Magnetic ‘Glue’ Revealed in a High-Temperature Superconductor

For nearly four decades, one question has stalked condensed matter physics: what actually binds electrons into superconducting pairs in the cuprates, the copper oxide materials that superconduct at temperatures far beyond anything conventional theory can explain? In conventional superconductors, described by the Bardeen–Cooper–Schrieffer (BCS) framework, the answer is elegant and settled. Electrons exchange virtual phonons, quantized vibrations of the crystal lattice, and this interaction welds them into Cooper pairs. The same electron–phonon coupling that creates the pairs also scatters electrons in the normal, resistive state, which means the critical temperature and the strength of a characteristic linear-in-temperature scattering rate rise and fall together through a single coupling constant. In the cuprates, no such relationship had ever been convincingly identified, leaving the pairing mechanism shrouded in uncertainty. Now, a study published in Nature Physics by Caitlin Duffy of Radboud University and the University of Grenoble Alpes, together with S. J. Tu, Q. H. Chen, Kui Jin, Nigel Hussey and colleagues in China, the Netherlands and the United Kingdom, reports the clearest experimental demonstration yet that in electron-doped cuprates, superconductivity is glued by magnetic spin fluctuations rather than lattice vibrations.

The team focused on lanthanum cerium copper oxide, La2−xCexCuO4, known as LCCO, an electron-doped cuprate in which cerium atoms donate electrons to the copper oxide planes. Measuring resistivity and magnetoresistance across the entire overdoped region of the phase diagram, they found a striking correlation between the strength of scattering by antiferromagnetic spin fluctuations and the superconducting transition temperature. As doping increased and the transition temperature fell from near its optimum of about 25 kelvin to zero, the strength of the anisotropic, temperature-linear scattering dropped by a full order of magnitude, mirroring the decline in superconductivity. In other words, the two quantities tracked each other just as the electron–phonon coupling constant links transition temperature and scattering in ordinary metals, but here the coupling was to magnetic, not lattice, excitations.

What makes this result remarkable is not merely the correlation itself, which had been glimpsed before, but the experimental rigor with which it was isolated. In overdoped cuprates, the coefficient of the linear-in-temperature resistivity, usually labeled A1, is known to fall in step with the critical temperature, and a similar relationship has been reported in organic Bechgaard salts and in the iron-based superconductor BaFe2Co2As2. But resistivity is a blunt instrument. It depends on carrier density, impurity content and band structure as well as on scattering, so it cannot on its own reveal whether the temperature-linear term really reflects a coupling whose strength varies. Alternative interpretations have flourished. Some researchers argued that linear resistivity in cuprates reflects universal Planckian dissipation, a quantum bound at which the scattering rate reaches roughly kBT divided by the reduced Planck constant, so that A1 would be fixed by thermodynamic quantities rather than by any pairing glue. Others questioned whether the scattering rate in cuprates is truly linear in temperature at all. Without a way to extract the scattering rate itself, the debate stalled.

The way out of the impasse was magnetoresistance. According to semiclassical transport theory, the fractional change in resistivity in a magnetic field is largely independent of carrier density and instead reflects the magnitude of the scattering rate and, crucially, how the rate varies around the Fermi surface. By measuring magnetoresistance in fields as high as 35 tesla at the High Field Magnet Laboratory in Nijmegen, the team could disentangle the contributions of impurity scattering, electron–electron scattering and inelastic scattering by bosonic fluctuations. The technique, however, demands exquisite control over doping, and this is where a decade of materials development paid off. Using a combinatorial thin-film growth technique, the group synthesized LCCO films with a continuous gradient of cerium concentration on a single strontium titanate substrate, allowing them to pattern 19 distinct doping levels with a resolution of roughly 0.003 in composition, spanning from just above optimal doping at x equals 0.116 to the very edge of the superconducting dome at x equals 0.188.

The magnetoresistance data showed behavior that conventional Kohler scaling could not explain. In a simple metal, as temperature falls and the mean free path grows, magnetoresistance increases in a predictable way. In LCCO, the opposite happened at low temperatures: the magnetoresistance shrank far faster than the resistivity itself decreased. The team concluded that the magnitude of the magnetoresistance is governed primarily by the degree of anisotropy in the temperature-dependent, inelastic scattering rate, not simply by the mean free path. Moreover, at high fields the magnetoresistance became strikingly linear in field strength, up to 65 tesla in some samples, a signature that the electrons encounter intense scattering centers, or hotspots, that impede their cyclotron motion around the Fermi surface. Those hotspots, the team showed, sit precisely where the Fermi surface crosses the antiferromagnetic Brillouin zone boundary, the locus at which electrons scatter resonantly by the wave vector (π, π) that connects neighboring magnetic sites in the copper oxide lattice.

To be sure that spin fluctuations and not charge order were responsible, the team turned to the Hall coefficient, which measures the effective carrier density and sign of the charge carriers. In LCCO, the Hall coefficient falls and can even flip sign as temperature rises, something that a Fermi surface with only hole-like curvature cannot produce under any amount of anisotropic impurity scattering. The resolution lies in current vertex corrections, a quantum-mechanical modification of ordinary Boltzmann transport theory first worked out by H Kontani. When electrons scatter strongly between hotspots connected by the antiferromagnetic wave vector, their velocities mix, and the resulting current at each hotspot is no longer perpendicular to the Fermi surface. Incorporating these corrections, the team showed that scattering by antiferromagnetic spin fluctuations naturally drives the Hall coefficient downward and negative with increasing temperature, while scattering by charge fluctuations at the antinodes would push it the other way. The data spoke unambiguously for the magnetic scenario.

With the nature of the scatterer settled, the doping analysis became the payoff. The team modeled the zero-field resistivity and magnetoresistance at 40 kelvin across the entire doping series with a scattering rate containing just one doping-dependent parameter, a dimensionless factor g(x) multiplying the temperature-linear, anisotropic scattering component. Everything else, the impurity rate, the quadratic scattering coefficient and the hotspot strength, was fixed. Across the series, g(x) dropped by roughly an order of magnitude as the critical temperature fell from near its optimum to zero, acting as an effective coupling parameter for superconductivity in direct analogy with the electron–phonon coupling constant in BCS theory. The analysis also ruled out the Planckian interpretation for the electron-doped side: because the scattering strength varies so much with doping, the linear-in-temperature resistivity in LCCO cannot be pinned to a universal quantum dissipation bound. For electron-doped cuprates at least, weak-coupling spin-fluctuation theory, long the workhorse of magnetic pairing models, appears to capture the physics.

The comparison with hole-doped cuprates is where the study turns provocative. On the hole-doped side of the cuprate phase diagram, the strange metal regime shows magnetoresistance that obeys a peculiar quadrature scaling in which the field derivative of the resistivity collapses onto a single curve when plotted against field divided by temperature. No version of quasiparticle transport theory has explained that scaling. The electron-doped materials, by contrast, behave like textbook quasiparticles throughout, admitting a full Boltzmann description with hotspot scattering and vertex corrections. The implication is stark: the higher critical temperatures of hole-doped cuprates cannot simply reflect a stronger coupling to the same antiferromagnetic fluctuations. If they did, hole-doped materials would show qualitatively similar magnetoresistance governed by an anisotropic inelastic scattering rate, and they do not. Something fundamentally different, possibly requiring physics beyond the quasiparticle picture altogether, must be operating on the hole-doped side, and resolving it will likely require more than a straightforward extension of BCS theory to spin-fluctuation pairing.

For the physics community, the result is both a triumph and a challenge. It provides the first quantitatively complete demonstration that a non-phononic glue, in this case low-energy antiferromagnetic spin fluctuations, can be isolated, characterized and linked to the pairing strength in a high-temperature superconductor, using nothing more exotic than resistivity, magnetoresistance and carefully applied transport theory. The same methodology, the authors note, could now be applied to the Bechgaard salts, where a similar relationship between linear resistivity and transition temperature has long tantalized researchers. At the same time, the very success of quasiparticle theory on the electron-doped side sharpens the mystery of its failure on the hole-doped side, where the strange metal persists and the highest superconducting temperatures live. In the cuprates’ asymmetry, it seems, lies a clue: whatever raises the critical temperature in hole-doped materials is not merely more of the same magnetic glue, but a mechanism physics has yet to write down.

Subject of Research: Spin-fluctuation-mediated superconductivity in electron-doped cuprate superconductors

Article Title: Evidence for spin-fluctuation-mediated superconductivity in electron-doped cuprates

Article References: Duffy, C. M., Tu, S. J., Chen, Q. H., Zhang, J. S., Cuoghi, A., Hinlopen, R. D. H., Sarkar, T., Greene, R. L., Jin, K., & Hussey, N. E. (2026). Evidence for spin-fluctuation-mediated superconductivity in electron-doped cuprates. Nature Physics. https://doi.org/10.1038/s41567-026-03454-6

Image Credits: AI Generated

DOI: 10.1038/s41567-026-03454-6

Keywords: superconductivity, cuprates, spin fluctuations, electron-doped LCCO, magnetoresistance, pairing mechanism, BCS theory, Planckian dissipation, Hall coefficient, strange metal, hotspot scattering, high-temperature superconductivity