Pressure and oxygen-isotope substitution on density-wave transitions in La₄⁢Ni₃⁢O₁₀

Understanding the interplay between magnetism and superconductivity in nickelate systems is a key objective in condensed matter physics. Gaining microscopic insights into magnetism—particularly as it emerges near superconductivity—requires a synergistic approach that combines complementary experimental techniques with controlled tuning of external parameters. In this paper, we present a systematic investigation of the three-layer Ruddlesden-Popper (RP) nickelate La₄⁢Ni₃⁢O₁₀ using muon-spin rotation/relaxation (𝜇⁢SR) and resistivity measurements. At ambient pressure, two incommensurate spin-density-wave (SDW) transitions are identified at 𝑇_SDW≃132K and 𝑇*≃80–90K. Comparison of the observed internal magnetic fields with dipole-field calculations reveals a magnetic structure consistent with antiferromagnetically coupled SDW order on the outer two Ni-O layers, with smaller moments on the inner Ni-O layer. Above 𝑇*, the moments lie primarily in the 𝑎⁢𝑏plane, but below this temperature they undergo a subtle distortion and develop a 𝑐-axis component. The internal fields at the muon stopping sites appear abruptly at 𝑇_SDW, suggesting a first-order-like nature of the SDW transition, which is closely linked to the charge-density wave (CDW) order occurring at the same temperature (𝑇_SDW=𝑇_CDW). Under applied pressure, all transition temperatures—including 𝑇_SDW, 𝑇*, and 𝑇_CDW—are suppressed at a nearly uniform rate of ≃−13 K/GPa. This behavior contrasts with that of the two-layer RP nickelate La₃⁢Ni₂⁢O₇, where pressure enhances the separation between the SDW and CDW transitions. The oxygen-isotope substitution (¹⁶O  → ¹⁸O) reveals that the CDW transition temperature shifts to higher values in the 18O-substituted samples. The isotope effect on 𝑇SDW and 𝑇* differs significantly. Specifically, when the CDW and SDW orders are intertwined, a notable isotope effect is observed on 𝑇SDW, leading to equal transition temperatures and nearly identical isotope shifts for both 𝑇_CDW and 𝑇_SDW. In contrast, at 𝑇*, where the SDW transition occurs independently of the CDW, no isotope effect is detected.