Multiple Magnetic Transitions in the Trilayer Nickelate Pr$_4$Ni$_3$O$_{10}$ Revealed by Muon-Spin Rotation

Abstract

A muon-spin rotation/relaxation ($\mu$SR) study of the trilayer Ruddlesden--Popper nickelate Pr$_4$Ni$_3$O$_{10}$ 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 $T_{\rm SDW} \simeq 158$ K, an intermediate-temperature transition at $T^{\ast} \simeq 90$--100 K, and a low-temperature transition at $T_{\rm SDW}^{\rm Pr} \simeq 25$--27 K. While the intermediate transition at $T^{\ast}$ induces only minor changes in the internal-field distribution, the transition at $T_{\rm SDW}^{\rm Pr}$ 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 $T_{\rm SDW}$ 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 $T_{\rm SDW}^{\rm warming} > T_{\rm SDW}^{\rm cooling}$, indicating weakly first-order-like behavior. Hydrostatic pressure suppresses $T_{\rm SDW}$ linearly and reduces the ordered Ni magnetic moment $M$, with corresponding rates of ${\rm d}T_{\rm SDW}/{\rm d}p = -4.9(1)$ K/GPa and ${\rm d}\ln M/{\rm d}p = -2.0(5)\times10^{-2}$ GPa$^{-1}$, respectively, thereby demonstrating a gradual weakening of the spin-density-wave instability under compression.