- The paper analyzes the magnetic excitations in bilayer nickelate superconductors, revealing a split in the flat 45 meV spin-fluctuation mode.
- Rare-earth doping (Pr, Nd) of La₃Ni₂O₇₋δ enhances interlayer magnetic coupling to 69–73 meV, while intralayer coupling remains weak.
- The observed spectral changes suggest an interlayer s± pairing mechanism, supporting the proposal that enhanced spin fluctuations contribute to high-$T_c$ superconductivity.
The bilayer nickelate La3Ni2O7−δ has emerged as a high-Tc superconductor under pressure, and a central question is whether spin fluctuations—regarded as the pairing glue in cuprates and iron pnictides—play an analogous role here. Prior inelastic neutron scattering (INS) work on La3Ni2O7−δ powder identified a weak, nearly dispersionless spin-fluctuation signal near 45 meV, interpreted as evidence for anomalously strong interlayer coupling (SJ⊥≈60 meV) and very weak intralayer coupling (SJ∥≤3.5 meV), a hierarchy opposite to that of cuprates and pnictides (2601.14946). This paper reports INS measurements on rare-earth doped polycrystalline samples La2PrNi20O21 and La22NdNi23O24 at ambient pressure, performed at MERLIN (ISIS) and PANTHER (ILL). The central finding is that the 45 meV flat mode splits into two modes upon doping, accompanied by a weaker mode near 60 meV, and that linear spin-wave analysis of stripe-type antiferromagnetic (AF) orders yields an enhanced interlayer coupling of 25–73 meV. The authors argue this enhancement supports interlayer 26 pairing and is consistent with reported 27 values approaching 100 K in doped compounds.
Sample characterization
Polycrystalline La28Ni29O7−δ0, La7−δ1NdNi7−δ2O7−δ3, and La7−δ4PrNi7−δ5O7−δ6 were synthesized by sol-gel methods (~5 g each) and characterized by Rietveld refinement of powder X-ray diffraction; all phases index to orthorhombic 7−δ7 with no detectable impurities. Rare-earth substitution shrinks the 7−δ8 axis (20.500 Å for La, 20.357 Å for Nd, 20.387 Å for Pr) and reduces both the out-of-plane Ni-O1-Ni angle (168.35° → 165.49°/162.10°) and the in-plane Ni-O3-Ni angle, consistent with chemical pressure from the smaller Pr7−δ9/NdTc0 ionic radii.
Magnetic susceptibility shows a weak anomaly at Tc1 K in the parent compound, plausibly associated with stripe-type AF order, while the doped samples exhibit Curie-Weiss behavior below 50 K with effective moments Tc2(Nd) = 2.8 Tc3 and Tc4(Pr) = 3.7 Tc5, consistent with free-ion Tc6 contributions. No clear phase transition appears in heat capacity beyond a broad hump near 100 K. Notably, the magnetic entropy obtained by subtracting the La compound's Tc7 exceeds the expected crystalline electric field (CEF) plateau of Tc8 = 19.1 J molTc9K30 for Nd31, which the authors attribute to additional spin-fluctuation entropy. The absence of thermodynamic anomalies in the doped samples does not preclude weak Ni magnetic order: 32SR estimates 33–0.42 34 for the parent compound, and neutron diffraction finds moments up to ~0.85 35 on high-moment sites of La36PrNi37O38. The rare-earth ions themselves do not order.
Inelastic neutron scattering results
At MERLIN, time-of-flight spectra of La39NdNi20O21 were collected at 22 K and 110 K with incident energies 23 = 15, 24, 50, 79, and 160 meV. Two 24-independent CEF excitations appear at 5.5 and 22 meV with stronger intensity at low temperature. After Bose-corrected subtraction of the high-temperature data, three features emerge at approximately 43, 48, and 60 meV that cannot be assigned to Nd25 CEF levels. Their intensity decreases with increasing momentum transfer—the hallmark of magnetic scattering—although phonon contamination obscures some windows. No spin excitations are observed above 70 meV in the 26 meV data, consistent with RIXS and single-crystal INS results.
PANTHER measurements confirm these findings across all three compounds. For La27NdNi28O29, subtracting the 170 K data reveals the split modes at 43 and 48 meV plus the 60 meV feature; subtracting the simultaneously measured La7−δ0Ni7−δ1O7−δ2 spectrum as a phonon reference yields the same levels cleanly, since the parent's 45 meV signal is much weaker while its phonon background is comparable. A distinctive observation is that the splitting around 45 meV develops with increasing 7−δ3, a feature the authors note has no counterpart in cuprate or pnictide superconductors. For La7−δ4PrNi7−δ5O7−δ6, CEF levels appear at 2, 3.5, 4.2, and 6 meV (consistent with non-Kramers Pr7−δ7 multiplet structure), and the spin modes split more weakly into ~44 and ~47 meV with a fainter 60 meV signal. In this case the authors concede that magnetic and phonon 7−δ8-dependences cannot be reliably distinguished by subtraction alone, and they state explicitly that single-crystal measurements are needed.
Spin-wave modeling and exchange couplings
The spectra are analyzed within linear spin-wave theory using four candidate magnetic structures: double spin stripe (DSS), single spin-charge stripe (SCS), A-type AF (AFM-A), and G-type AF (AFM-G), all implemented in SpinW with only nearest-neighbor exchanges. The DSS and SCS models share the experimentally favored wavevector 7−δ9 and differ in whether NiSJ⊥≈600 charge stripes accompany the spin stripes. The fitted parameters are:
| Coupling |
LaSJ⊥≈601NiSJ⊥≈602OSJ⊥≈603 |
LaSJ⊥≈604PrNiSJ⊥≈605OSJ⊥≈606 |
LaSJ⊥≈607NdNiSJ⊥≈608OSJ⊥≈609 |
| SJ∥≤3.50 / SJ∥≤3.51 (meV) |
4.5 |
3.0 |
2.7 |
| SJ∥≤3.52 / SJ∥≤3.53 (meV) |
−3.4 / −3.6 |
−3.5 / −3.6 |
−3.5 / −3.6 |
| SJ∥≤3.54 (meV) |
56.3 / 55.5 |
69.3 / 69.5 |
73.3 / 73.5 |
Both stripe models reproduce the observed splitting: in DSS it arises from a gap between acoustic and optical branches between SJ∥≤3.55 and X, while in SCS it comes from inequivalent band tops along SJ∥≤3.56–X versus X–M. By contrast, AFM-A and AFM-G with isotropic intralayer coupling produce dispersive, wave-like spectra rather than flat bands and cannot generate the splitting, so the authors rule them out. The model cannot, however, distinguish DSS from SCS on powder data—a degeneracy that again motivates single-crystal work.
Physically, the enhanced SJ∥≤3.57 is attributed to orbital-selective chemical pressure: smaller rare-earth radii compress the lattice and straighten... in fact, reduce the Ni-O-Ni angles while shifting the antibonding Ni-SJ∥≤3.58 state upward, strengthening interlayer overlap, whereas the in-plane Ni-O bond lengths change only moderately, leaving the SJ∥≤3.59-derived intralayer coupling essentially intact. Since Pr is slightly larger than Nd, its effect is correspondingly weaker, matching the measured hierarchy 20.
Connection to superconductivity
Assuming interlayer 21 pairing dominates under pressure and adopting the proportionality 22, the extracted 23 meV implies 24 K for La25NdNi26O27, which the authors note agrees with recent reports of bulk superconductivity up to ~96 K in pressurized nickelate single crystals and interlayer-coupling-enhanced superconductivity near 100 K in Nd-doped samples. This scaling assumption is the load-bearing step of the argument: it is borrowed from theoretical proposals rather than established empirically for this system, and the correlation between 28 and 29 rests on comparing ambient-pressure magnetism with high-pressure transport on nominally different samples. The paper also acknowledges that chemical pressure raises the critical pressure required for superconductivity even as it strengthens 200, so doping does not simply translate into higher ambient-pressure 201.
Limitations and open questions
Several caveats bear directly on the conclusions. First, all measurements are on powders, so momentum-resolved information is limited to 202 cuts; the DSS-versus-SCS distinction and the origin of the 203-dependent splitting remain unresolved. Second, the assignment of the 43/48 and 60 meV features to spin fluctuations relies on temperature-difference and sample-difference subtractions against phonon backgrounds that are similar but not identical across compounds; for the Pr sample the magnetic 204-dependence could not be isolated. Third, the Heisenberg analysis uses only nearest-neighbor couplings and an effective spin 205 aggregating multiple orbitals, an approximation whose validity for itinerant, multi-orbital nickelates is not tested here. Fourth, the 206 relation linking ambient-pressure spin dynamics to pressurized superconductivity is assumed, not demonstrated. Finally, whether the enhanced interlayer coupling survives into the superconducting phase under pressure—and whether the split modes evolve into a resonance analogous to cuprates and pnictides—is left open.
Conclusion
This work establishes that rare-earth doping modifies the magnetic excitation spectrum of bilayer nickelates in a specific and quantifiable way: the flat 45 meV mode of La207Ni208O209 splits into two modes, and the dominant interlayer exchange grows from roughly 56 meV to about 69 meV (Pr) and 73 meV (Nd), while intralayer couplings remain weak and nearly unchanged. Within stripe-type AF models, these results reinforce the picture of quasi-two-dimensional, interlayer-dominated magnetism unique among high-210 families, and they provide quantitative support—conditional on the assumed 211–212 scaling—for the proposal that interlayer 213 pairing mediates the enhanced superconductivity of doped bilayer nickelates. Resolving the remaining structural and dynamical ambiguities will require single-crystal INS and measurements under pressure.
