Pressure-Invariant Isotope Effect as Evidence for Electronically Driven Intertwined Order in Pr$_4$Ni$_3$O$_{10}$

Abstract

We report muon-spin rotation measurements of the pressure dependence of the oxygen-isotope ($^{16}$O/$^{18}$O) effect on the spin-density wave (SDW) transition in the trilayer Ruddlesden-Popper nickelate Pr$_4$Ni$_3$O$_{10}$. At ambient pressure, the SDW transition shows a finite isotope shift, with $^{16}T_{\rm SDW}=158.04(5)$ K and $^{18}T_{\rm SDW}=159.81(6)$ K. Under hydrostatic pressure, $T_{\rm SDW}$ decreases linearly at nearly identical rates for the two isotope compositions, ${\rm d}\,^{16}T_{\rm SDW}/{\rm d}p=-4.93(5)$ K/GPa and ${\rm d}\,^{18}T_{\rm SDW}/{\rm d}p=-4.90(7)$ K/GPa, such that the isotope shift remains essentially unchanged 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 new regime of intertwined order in trilayer RP nickelates, which is stabilized by strong spin interactions.

Figures (3)

• Figure 1: (a) Raman spectra of Pr$_4$Ni$_3$$^{16}$O$_{10}$ (red) and Pr$_4$Ni$_3$$^{18}$O$_{10}$ (blue). Vertical dashed lines indicate the Raman mode positions. Solid lines are Lorenzian fits. (b) Oxygen participation parameter $f_{\rm O}$ extracted using the partial mass-scaling formalism. The dashed line marks $f_{\rm O}=1$, corresponding to purely oxygen dominated vibrations.
• Figure 2: (a)–(c) Weak-transverse-field (WTF) $\mu$SR time spectra measured at ambient pressure in $B_{\rm WTF}=5$ mT at $T=150$ K (a), 159 K (b), and 180 K (c) for the Pr$_4$Ni$_3$$^{16}$O$_{10}$ (red) and Pr$_4$Ni$_3$$^{18}$O$_{10}$ (blue). (d) Temperature dependence of the magnetic volume fraction $f_{\rm m}$ extracted from the fits. (e) Enlarged view of the transition region. Solid lines are fits using Eq \ref{['eq:Fermi']} with $^{16}T_{\rm SDW}=158.04(5)$ K, $\Delta$$^{16}T_{\rm SDW}=0.69(5)$ K and $^{18}T_{\rm SDW}=159.81(6)$ K, $\Delta$$^{18}T_{\rm SDW}=0.61(6)$ K.
• Figure 3: (a) Temperature dependence of the magnetic volume fraction $f_{\rm m}$ for Pr$_4$Ni$_3$$^{16}$O$_{10}$ and Pr$_4$Ni$_3$$^{18}$O$_{10}$ measured at zero pressure (solid symbols) and at the highest applied pressures (open symbols). Solid lines are fits using Eq. \ref{['eq:Fermi']}. (b) Pressure dependence of the SDW transition temperature. Linear fits yield $^{16}T_{\rm SDW}(p) = 157.52(11)\,{\rm ~K} - p \cdot 4.93(5)\, {\rm ~K/GPa }$ and $^{18}T_{\rm SDW}(p) = 159.17(10)\,{\rm ~K} - p \cdot 4.90(7)\, {\rm ~K/GPa }$. Within experimental uncertainty, the pressure slopes are identical. (c) Pressure dependence of the transition width $\Delta T_{\rm SDW}$.