Jaccarino–Peter effect: exchange compensation and its evidence

Scope

The Jaccarino–Peter effect is compensation of the spin-splitting field experienced by conduction electrons. An exchange contribution opposite to the applied field can reduce Zeeman pair breaking near a finite field. It does not cancel the applied field everywhere in space or remove orbital coupling. A large critical field, a second superconducting pocket or the presence of magnetic ions alone does not establish this mechanism. The original proposal dates to 1962; its identity is verified here, but its full derivation has not been reread. R1 R3

Meul and colleagues' 1984 work reports field-induced superconductivity in a Eu–Sn molybdenum chalcogenide system and interprets it through compensation. The original abstract supports that historical connection. Exact composition, numerical field endpoints and complete measurement methods have not been verified here, so they are not promoted to universal material parameters. A classical example cannot supply the missing exchange measurement for a different compound. R2

Mathematical assumptions

Choose the positive direction along the applied field and define the signed effective field as $B_{\mathrm{eff}}=B_{\mathrm{ext}}+B_{\mathrm{ex}}$. Compensation requires $B_{\mathrm{ex}}\lt0$ in this convention. In the collinear single-band illustration, spin energies are $E_\pm=\pm h$, with $h=g\mu_B B_{\mathrm{eff}}/2$ and positive $g$. Their full separation is $2|h|=g\mu_B|B_{\mathrm{eff}}|$. A source using another sign for its exchange constant must first be translated into this convention; the sign of a symbol called J is not transferable without its Hamiltonian. R1 R3

An independent synthetic example isolates an inference used in shift measurements. Suppose corrected frequency shifts obey $y=m(B-B_*)$, with nonzero, field-independent slope and a saturated exchange contribution. A fitted line $y=mB+c$ gives $B_*=-c/m$. Four imposed fields, 14.5, 21, 26 and 28 T, recover six noiseless examples with target intercepts of 20, 32 and 40 T and both slope signs. The latter two targets are extrapolations outside this measurement interval. These calculations reproduce the algebra, not published spectra. R4

A residual constant correction $d$ moves the inferred intercept by $-d/m$. In the synthetic examples, a 0.06 MHz offset shifts it by +2 T for a slope of -0.03 MHz/T, or by -1.2 T for +0.05 MHz/T. A zero slope leaves the intercept unidentifiable. Nine separate spin-energy checks verify the distinction between half splitting and full splitting, including negative effective fields. Neither exercise contains orbital coupling, spin-flip scattering or a gap equation, so neither demonstrates a superconducting transition. R4 R5

Experimental criteria

Balicas and colleagues measured four-terminal transport in lambda-(BETS)2FeCl4 with field near the conducting plane. Their phase diagram distinguishes resistive midpoints from resistance below instrumental sensitivity; the broad 18–41 T field-induced region is not uniformly a zero-resistance region. Below 2 K, resistance reaches the experimental zero near 33 T. Tilting introduces a transverse component that suppresses the state. Figure 3's pairing-state curves are theoretical fits, not direct imaging of a modulated order parameter. These results support a compensation interpretation while retaining orbital and measurement limits. R3

Hiraki and colleagues provide a different probe: corrected 77Se NMR shifts in the metallic state at 1.5 K and fields up to 28 T. They infer an exchange-field magnitude of 32 ± 2 T by extrapolating a field-dependent shift. This is not an observed zero crossing at 32 T. Chemical, dipolar and demagnetization corrections enter the analysis; demagnetization dominates their stated uncertainty. The interpretation assumes sufficiently saturated local moments and suitable field-independent electronic response. The transport specimen discussed alongside the NMR came from the same batch, not necessarily the identical crystal. R4

Wu and colleagues instead infer an exchange field of -32.7 ± 1.5 T from a 9 T, 5 K angular-shift experiment. Their author manuscript uses a hyperfine calibration partly informed by the nonmagnetic Ga analogue, and explicitly excludes an unknown uncertainty in its axial Knight-shift coefficient. Its predicted value at 33 T is a further model adjustment. Keep the applied field, temperature, inferred exchange field and uncertainty scope separate; the quoted exchange magnitude is not the applied field at which these spectra were taken. R5

For a new material, the evidence should connect a measured local-moment response to a signed electronic exchange contribution, then test whether its field and angle dependence account for the superconducting observations. Compare transport with independent magnetic or thermodynamic evidence where available. Different samples, transition criteria, pressure conditions and temperatures must remain identifiable. A numerical similarity between a resistance minimum and an inferred exchange field is supporting evidence, not a replacement for calibration or alternative-mechanism tests. R3 R4 R5

Limits and disputes

The selected Wu author manuscript has a convention issue requiring further review: the signed angular-difference formula and the subsequent printed numerical input do not match under direct substitution. The final publisher abstract confirms the reported exchange value, but the full final calibration has not been compared. This page therefore attributes the value to the authors and does not claim to reproduce it independently. The discrepancy is an unresolved source-version issue, not evidence that the experimental phenomenon is false. Complete scientific acceptance remains open. R5

The 2026 Eu-rich Sm/Ca/Eu nickelate study reports reentrance and discusses exchange compensation alongside other magnetic physics. Its selected later author version leaves the magnetic order unresolved and includes sample-dependent angular behavior. It does not justify a universal claim of established ferromagnetism or triplet pairing. A separate Nd/Eu nickelate study develops a paramagnetic-compensation interpretation using different material and substrate conditions. Their similarities motivate tests; they do not make the two systems interchangeable or establish one uniquely complete mechanism. R6 R7

Discovery implications

Store the exchange-field estimate with its sign convention, probe, applied field, temperature, correction model and uncertainty coverage. Record whether compensation was measured directly, extrapolated or assumed in fitting a phase boundary. Separate those records from superconducting transition temperatures. For multiband systems, test whether one effective exchange field is adequate rather than assuming every band has the same coupling. Preserve the independently measured orbital constraints when evaluating candidate compensation windows. R4 R5 R6

Related topics

Field-induced superconductivity, reentrant superconductivity, ferromagnetism and superconductivity, and nickelates.

Material cases

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