Unstable Spin-Ice Order in the Stuffed Metallic Pyrochlore Pr$_{2+x}$Ir$_{2-x}$O$_{7-\delta}$

TL;DR

This study investigates the magnetic order and fluctuations in a stuffed Pr$_{2+x}$Ir$_{2-x}$O$_{7- ext{delta}}$ sample, revealing long-range spin-ice order with unusual local field behavior likely due to slow Pr-moment fluctuations.

Contribution

It provides the first detailed experimental analysis of spin-ice order and fluctuations in a stuffed metallic pyrochlore, highlighting the role of slow Pr-moment dynamics.

Findings

Long-range spin-ice order appears below 0.93 K with a 1.7 μB moment.

Muon experiments show a much smaller local field than expected for static order.

Evidence suggests slow Pr-moment fluctuations cause the reduced local field.

Abstract

Specific heat, elastic neutron scattering, and muon spin rotation ($\mu$SR) experiments have been carried out on a well-characterized sample of "stuffed" (Pr-rich) Pr$_{2+x}$Ir$_{2-x}$O$_{7-\delta}$. Elastic neutron scattering shows the onset of long-range spin-ice "2-in/2-out" magnetic order at $T_M = 0.93$ K, with an ordered moment of 1.7(1)$\mu_\mathrm{B}$/Pr ion at low temperatures. Approximate lower bounds on the correlation length and correlation time in the ordered state are 170 \AA\ and 0.7 ns, respectively. $\mu$SR experiments yield an upper bound 2.6(7) mT on the local field $B_\mathrm{loc}^{4f}$ at the muon site, which is nearly two orders of magnitude smaller than the expected dipolar field for long-range spin-ice ordering of 1.7$\mu_B$ moments (120--270 mT, depending on muon site). This shortfall is due in part to splitting of the non-Kramers crystal-field ground-state doublets of near-neighbor Pr$^{3+}$ ions by the $\mu^+$-induced lattice distortion. For this to be the only effect, however, $\sim$160 Pr moments out to a distance of $\sim$14 \AA\ must be suppressed. An alternative scenario, which is consistent with the observed reduced nuclear hyperfine Schottky anomaly in the specific heat, invokes slow correlated Pr-moment fluctuations in the ordered state that average $B_\mathrm{loc}^{4f}$ on the $\mu$SR time scale (${\sim}10^{-7}$ s), but are static on the time scale of the elastic neutron scattering experiments (${\sim}10^{-9}$ s). In this picture the dynamic muon relaxation suggests a Pr$^{3+}$ $4f$ correlation time of a few nanoseconds, which should be observable in a neutron spin echo experiment.