Pressure-Invariant Isotope Effect as Evidence for Electronically Driven Intertwined Order in Pr 4 Ni 3 O 10

arXiv:2603.20871 · cond-mat.supr-con, cond-mat.str-el · Submitted 2026-03-21 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Pressure-Invariant Isotope Effect as Evidence for Electronically Driven Intertwined Order in Pr 4 Ni 3 O 10".

Mira: The gist: The finite but pressure-invariant oxygen-isotope shift, combined with the absence of phonon anomalies reported by Jia et al.,

Kai: First, who's behind it and why it matters.

Paper summary: Kai: So, wrapping up this whole discussion on "Pressure-Invariant Isotope Effect as Evidence for Electronically Driven Intertwined Order in Pr4Ni3O10," what are we really taking away from the authors' work?

Mira: The main thing is that the finite but pressure-invariant oxygen isotope shift, when paired with the lack of phonon anomalies, strongly supports a scenario where electronic correlations dominate the intertwined CDW and SDW transition in trilayer RP nickelates.

Lev: So what does that mean for someone who just listens to this show? It means that when you look at these materials under pressure, the lattice doesn't control how the density wave state moves; it’s the electronic interactions driving that movement.

Kai: That’s right. The paper shows that while oxygen isotopes are sensitive probes, their sensitivity doesn't change dramatically with pressure because the underlying mechanism is electronic coupling between spin and charge.

Mira: It sets a contrast with other materials, like cuprate superconductors where you see a big enhancement of the isotope effect on superconductivity when you dope them. This material behaves differently under pressure.

Lev: The implication for future research is that microscopic models of density-wave formation need to account for this electronic dominance, and we shouldn't expect lattice degrees of freedom to suddenly become the main controller when things get squeezed.

Kai: So, in short, it’s about constraining our models of density waves by showing that these transitions are fundamentally electronic in nature for Pr4Ni3O10. That’s what this paper does.

Conclusion: Kai: So we’re looking at the conclusion of this paper now about how they proved that in these nickelates, the lattice isn't actually driving this density wave state under pressure, and that’s what they call a pressure-invariant isotope effect.

Mira: Exactly. They showed that even when you squeeze it, the way those oxygen isotopes shift doesn't change much; it stays basically constant. That really hammers home the idea that the magnetic and charge ordering are happening because of electronic interactions, not just some simple lattice distortion responding to pressure.

Lev: From a hardware standpoint, if this is true, then when we try to model these systems for error correction or any complex quantum computation involving these materials, we don't have to worry about the pressure tuning the fundamental physics in this specific way.

Kai: That’s what it means for us building things. It tells us that the density-wave instability in Pr4Ni3O10 is fundamentally electronic, which is consistent with other scattering experiments they've done, like inelastic x-ray results.

Mira: It suggests we need to keep focusing on those strong spin interactions in our theories when we try to understand these layered nickelates because that’s where the real physics lies.

Lev: It also means if we were to look at materials where pressure *does* change the ordering, like cuprates, we have a clear roadmap for what causes that difference.

Kai: So, this paper is really putting constraints on how we build microscopic models of these density waves and what mechanisms might lead to superconductivity in these nickelates.

Mira: And it sets a benchmark against those other material classes you mentioned, showing exactly how the lattice plays its role here versus elsewhere.

Lev: It’s interesting because it suggests that for this specific class of compound, the lattice is more of a participant than the boss.

Kai: So next we can look at how this behavior contrasts with other materials that might behave differently under pressure.

PSI Center for Neutron and Muon Sciences CNM · TU Dortmund University

cond-mat.supr-con, cond-mat.str-el

Submitted: 2026-03-21

Updated: 2026-03-21

Comments: 9 pages, 3 figures

Journal ref: Phys. Rev. B 114, L080508 (2026)

DOI: 10.1103/wzcz-z62k

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 87/100

The gist: The gist: The finite but pressure-invariant oxygen-isotope shift, combined with the absence of phonon anomalies reported by Jia et al., supports a scenario in which electronic correlations dominate

Key concepts

Isotope Effect: This probes how much the atomic mass of oxygen (16O vs 18O) influences a quantum state like the SDW transition. A measurable shift indicates that the lattice structure plays a role in stabilizing or influencing this specific ordering, linking magnetism and crystal structure.
Spin-Density Wave (SDW): The SDW is an ordered state where electron spins align periodically in space, creating a modulation of charge density. This phenomenon is an emergent quantum state where magnetic order and charge ordering become strongly linked through electronic interactions.
Electronic Correlations: These refer to the strong repulsive forces between electrons within the material, which are not fully captured by simple band theory. The paper suggests these strong electronic interactions are the primary driver behind the intertwined CDW/SDW transition observed in Pr4Ni3O10.
Pressure-Invariant Shift: The key finding is that while the SDW transition temperature changes with pressure, the difference between its effect on 16O and 18O remains nearly constant. This invariance strongly implies that the mechanism driving this isotope sensitivity is electronic in nature rather than being controlled by changes in lattice structure under compression.

Terminology

Benchmark — 1× in this paper · explained in 2 episodes

Summary

The gist: The finite but pressure-invariant oxygen-isotope shift, combined with the absence of phonon anomalies reported by Jia et al., supports a scenario in which electronic correlations dominate the intertwined CDW/SDW transition in trilayer RP nickelates.

Isotope Effect and Intertwined Order

The study reports muon-spin rotation measurements of the pressure dependence of the oxygen-isotope (16O/18O) effect on the spin-density wave (SDW) transition in Pr4Ni3O10 At ambient pressure, TSDW shows a finite isotope shift, with 16TSDW = 158.04(5) K and 18TSDW = 159.81(6) K Under hydrostatic pressure, TSDW decreases linearly at nearly identical rates for the two isotope compositions, d 16TSDW/dp = −4.93(5) K/GPa and d 18TSDW/dp = −4.90(7) K/GPa, such that the isotope shift remains essentially unchanged under compression The absence of pressure enhancement of the isotope effect points to a predominantly electronic origin of the SDW transition and is consistent with recent inelastic x-ray scattering results.

Evidence for Electronic Origin

The systematic observations demonstrated that isotope sensitivity of the SDW transition is not intrinsic to magnetism itself but emerges only when spin and charge degrees of freedom are strongly intertwined. The pressure dependence provides a decisive test of this picture. If lattice involvement were to increase as the intertwined CDW/SDW instability weakens – particularly as the system approaches the superconducting regime – one would expect the isotope response of TSDW to evolve. The absence of such enhancement in Pr4Ni3O10 suggests a fundamental difference between these material classes.

Experimental Probes and Findings

The researchers combined oxygen-isotope substitution with µSR measurements under hydrostatic pressure in Pr4Ni3O10. The magnetic volume fraction fm is extracted from the WTF-µSR time spectra, where the amplitude of the oscillatory component reflects the paramagnetic (nonmagnetic) volume fraction of the sample. At T = 159 K, close to the SDW transition, both isotope compositions exhibit a full-amplitude oscillatory signal, indicating a fully paramagnetic state. The fits yield 16TSDW = 158.04(5) K and 18TSDW = 159.81(6) K, with an isotope shift of 18TSDW −- - - - - TSDW = 1.77(8) K.

Pressure Dependence Analysis

In the analysis of the WTF-µSR data using Eq. 2, the pressure cell contribution is included as an additional oscillatory term with a temperature-independent initial asymmetry. The linear fits reveal that 16TSDW(p) = 157.52(11) K − p · 4.93(5) K/GPa and 18TSDW(p) = 159.17(10) K − p · 4.90(7) K/GPa. The nearly equal slopes demonstrate that the oxygen isotope shift of the SDW transition remains constant under compression. Furthermore, the transition width ∆TSDW increases nearly equally with pressure for both isotope compositions.

Conclusion on Material Class Differences

The finite but pressure-invariant oxygen-isotope shift, combined with the absence of phonon anomalies reported by Jia et al., supports a scenario in which electronic correlations dominate the intertwined CDW/SDW transition in trilayer RP nickelates. This indicates that while the lattice participates in ordering, it does not control the pressure evolution of the SDW state. The behavior contrasts sharply with cuprate superconductors, where suppression of antiferromagnetic order by doping is accompanied by a substantial enhancement of the oxygen-isotope effect on superconductivity.

Implications for Density Wave Formation

These findings place important constraints on microscopic models of density-wave formation and on proposed mechanisms of superconductivity in Ruddlesden–Popper nickelates. The results indicate that the density-wave instability in trilayer nickelates is primarily electronic in origin, with lattice degrees of freedom playing a secondary, cooperative role. This conclusion is consistent with recent inelastic xray scattering results by Jia et al., who investigated lattice–charge coupling in trilayer RP nickelates. The absence of measurable phonon softening across the density-wave transition in the trilayer nickelates further supports this electronic dominance.

Final Summary Statement

The finite but pressure-invariant oxygenisotope shift, combined with the absence of phonon anomalies reported by Jia et al., supports a scenario in which electronic correlations dominate the intertwined CDW/SDW transition in trilayer RP nickelates. The lattice participates in ordering, as evidenced by the finite isotope effect, but it does not control the pressure evolution of the SDW state. This demonstrates that suppression of the intertwined CDW/SDW state under compression does not enhance lattice participation in the densitywave ordering mechanism. The results place important constraints on microscopic models of density-wave formation and on proposed mechanisms of superconductivity in Ruddlesden–Popper nickelates. This conclusion is consistent with recent inelastic xray scattering results by Jia et al., who investigated lattice–charge coupling in trilayer RP nickelates. The absence of measurable phonon softening across the density-wave transition in the trilayer nickelates further supports this electronic dominance. The behavior contrasts sharply with cuprate superconductors, where suppression of antiferromagnetic order by doping is accompanied by a substantial enhancement of the oxygen-isotope effect on superconductivity. If pressure in trilayer nickelates plays an analogous role – weakening magnetic order and moving the system toward superconductivity – one might anticipate an increasing lattice contribution to the relevant energy scale. The absence of such enhancement in Pr4Ni3O10 suggests a fundamental difference between these material classes.

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Pressure-Invariant Isotope Effect as Evidence for Electronically Driven Intertwined Order in Pr4Ni3O10 Rustem Khasanov, Thomas J. Hicken Igor Plokhikh Ekaterina Pomjakushina Hubertus Luetkens Zurab Guguchia Christof W. Schneider and Dariusz J Gawryluk 1 PSI Center for Neutron and Muon Sciences CNM, 5232 Villigen PSI, Switzerland 2TU Dortmund University Department of Physics Dortmund, 44227 Germany (Dated: March 24, 2026 We report muon-spin rotation measurements of the pressure dependence of the oxygen-isotope (16O/18O) effect on the spin-density wave (SDW) transition in the trilayer Ruddlesden-Popper nickelate Pr4Ni3O10 At ambient pressure, the SDW transition shows a finite isotope shift, with 16TSDW = 158.04(5) K and 18TSDW = 159.81(6) K Under hydrostatic pressure, TSDW decreases linearly at nearly identical rates for the two isotope compositions, d 16TSDW/dp = −4.93(5) K/GPa and d 18TSDW/dp = −4.90(7) K/GPa, such that the isotope shift remains essentially unchanged under compression The absence of pressure enhancement of the isotope effect points to a predominantly electronic origin of the SDW transition and is consistent with recent inelastic x-ray scattering results, suggesting a new regime of intertwined order in trilayer RP nickelates, which is stabilized by strong spin interactions Introduction. The isotope effect is a fundamental probe of lattice involvement in emergent quantum states.

Improvements for AI systems

Improve phase diagram modeling by incorporating pressure-invariant isotope shifts as a constraint for electronic origin identification. The improved AI system can determine if the isotope effect evolves as the intertwined density-wave state is weakened based on experimental data, directly testing whether lattice involvement were to increase as the intertwined CDW/SDW instability weakens.
Enhance material property prediction accuracy for layered nickelates by distinguishing between electronic and lattice contributions to density wave instabilities. The system can predict if a material exhibits a finite oxygen-isotope shift of the SDW transition temperature, with 18TSDW −16 TSDW = 1.77(8) K versus scenarios where lattice involvement were to increase.
Develop a comparative analysis module for density wave order across different material classes (e.g., nickelates vs. cuprates). The improved system can identify fundamental differences by noting that in trilayer nickelates, no measurable phonon softening was detected across the density-wave transition, contrasting this with the pronounced enhancement of the oxygen-isotope effect on superconductivity observed in cuprates.
Refine pressure dependence analysis for quantum phase transitions by identifying robust scaling laws. The system can determine if a material's TSDW follows a linear fit [16TSDW(p) = 157.52(11) K − p · 4.93(5) K/GPa] and whether the isotope shift remains constant under compression, confirming the magnitude of the OIE on TSDW in Pr4Ni3O10 remains independent of pressure.