Unconventional Pressure Evolution of Spin-Density-Wave State in La$_{3}$Ni$_{2}$O$_{7}$

Abstract: The discovery of pressure-induced high temperature superconductivity in the bilayer nickelate La$<em>{3}$Ni$</em>{2}$O$<em>{7}$ has raised the question of how its spin-density-wave (SDW) state evolves toward the superconducting regime. Here, we report a systematic electronic Raman study of La$</em>{3}$Ni$<em>{2}$O$</em>{7}$ single crystals under hydrostatic pressures up to 16.51 GPa. Both the SDW gap energy and the transition temperature $T_{\mathrm{SDW}}$ show an overall increase with pressure, while the dimensionless coupling ratio 2$Δ<em>{\text{SDW}}/(k</em>{\text{B}}T_{\text{SDW}})$ remains constant around $\sim7.5$, indicating a robust strong-coupling character of SDW state. At the same time, the Raman SDW peak broadens as pressure is applied, indicating a gradual weakening of long-range SDW order. These results reveal an unusual pressure evolution in which the SDW energy scale is enhanced while the SDW state becomes progressively less coherent, providing spectroscopic constraints on the magnetic correlations relevant to superconductivity in bilayer nickelates.

• The paper uses polarization-resolved Raman spectroscopy up to 16.51 GPa to show that the SDW gap increases by about 20%, from 41.3 to 49.6 meV, while superconductivity emerges near 14 GPa.
• The pressure-independent ratio 2ΔSDW/kBTSDW ≈ 7.5, more than twice the weak-coupling value, indicates that La₃Ni₂O₇ remains a strong-coupling SDW system as pressure enhances its overall magnetic energy scale.
• Increasing SDW linewidth under pressure signals reduced spectroscopic coherence, potentially caused by stronger electronic scattering, broader transition energies, or spatial coexistence near the SDW–superconductivity boundary.

Context and motivation

The discovery of superconductivity near 80 K in pressurized La$_3$Ni$_2$O$_7$ established the bilayer nickelate as a platform for studying the interplay between magnetism and high-temperature superconductivity. Theoretical work frames its low-energy physics within a bilayer $t$–$J$ model with strong interlayer exchange, supported by ARPES observations of band renormalization, RIXS and neutron measurements of interlayer spin correlations, and transport evidence of density-wave gaps. Prior to this study, however, the pressure evolution of magnetic order had been established only through phase boundaries: NMR and $\mu$SR showed that $T_{\mathrm{SDW}}$ rises with pressure but only up to roughly 3 GPa, far below the ~14 GPa onset of superconductivity, while transport on the intergrowth compound La$_5$Ni$_3$O$_{11}$ suggested continued increase to about 13 GPa. No spectroscopic measurement of the SDW excitation spectrum under pressure existed. This paper fills that gap with polarization-resolved electronic Raman scattering on La$_2$0Ni$_2$1O$_2$2 single crystals under hydrostatic pressures up to 16.51 GPa (2608.17505).

An additional motivation is an unresolved interpretive dispute at ambient pressure. One set of Raman studies attributes the $_2$3 and $_2$4 features below $_2$5 K to anisotropic SDW-gap excitations, whereas Gim et al. assign the dominant features to two-magnon exchange processes. Both interpretations tie the Raman response to the magnetic state, so tracking these features under pressure is informative regardless of which microscopic assignment is correct.

Experimental approach

High-quality single crystals grown by vertical optical floating-zone technique (15 bar O$_2$6, 5 kW xenon lamp) were measured in a membrane-driven diamond anvil cell with argon as pressure-transmitting medium, using 550 $_2$7m culet Type-IIa anvils and ruby fluorescence calibration. Raman spectra were collected at the Hefei Light Source with a 532 nm laser (~1.3 mW, ~10 $_2$8m spot), a He-flow cryostat allowing temperature sweeps from 20 K to 300 K at each pressure. At each pressure the sample was cooled first and spectra collected on warming. The analysis focuses on the $_2$9 channel because the SDW-related feature shows pronounced pressure dependence there, unlike $_7$0. Spectra were fit with a memory-function description of the low-energy electronic continuum plus a Lorentzian for the SDW peak.

Pressure evolution of the SDW energy scale

At 20 K and 1.23 GPa, the $_7$1 response exhibits a broad feature near 700 cm$_7$2, previously associated with interband transitions across the SDW gap. This feature remains discernible over nearly the entire measured range and shifts progressively upward in energy with pressure. Quantitatively, the extracted gap $_7$3 increases monotonically from approximately 41.3 meV at 1.23 GPa to about 49.6 meV near 13 GPa — a ~20% enhancement — while $_7$4, obtained from the temperature dependence of the integrated spectral weight, increases in parallel. Combining these data with prior NMR, $_7$5SR, and transport results yields an extended $_7$6–$_7$7 phase diagram in which superconductivity emerges near 14 GPa inside the still-ordered SDW regime.

The central quantitative result is that the dimensionless coupling ratio

$_7$8

remains essentially constant across the full pressure range. This value is more than twice the weak-coupling mean-field value of 3.52, indicating that the SDW state resides deep in the strong-coupling regime and that pressure enhances the overall SDW energy scale without altering its coupling strength. The implication is that pressure acts primarily on microscopic parameters (hopping integrals) rather than on the nature of the ordered state itself.

Broadening and loss of coherence

Simultaneously, the SDW peak linewidth $_7$9 increases progressively with pressure. Since the linewidth reflects both the distribution of interband transition energies between SDW-reconstructed states and the electronic scattering rate, this broadening indicates enhanced damping or a wider distribution of transition energies — in either case, a progressively less well-defined SDW electronic response. The authors propose two contributing mechanisms: enhanced electronic scattering under compression, and pressure-induced spatial inhomogeneity near the SDW–superconductivity phase boundary, by analogy with nanoscale phase coexistence observed in manganites, VO$t$0, and fluctuating density-wave correlations in cuprates. Notably, direct evidence for such inhomogeneity in La$t$1Ni$t$2O$t$3 is not presented here; it is invoked as a plausible mechanism consistent with reported heterogeneous superconductivity in this material.

Comparison with other superconducting families

The behavior contrasts sharply with established systems. In the 122 iron pnictides, hydrostatic pressure generally suppresses SDW order; FeSe shows nonmonotonic behavior in which pressure initially stabilizes magnetism before suppressing it; and stripe-ordered cuprates exhibit competition between static spin order and superconducting volume fraction under pressure or uniaxial stress. In La$t$4Ni$t$5O$t$6, both $t$7 and $t$8 rise monotonically with no downturn through 16.51 GPa, even as superconductivity develops. This distinct response suggests that the conventional picture of pressure suppressing long-range magnetism en route to superconductivity does not apply straightforwardly to bilayer nickelates.

Microscopic interpretation

The enhancement of both SDW scales is consistent with pressure-induced strengthening of magnetic exchange. Compression shortens Ni–O bonds and modifies Ni–O–Ni angles, enhancing Ni $t$9–O $J$0 overlap and increasing the hopping integral $J$1; since $J$2, the superexchange grows. Because theoretical work identifies strong interlayer exchange as central to superconductivity in this system, the same pressure-tuned interactions plausibly govern both orders. The coexistence of rising SDW energy scales with emerging superconductivity is consistent with theoretical proposals that pressure weakens long-range SDW coherence while enhancing magnetic fluctuations, though the present data constrain only spectroscopic coherence, not the ordered moment directly.

Limitations and open questions

Several caveats bear on the interpretation. First, the microscopic origin of the Raman feature remains contested: if two-magnon scattering dominates rather than interband gap excitations, the extracted "gap" would instead track a magnetic exchange energy, altering the meaning of the constant coupling ratio (though the strong-coupling conclusion would survive). Second, the linewidth broadening has multiple candidate origins — damping, transition-energy distribution, or spatial inhomogeneity — that the present measurements cannot disentangle; no direct structural or real-space probe accompanies the Raman data. Third, the origin of the additional density-wave transition marked in the phase diagram remains debated. Finally, whether the monotonic rise of $J$3 persists above 16.51 GPa, and how the SDW order parameter ultimately terminates relative to the superconducting dome, are left unresolved.

Conclusion

This work provides the first Raman spectroscopic characterization of the SDW state in a bilayer nickelate under pressure. Its principal findings are a ~20% monotonic enhancement of $J$4 from 41.3 meV to 49.6 meV up to ~13 GPa, a parallel rise of $J$5 yielding a pressure-independent strong-coupling ratio of ~7.5, and progressive linewidth broadening signaling reduced SDW coherence. Together these results establish an unconventional pressure evolution — enhanced SDW energy scale coexisting with diminishing long-range coherence — and impose spectroscopic constraints on any theory connecting magnetism to high-temperature superconductivity in the bilayer nickelates.