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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 showsthe 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 theordered state are 170 \AA\ and 0.7 ns, respectively. $\mu$SR experiments yieldan upper bound 2.6(7) mT on the local field $B_\mathrm{loc}^{4f}$ at the muonsite, which is nearly two orders of magnitude smaller than the expected dipolarfield 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 thenon-Kramers crystal-field ground-state doublets of near-neighbor Pr$^{3+}$ ionsby the $\mu^+$-induced lattice distortion. For this to be the only effect,however, $\sim$160 Pr moments out to a distance of $\sim$14 \AA\ must besuppressed. An alternative scenario, which is consistent with the observedreduced nuclear hyperfine Schottky anomaly in the specific heat, invokes slowcorrelated Pr-moment fluctuations in the ordered state that average$B_\mathrm{loc}^{4f}$ on the $\mu$SR time scale (${\sim}10^{-7}$ s), but arestatic on the time scale of the elastic neutron scattering experiments(${\sim}10^{-9}$ s). In this picture the dynamic muon relaxation suggests aPr$^{3+}$ $4f$ correlation time of a few nanoseconds, which should beobservable in a neutron spin echo experiment.

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