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

Abstract

A muon-spin rotation/relaxation ($μ$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.

Figures (7)

• Figure 1: (a) Room-temperature X-ray powder diffraction pattern of Pr$_4$Ni$_3$O$_{10}$ measured in Bragg--Brentano geometry using Cu K$\alpha$ radiation. Black circles represent the experimental data, and the red solid line shows the Le Bail refinement using the monoclinic $P2_1/a$ space group (No. 14). (b) Neutron powder diffraction pattern collected at $T = 180$ K using the high-resolution thermal neutron diffractometer HRPT HRPT with a wavelength of $\lambda = 1.89$ Å in the $2\theta$ range $3.55^\circ$--$164.50^\circ$ with a step size of $0.05^\circ$. Black circles represent the experimental data, the red solid line shows the Rietveld refinement using the monoclinic $P2_1/a$ space group (No. 14). The ticks and the grey curves in (a) and (b) indicate Bragg reflection positions, and the difference between experimental and calculated intensities, respectively. (c) Thermogravimetric analysis of Pr$_4$Ni$_3$O$_{10}$ measured during hydrogen reduction (7 vol.% H$_2$ in He) with a heating rate of 1 $^\circ$C/min. The total mass loss corresponds to the reduction of fully oxidized Pr$_4$Ni$_3$O$_{10.08(2)}$ to metallic Ni and Pr$_2$O$_3$.
• Figure 2: (a) WTF-$\mu$SR time spectra measured at $B_{\rm WTF}=5$ mT at $T=10$ K and 200 K. The solid lines represent fits using Eq. \ref{['eq:WTF']}. (b) Temperature dependence of the nonmagnetic volume fraction $1-f_{\rm m}$. The solid line represents a fit of $(1-f_{\rm m})$ vs. $T$ in the vicinity of the SDW transition. (c) Temperature dependence of $1-f_{\rm m}$ measured upon warming (black symbols) and cooling (red symbols). The solid lines represent fits using Eq. \ref{['eq:WTF']}. The sample used in hysteresis experiments underwent additional annealing (see Sec. \ref{['sec:Sample_preparation']}), which may have resulted in a slightly different oxygen content ($\delta$) in Pr$_4$Ni$_3$O$_{10+\delta}$. Given the sensitivity of density-wave transitions to oxygen stoichiometry, such small variations in $\delta$ can account for the minor shift in $T_{\rm SDW}$. The larger offset likely reflects a small residual nonmagnetic fraction and/or a slightly different background contribution.
• Figure 3: (a)--(c) ZF-$\mu$SR time spectra measured at $T = 120$ K [panel (a)], 45 K panle (b) and $T = 120$ K [panel (c)]. Solid lines represent fits using Eq. \ref{['eq:asymmetry']} with the sample contribution described by Eqs. \ref{['eq:incommensurate']} and \ref{['eq:GKT']}. The number of magnetic components: 4 in panels (a) and 5 in panles (b) and (c). (d)--(f) Fourier transforms of the data in panels (a)--(c). The selection of the components is arbitrary and it is similar for $T = 45$ K and $T = 10$ K data sets, where the components are labeled from 1 to 8 in order of decreasing internal field, i.e. from the highest to the lowest values. For the $T = 120$ K data set, the components are named according to their continuity from the intermediate- to high-temperature region, as follows form Fig. \ref{['fig:Internal-Fields_Volume-Fractions']}(a).
• Figure 4: Temperature dependence of (a) the internal fields $B_{{\rm int},1}$ to $B_{{\rm int},7}$, and (b) the magnetic volume fractions $f_{{\rm m},1}$ to $f_{{\rm m},5}$ together with the total magnetic fraction $f_{\rm m}=\sum_i f_{{\rm m},i}$ obtained from fits to the ZF-$\mu$SR data. Colored stripes indicate the transition temperatures $T_{\rm SDW}$, $T^{\ast}$, and $T_{\rm SDW}^{\rm Pr}$ separating distinct magnetic regimes. The color coding of the individual components is the same as in Fig. \ref{['fig:ZF-signals']}.
• Figure 5: Temperature dependence of the internal field $B_{{\rm int,}4}$ extracted from the ZF-$\mu$SR analysis. The systematic decrease of $B_{{\rm int,}4}$ toward $T_{\rm SDW}$ reflects the suppression of the ordered magnetic moment at the SDW transition.