-phase anomaly; not onset from normal state or a new zero-field Tc. Thermodynamic equilibrium is not established by this scoped source review. | measurement; internal-phase-anomaly | Specific heat | ambient; unknown GPa | unknown | experiment; [source](#ref-source-a626e7fcb17b94fa) |
| CeCoIn5 (aliases: heavy fermion, heavy fermions); Bianchi field along [110] first/second-order crossover | 1.1 K; Reported T0=1.1+/-0.1K at change of boundary order, not independent zero-field Tc. Thermodynamic equilibrium is not established by this scoped source review. | measurement; transition-order-crossover | Specific heat | ambient; unknown GPa | unknown | experiment; [source](#ref-source-a626e7fcb17b94fa) |
| UTe2 (aliases: heavy fermion, heavy fermions); Lewin typical pulsed-field measurement | 0.63 K; Typical measurement temperature unless otherwise stated; no Tc assigned from temperature held during field sweep. Thermodynamic equilibrium is not established by this scoped source review. | measurement; pulsed-field-measurement | Resistance | ambient; unknown GPa | unknown | experiment; [source](#ref-source-0c4d7cebb12a0d5b) |
| UTe2 (aliases: heavy fermion, heavy fermions); Lewin PDO low-temperature example | 0.64 K; Frequency shift probes conductivity; fixed measurement temperature not Tc. Thermodynamic equilibrium is not established by this scoped source review. | measurement; conductivity-proxy-measurement | Proximity detector oscillator | ambient; unknown GPa | unknown | experiment; [source](#ref-source-0c4d7cebb12a0d5b) |
| UTe2 (aliases: heavy fermion, heavy fermions); Lewin PDO normal-state comparison | 2.09 K; Superconducting feature absent in this comparison; must not become a 2.09 K transition record. Thermodynamic equilibrium is not established by this scoped source review. | normal-state; normal-state-comparison | Proximity detector oscillator | ambient; unknown GPa | unknown | experiment; [source](#ref-source-0c4d7cebb12a0d5b) |
| UTe2 (aliases: heavy fermion, heavy fermions); Zambra magnetotropic field-angle scans | 4 K; All superconducting phases suppressed at 4 K; borrowed 300 mK phase diagram is a separate dataset. Thermodynamic equilibrium is not established by this scoped source review. | normal-state; normal-state-magnetotropic-response | Cantilever frequency shift | ambient; unknown GPa | unknown | experiment; [source](#ref-source-15cfc4a2f9587af0) |
| CeCoIn5 (aliases: Bianchi entropy reference, heavy fermion, heavy fermions); Bianchi [100] entropy-gain reference in author-v1 Figure 3c | 0.13 K; Lower reference of the plotted entropy-gain integral. Not an absolute-entropy measurement, an experimental base-temperature claim, an internal phase boundary or a transition Tc. | measurement; entropy-integration-reference | Specific-heat entropy integral | ambient; unknown GPa | unknown | experiment; [source](#ref-source-a626e7fcb17b94fa) |

## Sources

### Ref source-7ba854cc57960377

[R1] Enhancement of the upper critical field by nonmagnetic impurities in dirty two-gap superconductors (2003). [DOI 10.1103/PhysRevB.67.184515](https://doi.org/10.1103/PhysRevB.67.184515). Publication: journal-article. Check: selected-final-orbital-equation-and-normalization. Checked: 2026-10-20. Final pp. 4–5 Eqs. 31/34–39 and Figure 1 reread and visually inspected; author v1 p. 4 visually compared again. Final U uses a difference, whereas v1 prints a sum. Equal-diffusivity orbital equation is normalized by Tc times the near-Tc slope; nine roots checked independently by an integral representation. No full two-band, WHH spin/orbit or experimental fit.
### Ref source-16926b3817cff55d

[R2] Temperature and Purity Dependence of the Superconducting Critical Field, Hc2. III. Electron Spin and Spin-Orbit Effects (1966). [DOI 10.1103/PhysRev.147.295](https://doi.org/10.1103/PhysRev.147.295). Publication: journal-article. Check: reused-publisher-abstract-scope. Checked: 2026-10-18. A6 original publisher-abstract check reused: orbital, Pauli and spin-orbit treatment. Full WHH derivation and experimental fits not independently reviewed. The restricted orbital coefficient is checked separately through Gurevich final text and explicit asymptote.
### Ref source-a1695d99aaf064c8

[R3] Effect of Pauli Paramagnetism on Magnetic Properties of High-Field Superconductors (1966). [DOI 10.1103/PhysRev.148.362](https://doi.org/10.1103/PhysRev.148.362). Publication: journal-article. Check: publisher-abstract-only. Checked: 2026-10-18. Published5August1966. Abstract read: Pauli and spin-orbit assumptions affect first/second-order behavior. Extracted symbols incomplete; no numeric FFLO threshold or full derivation audited.
### Ref source-5962cf8038597944

[R4] Heavy-fermion superconductivity in CeCoIn5 at 2.3 K (2001). [DOI 10.1088/0953-8984/13/17/103](https://doi.org/10.1088/0953-8984/13/17/103). Publication: journal-article. Check: selected-author-discovery-and-field-comparison. Checked: 2026-10-20. Author v1 pp. 3–5 reread: 2.3 K zero resistance/full shielding; c-axis field comparison between zero resistance and heat capacity; transverse-field anisotropy at least two. The authors caution that changing normal-state C/T complicates a simple coupling-strength estimate. Final-version comparison and raw-data analysis remain open.
### Ref source-a626e7fcb17b94fa

[R5] Possible Fulde-Ferrell-Larkin-Ovchinnikov Superconducting State in CeCoIn5 (2003). [DOI 10.1103/PhysRevLett.91.187004](https://doi.org/10.1103/PhysRevLett.91.187004). Publication: journal-article. Check: selected-author-calorimetry-entropy-and-conventions. Checked: 2026-10-20. Only arXiv v1 is listed (18 April 2003); selected pp. 1–3 and Figures 1–3 visually inspected. Figure 3c entropy gain starts at 0.13 K. [100] heating/cooling hysteresis and [110] order-change temperature are separate. The v1 Maki definition omits the sqrt(2) used on this page; no final erratum inferred. Final publisher title says Possible, dated 28 October 2003, with a different author list. Printed 2018 typesetting date is not publication. Complete final comparison remains open.
### Ref source-fda01ade7737b638

[R6] Coupled Superconducting and Magnetic Order in CeCoIn5 (2008). [DOI 10.1126/science.1161818](https://doi.org/10.1126/science.1161818). Publication: journal-article. Check: original-abstract-only. Checked: 2026-10-18. Online21August2008,issue19September. Original abstract via PubMed and authors LANL record read; magnetic order and symmetry interpretation distinct. Full methods and supplement not retrieved.
### Ref source-0c4d7cebb12a0d5b

[R7] High-field superconducting halo in UTe2 (2025). [DOI 10.1126/science.adn7673](https://doi.org/10.1126/science.adn7673). Publication: journal-article. Check: selected-final-pulsed-field-and-angle-methods. Checked: 2026-10-20. Final pp. 512–513 reread; p. 513 Figure 1 and adjacent discussion visually inspected. Four specimens, fixed measurement temperatures, symmetrized angular map and possible field-induced heating are explicit. Persistence beyond the 73 T field ceiling is an inference, not an observed upper boundary; ab-plane non-observation is bounded by the available field window. No complete supplement, raw-data or order-parameter reconstruction.
### Ref source-15cfc4a2f9587af0

[R8] Giant transverse magnetic fluctuations at the edge of re-entrant superconductivity in UTe2 (2026). [DOI 10.1038/s41467-026-71899-7](https://doi.org/10.1038/s41467-026-71899-7). Publication: journal-article. Check: selected-final-results-methods-and-figure. Checked: 2026-10-18. Published29April2026; NatCommun17,3742. Selected final pp1–3 and5–6 discussion/methods read, p2Fig1 visual checked.4K measurements versus borrowed300mK/1.4K panels; below15T displaymask and calibration/orientation limits retained. Full supplement and pairing-kernel reconstruction open.
### Ref source-d32df19524b2a1c8

[R9] Upper Limit for the Critical Field in Hard Superconductors (1962). [DOI 10.1103/PhysRevLett.9.266](https://doi.org/10.1103/PhysRevLett.9.266). Publication: journal-article. Check: reused-publisher-identity-only. Checked: 2026-10-18. A6 identity check reused; complete original derivation not retrieved. Pauli calculation uses explicit weak-coupling assumptions and separately checked perspective.
### Ref source-b717fb1db41e9f29

[R10] Ising superconductivity: A first-principles perspective (2023). [DOI 10.1063/5.0153345](https://doi.org/10.1063/5.0153345). Publication: journal-article. Check: reused-selected-perspective-free-energy-check. Checked: 2026-10-18. A6 selected sectionII pp240503-2 to-3 susceptibility/free-energy and orientation check reused. Not a complete material or Ising-mechanism audit.

## Claim evidence and conditions

### scwiki-e5-claim-scope-1

Magnetic field is both a control parameter and a probe of superconductivity. Orbital currents, Zeeman splitting, vortex motion and changes in the magnetic background can produce different boundaries. A resistive onset, loss of zero resistance, heat-capacity anomaly and magnetic transition need not coincide. Retain temperature, crystal orientation, sample history, sweep direction and pulse conditions when comparing field scales.

Evidence: experiment. Sources: source-7ba854cc57960377, source-a626e7fcb17b94fa, source-0c4d7cebb12a0d5b.

Source relationship: context-for-editorial-analysis. Selected source observations provide context for editorial comparisons and evidence requirements, not a new measured phase or pairing mechanism.

Conditions: Keep field orientation, source version, specimen, thermal or pulse history, response criterion and finite measurement window attached. Unknown equilibrium does not assert nonequilibrium.

Verification scope: Named selected primary passages/figures, explicitly limited abstracts and independent bounded algebra; full scientific acceptance remains open.

### scwiki-e5-claim-scope-2

This article uses $B$ in tesla for the field scale; experimental papers often label that axis $H$ while reporting tesla, meaning an applied $\mu_0H$ scale. Converting an applied field to local induction requires the magnetization and demagnetizing geometry. Neither an unusually large upper critical field nor field-induced superconductivity alone identifies a pairing symmetry.

Evidence: experiment. Sources: source-16926b3817cff55d, source-0c4d7cebb12a0d5b, source-b717fb1db41e9f29.

Source relationship: context-for-editorial-analysis. Selected source observations provide context for editorial comparisons and evidence requirements, not a new measured phase or pairing mechanism.

Conditions: Keep field orientation, source version, specimen, thermal or pulse history, response criterion and finite measurement window attached. Unknown equilibrium does not assert nonequilibrium.

Verification scope: Named selected primary passages/figures, explicitly limited abstracts and independent bounded algebra; full scientific acceptance remains open.

### scwiki-e5-claim-mathematical-assumptions-1

For a weak-coupling singlet reference with Zeeman levels shifted by $\pm g\mu_B B/2$, zero residual superconducting spin susceptibility and no orbital cost, condensation-energy balance gives $B_P=\sqrt{2}\Delta_0/(g\mu_B)$. Using $\Delta_0=\pi e^{-\gamma_E}k_BT_c$ and $g=2$ gives about $1.86\,T_c$ tesla when $T_c$ is in kelvin. This is a conditional reference, not a universal upper bound. Spin-orbit coupling, anisotropic spin response and strong coupling change the comparison. Clogston's historical identity is retained; its complete original derivation was not retrieved here.

Evidence: theory. Sources: source-d32df19524b2a1c8, source-b717fb1db41e9f29.

Source relationship: mixed-source-and-local-derivation. Source models are separated from the local normalization, numerical solution and kinematic or entropy illustrations; no empirical fit is implied.

Conditions: Keep field orientation, source version, specimen, thermal or pulse history, response criterion and finite measurement window attached. Unknown equilibrium does not assert nonequilibrium.

Verification scope: Named selected primary passages/figures, explicitly limited abstracts and independent bounded algebra; full scientific acceptance remains open.

### scwiki-e5-claim-mathematical-assumptions-2

A second restricted reference is the dirty, single-band, purely orbital result $B_{c2}^{\rm orb}(0)\simeq0.693\,T_c|dB_{c2}/dT|_{T_c}$. Gurevich's final paper recovers it when the two diffusivities are equal. The near-transition slope must refer to the same field orientation and criterion being extrapolated. Its Eq. (31) defines $U(x)=\psi(1/2+x)-\psi(1/2)$, satisfying $U(0)=0$. The early author v1 prints a plus sign at that location; use the final definition. For clarity, let $t=T/T_c$, $s=|dB_{c2}/dT|_{T_c}$ and $b=B_{c2}/(T_cs)$. The restricted equation is $\ln t+U(2b/(\pi^2t))=0$. Its limits are $b\simeq1-t$ near $t=1$ and $b(0)=\pi^2e^{-\gamma_E}/8\simeq0.6927$. Our local solution gives $b(0.5)\simeq0.4505$, checked against an independent integral representation. These are dimensionless model values, not measured tesla. Unequal diffusivities produce different curves. This calculation does not validate a full WHH fit with Zeeman and spin-orbit terms, or a multiband fit to a particular material.

Evidence: theory. Sources: source-7ba854cc57960377, source-16926b3817cff55d.

Source relationship: mixed-source-and-local-derivation. Source models are separated from the local normalization, numerical solution and kinematic or entropy illustrations; no empirical fit is implied.

Conditions: Keep field orientation, source version, specimen, thermal or pulse history, response criterion and finite measurement window attached. Unknown equilibrium does not assert nonequilibrium.

Verification scope: Named selected primary passages/figures, explicitly limited abstracts and independent bounded algebra; full scientific acceptance remains open.

### scwiki-e5-claim-mathematical-assumptions-3

The Maki parameter compares those reference scales, $\alpha_M=\sqrt{2}B_{c2}^{\rm orb}(0)/B_P$; it is not by itself an FFLO detection criterion. In a parabolic band with small splitting, the Fermi-wavevector mismatch is $\delta k\simeq g\mu_B B/(\hbar v_F)$. The inherited expression contains an extra factor of two under the stated Zeeman convention. This kinematic estimate does not solve for the optimum finite-momentum pair wavevector or establish the stability of a Fulde–Ferrell–Larkin–Ovchinnikov state. Disorder, orbital effects, dimensionality and competing orders matter. Bianchi's author v1 writes its parameter as $H_{c2}^{0}/H_P$, without the $\sqrt{2}$ used in this page's definition; a numerical threshold must not be moved between those conventions without reconciliation. This identifies a source-convention difference, not a verified correction to the final paper.

Evidence: theory. Sources: source-a1695d99aaf064c8, source-a626e7fcb17b94fa.

Source relationship: mixed-source-and-local-derivation. Source models are separated from the local normalization, numerical solution and kinematic or entropy illustrations; no empirical fit is implied.

Conditions: Keep field orientation, source version, specimen, thermal or pulse history, response criterion and finite measurement window attached. Unknown equilibrium does not assert nonequilibrium.

Verification scope: Named selected primary passages/figures, explicitly limited abstracts and independent bounded algebra; full scientific acceptance remains open.

### scwiki-e5-claim-experimental-criteria-1

Petrovic's discovery report describes zero resistance and full diamagnetic shielding at approximately 2.3 K in CeCoIn5. Its field–temperature paragraph compares specific heat with zero resistance for field along the c-axis. That zero-field transition is distinct from lower-temperature anomalies inside the superconducting phase. The same report finds an upper-critical-field anisotropy of at least two from additional transverse-field transport measurements, so one orientation cannot stand in for every field direction. It also cautions that a temperature-dependent normal-state heat-capacity coefficient complicates a simple weak-versus-strong-coupling inference from the jump size.

Evidence: experiment. Sources: source-5962cf8038597944.

Source relationship: direct-support. Source observations support only their stated specimen, temperature, orientation and protocol; interpretation limits are retained.

Conditions: Keep field orientation, source version, specimen, thermal or pulse history, response criterion and finite measurement window attached. Unknown equilibrium does not assert nonequilibrium.

Verification scope: Named selected primary passages/figures, explicitly limited abstracts and independent bounded algebra; full scientific acceptance remains open.

### scwiki-e5-claim-experimental-criteria-2

Bianchi's selected author-manuscript passages describe heat-pulse and temperature-decay calorimetry, including subtraction of the In/Co nuclear Schottky contribution. Figure 1 uses different vertical quantities in its panels: $(C-C_{\rm Sch})/T$ and $C$, with a $C/T$ inset. Equal-entropy construction concerns the integral of $C/T$, not equal areas under an unconverted $C$ curve. At high in-plane fields the report finds a first-order upper boundary and an internal anomaly around 0.3 K. These are not new zero-field transition temperatures. Figure 3c reports entropy gain starting at 0.13 K, not absolute entropy measured down to zero. The first-order-boundary evidence includes heating/cooling hysteresis in the [100] scans at 11.2 and 11.4 T; the 1.1 ± 0.1 K order-change temperature refers to [110]. These orientations and thermal paths must accompany the values. Its final title explicitly says “Possible” FFLO state; calorimetry does not directly measure pair momentum.

Evidence: experiment. Sources: source-a626e7fcb17b94fa.

Source relationship: direct-support. Source observations support only their stated specimen, temperature, orientation and protocol; interpretation limits are retained.

Conditions: Keep field orientation, source version, specimen, thermal or pulse history, response criterion and finite measurement window attached. Unknown equilibrium does not assert nonequilibrium.

Verification scope: Named selected primary passages/figures, explicitly limited abstracts and independent bounded algebra; full scientific acceptance remains open.

### scwiki-e5-claim-experimental-criteria-3

The later Kenzelmann neutron-scattering report finds magnetic order coupled to superconductivity in this high-field region. Its symmetry interpretation suggests a modulated superconducting state, while the observed magnetic order does not alone reconstruct the spatial pair field. This article checked that paper's original abstract, not its complete neutron methods or supplementary analysis.

Evidence: experiment. Sources: source-fda01ade7737b638.

Source relationship: direct-support. Source observations support only their stated specimen, temperature, orientation and protocol; interpretation limits are retained.

Conditions: Keep field orientation, source version, specimen, thermal or pulse history, response criterion and finite measurement window attached. Unknown equilibrium does not assert nonequilibrium.

Verification scope: Named selected primary passages/figures, explicitly limited abstracts and independent bounded algebra; full scientific acceptance remains open.

### scwiki-e5-claim-experimental-criteria-4

Lewin's UTe2 experiments combine pulsed-field resistance and proximity-detector-oscillator measurements. Typical pulses reached 60 T or, in a different magnet, 73 T; the common measurement temperature was about 0.63 K. The high-field zero-resistance region depends strongly on both field angles. The oscillator frequency is a conductivity-sensitive proxy, and a comparison at 2.09 K without the superconducting feature is a normal-state measurement, not a 2.09 K transition determination. Four specimens contribute resistance or oscillator data, and the authors discuss sample dependence and possible field-induced heating. The angular map is symmetrized for visualization. At the source's $\theta_{bc}=8^\circ$ setting the oscillator feature persists to the 73 T magnet ceiling; continuation above that ceiling is inferred from its trend, not directly measured. In the ab plane, non-observation within the available field window does not exclude a higher-field onset. A measured field extent is not necessarily an observed upper critical field.

Evidence: experiment. Sources: source-0c4d7cebb12a0d5b.

Source relationship: direct-support. Source observations support only their stated specimen, temperature, orientation and protocol; interpretation limits are retained.

Conditions: Keep field orientation, source version, specimen, thermal or pulse history, response criterion and finite measurement window attached. Unknown equilibrium does not assert nonequilibrium.

Verification scope: Named selected primary passages/figures, explicitly limited abstracts and independent bounded algebra; full scientific acceptance remains open.

### scwiki-e5-claim-experimental-criteria-5

Zambra's April 2026 study measures magnetotropic response at 4 K, where the superconducting phases are suppressed. Its Figure 1 separately reproduces a 300 mK superconducting phase diagram and 1.4 K magnetization from earlier work. These temperatures must not be merged into a claim of superconductivity at 4 K. “Transverse” refers to response perpendicular to the static field, not automatically an off-diagonal susceptibility element. The final article number is 3742, correcting the inherited 3814.

Evidence: experiment. Sources: source-15cfc4a2f9587af0.

Source relationship: direct-support. Source observations support only their stated specimen, temperature, orientation and protocol; interpretation limits are retained.

Conditions: Keep field orientation, source version, specimen, thermal or pulse history, response criterion and finite measurement window attached. Unknown equilibrium does not assert nonequilibrium.

Verification scope: Named selected primary passages/figures, explicitly limited abstracts and independent bounded algebra; full scientific acceptance remains open.

### scwiki-e5-claim-limits-and-disputes-1

Magnetotropic susceptibility, an angular derivative of torque measured through a cantilever frequency shift, probes a different response from longitudinal magnetization. Zambra's long-wavelength result supports an inference of enhanced transverse ferromagnetic fluctuations; it does not measure a complete frequency-dependent pairing interaction. Values below 15 T in one normalized color map were set to zero to suppress amplified noise, rather than demonstrating a physically vanishing susceptibility. Alignment and calibration details remain relevant to comparisons with phase boundaries.

Evidence: experiment. Sources: source-15cfc4a2f9587af0.

Source relationship: context-for-editorial-analysis. Selected source observations provide context for editorial comparisons and evidence requirements, not a new measured phase or pairing mechanism.

Conditions: Keep field orientation, source version, specimen, thermal or pulse history, response criterion and finite measurement window attached. Unknown equilibrium does not assert nonequilibrium.

Verification scope: Named selected primary passages/figures, explicitly limited abstracts and independent bounded algebra; full scientific acceptance remains open.

### scwiki-e5-claim-limits-and-disputes-2

Keep measured phenomena separate from candidate explanations. A heat-capacity anomaly, magnetic Q phase and proposed FFLO modulation are distinct statements. Likewise, the multicomponent triplet model discussed for the UTe2 field-angle halo is an interpretation, not a direct determination of topology. Selected original passages and figures were checked here; remaining final-version comparisons, full supplements, raw-data reproduction and complete scientific acceptance remain open.

Evidence: experiment. Sources: source-a626e7fcb17b94fa, source-fda01ade7737b638, source-0c4d7cebb12a0d5b.

Source relationship: context-for-editorial-analysis. Selected source observations provide context for editorial comparisons and evidence requirements, not a new measured phase or pairing mechanism.

Conditions: Keep field orientation, source version, specimen, thermal or pulse history, response criterion and finite measurement window attached. Unknown equilibrium does not assert nonequilibrium.

Verification scope: Named selected primary passages/figures, explicitly limited abstracts and independent bounded algebra; full scientific acceptance remains open.

### scwiki-e5-claim-discovery-implications-1

Construct a field–temperature–angle map with explicit criteria and uncertainties. Compare transport with thermodynamic or magnetic probes where possible, retain pulsed-field heating and alignment controls, and distinguish re-entrant regions from a simple monotonic critical field. The local equation checks verify declared Zeeman conventions, an orbital asymptote and an illustrative entropy construction. They do not establish a new superconducting phase, fit an experimental boundary or certify a universal pairing mechanism.

Evidence: theory. Sources: source-7ba854cc57960377, source-a626e7fcb17b94fa, source-0c4d7cebb12a0d5b, source-15cfc4a2f9587af0.

Source relationship: context-for-editorial-analysis. Selected source observations provide context for editorial comparisons and evidence requirements, not a new measured phase or pairing mechanism.

Conditions: Keep field orientation, source version, specimen, thermal or pulse history, response criterion and finite measurement window attached. Unknown equilibrium does not assert nonequilibrium.

Verification scope: Named selected primary passages/figures, explicitly limited abstracts and independent bounded algebra; full scientific acceptance remains open.

## Revision and review

Article ID: scwiki-e5. Revision: 1818709a228fddf857ab. Updated: 2026-10-19T18:58:10.433841+00:00.

Review scope: Selected Gurevich final pp. 4–5 and author-v1 sign comparison; Petrovic author-v1 pp. 3–5; Bianchi author-v1 pp. 1–3 and Figures 1–3 with final-title metadata; Lewin final pp. 512–513 and selected Zambra figure context; restricted orbital-curve arithmetic.

- Complete scientific acceptance, full final-version comparisons, supplements and raw-data reconstruction remain open.
- WHH, Maki and Kenzelmann original sources retain their prior abstract-level scopes; Clogston identity is not a complete original-derivation audit.
- The 0.693 coefficient, normalized orbital curve and synthetic entropy integral are conditional mathematical checks, not material fits.
- Source-v1 Maki normalization is explicitly distinguished; no verified final-paper correction or universal FFLO threshold is asserted.
- Measurement temperatures, internal anomalies and finite field limits must not become new transition temperatures or exact critical fields. Thermodynamic equilibrium is not certified.

Source: [E_tuning_parameters/E5_magnetic_field.md](https://github.com/JackZH26/jzis-superconductivity/blob/0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf/E_tuning_parameters/E5_magnetic_field.md), commit 0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf, SHA-256 e95bc5d022e6dbdc433f274536762ad4d93e9e6b19005b40e0a37ff41ee41eeb.