Pressure-invariant isotope effect as evidence for electronically driven intertwined order in Pr₄Ni₃O₁₀

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 ¹⁶T_SDW = 158.04(5) K and ¹⁸T_SDW = 159.81(6) K. Under hydrostatic pressure, T_SDW decreases linearly at rates that are equal within uncertainty for the two isotope compositions, d¹⁶T_SDW /dp= −4.93(5) K/GPa and d¹⁸T_SDW /dp= −4.90(7) K/GPa, such that the isotope shift remains constant within uncertainty 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 regime of intertwined order in trilayer RP nickelates, which is stabilized by strong spin interactions.