Multiple magnetic transitions in the trilayer nickelate Pr₄Ni₃O₁₀ revealed by muon-spin rotation

A muon-spin rotation/relaxation (µSR) study of the trilayer Ruddlesden–Popper nickelate Pr₄Ni₃O₁₀ was performed at ambient pressure and under hydrostatic pressure up to 2.2 GPa. Three magnetic transitions were identified at ambient pressure: the onset of spin-density-wave (SDW) order at T_SDW ≃ 158 K, an intermediate-temperature transition at T^∗ ≃ 90–100 K, and a low-temperature transition at T_SDW^Pr ≃ 25–27 K. While the intermediate transition at T^∗ induces only minor changes in the internal-field distribution, the transition at T_SDW^Pr is accompanied by a pronounced reconstruction of the magnetic structure, consistent with previous reports attributing enhanced interlayer coherence to the ordering of the Pr sublattice. The high-temperature transition at TSDW is characterized by the sharp development of static internal magnetic fields with a narrow transition width of 0.65(4) K. Weak-transverse-field measurements reveal a finite thermal hysteresis of 0.27(6) K, with T_SDW^warming > T_SDW^cooling , indicating weakly first-order-like behavior. Hydrostatic pressure suppresses T_SDW linearly and reduces the ordered Ni magnetic moment M, with corresponding rates of dT_SDW/dp = −4.9(1) K/GPa and d ln M/dp = −2.0(5) ×10⁻² GPa⁻¹, respectively, thereby demonstrating a gradual weakening of the SDW instability under compression.