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Register a new userSelective probing of magnetic order on Tb and Ir sites in stuffed Tb$_{2+x}$Ir$_{2-x}$O$_{7-y}$ using resonant X-ray scattering
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We study the magnetic structure of the stuffed (Tb-rich) pyrochlore iridate Tb$_{2+x}$Ir$_{2-x}$O$_{7-y}$, using resonant elastic x-ray scattering (REXS). In order to disentangle contributions from Tb and Ir magnetic sublattices, experiments were performed at the Ir $L_3$ and Tb $M_5$ edges, which provide selective sensitivity to Ir $5d$ and Tb $4f$ magnetic moments, respectively. At the Ir $L_3$ edge, we found the onset of long-range ${bf k}={bf 0}$ magnetic order below $T_{N}^text{Ir}sim$ 71 K, consistent with the expected signal of all-in all-out (AIAO) magnetic order. Using a single-ion model to calculate REXS cross-sections, we estimate an ordered magnetic moment of $mu_{5d}^{text{Ir}} approx 0.34(3),mu_B$ at 5 K. At the Tb $M_5$ edge, long-range ${bf k}={bf 0}$ magnetic order appeared below $sim40$ K, also consistent with an AIAO magnetic structure on the Tb site. Additional insight into the magnetism of the Tb sublattice is gleaned from measurements at the $M_5$ edge in applied magnetic fields up to 6 T, which is found to completely suppress the Tb AIAO magnetic order. In zero applied field, the observed gradual onset of the Tb sublattice magnetisation with temperature suggests that it is induced by the magnetic order on the Ir site. The persistence of AIAO magnetic order, despite the greatly reduced ordering temperature and moment size compared to stoichiometric Tb$_{2}$Ir$_{2}$O$_{7}$, for which $T_{N}^{text{Ir}} =130$ K and $mu_{5d}^{text{Ir}}=0.56,mu_B$, indicates that stuffing could be a viable means of tuning the strength of electronic correlations, thereby potentially offering a new strategy to achieve topologically non-trivial band crossings in pyrochlore iridates.
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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 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.
Spin correlations of the frustrated pyrochlore oxide Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$ have been investigated by using inelastic neutron scattering on single crystalline samples ($x=-0.007, 0.000,$ and $0.003$), which have the putative quantum-spin-liquid (QSL) or electric-quadrupolar ground states. Spin correlations, which are notably observed in nominally elastic scattering, show short-ranged correlations around $L$ points [$q = (tfrac{1}{2},tfrac{1}{2},tfrac{1}{2})$], tiny antiferromagnetic Bragg scattering at $L$ and $Gamma$ points, and pinch-point type structures around $Gamma$ points. The short-ranged spin correlations were analyzed using a random phase approximation (RPA) assuming the paramagnetic state and two-spin interactions among Ising spins. These analyses have shown that the RPA scattering intensity well reproduces the experimental data using temperature and $x$ dependent coupling constants of up to 10-th neighbor site pairs. This suggests that no symmetry breaking occurs in the QSL sample, and that a quantum treatment beyond the semi-classical RPA approach is required. Implications of the experimental data and the RPA analyses are discussed.
The ground states of the frustrated pyrochlore oxide Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$ have been studied by inelastic neutron scattering experiments. Three single-crystal samples are investigated; one shows no phase transition ($x=-0.007<x_{text{c}}sim -0.0025$), being a putative quantum spin-liquid (QSL), and the other two ($x=0.000, 0.003$) show electric quadrupole ordering (QO) below $T_{text{c}} sim 0.5$ K. The QSL sample shows continuum excitation spectra with an energy scale 0.1 meV as well as energy-resolution limited (nominally) elastic scattering. As $x$ is increased, pseudospin wave of the QO state emerges from this continuum excitation, which agrees with that of powder samples and consequently verifies good $x$ control for the present single crystal samples.
In this study, we employ bulk electronic properties characterization and x-ray scattering/spectroscopy techniques to map the structural, magnetic and electronic properties of (Eu$_{1-x}$Ca$_{x}$)$_{2}$Ir$_{2}$O$_{7}$ as a function of Ca-doping. As expected, the metal-insulator transition temperature, $T_{MIT}$, decreases with Ca-doping until a metallic state is realized down to 2 K. In contrast, $T_{AFM}$ becomes decoupled from the MIT and (likely short-range) AFM order persists into the metallic regime. This decoupling is understood as a result of the onset of an electronically phase separated state, the occurrence of which seemingly depends on both synthesis method and rare earth site magnetism. PDF analysis suggests that electronic phase separation occurs without accompanying chemical phase segregation or changes in the short-range crystallographic symmetry while synchrotron x-ray diffraction confirms that there is no change in the long-range crystallographic symmetry. X-ray absorption measurements confirm the $J_{eff}$ = 1/2 character of (Eu$_{1-x}$Ca$_{x}$)$_{2}$Ir$_{2}$O$_{7}$. Surprisingly these measurements also indicate a net electron doping, rather than the expected hole doping, indicating a compensatory mechanism. Lastly, XMCD measurements show a weak Ir magnetic polarization that is largely unaffected by Ca-doping.
Recent low temperature heat capacity (C$_P$) measurements on polycrystalline samples of the pyrochlore antiferromagnet Tb$_{2+x}$Ti$_{2-x}$O$_{7+delta}$ have shown a strong sensitivity to the precise Tb concentration $x$, with a large anomaly exhibited for $x sim 0.005$ at $T_C sim 0.5$ K and no such anomaly and corresponding phase transition for $x le 0$. We have grown single crystal samples of Tb$_{2+x}$Ti$_{2-x}$O$_{7+delta}$, with approximate composition $x=-0.001, +0.0042$, and $+0.0147$, where the $x=0.0042$ single crystal exhibits a large C$_P$ anomaly at $T_C$=0.45 K, but neither the $x=-0.001$ nor the $x=+0.0147$ single crystals display any such anomaly. We present new time-of-flight neutron scattering measurements on the $x=-0.001$ and the $x=+0.0147$ samples which show strong $left(frac{1}{2},frac{1}{2},frac{1}{2}right)$ quasi-Bragg peaks at low temperatures characteristic of short range antiferromagnetic spin ice (AFSI) order at zero magnetic field but only under field-cooled conditions, as was previously observed in our $x = 0.0042$ single crystal. These results show that the strong $left(frac{1}{2},frac{1}{2},frac{1}{2}right)$ quasi-Bragg peaks and gapped AFSI state at low temperatures under field cooled conditions are robust features of Tb$_2$Ti$_2$O$_7$, and are not correlated with the presence or absence of the C$_P$ anomaly and phase transition at low temperatures. Further, these results show that the ordered state giving rise to the C$_P$ anomaly is confined to $0 leq x leq 0.01$ for Tb$_{2+x}$Ti$_{2-x}$O$_{7+delta}$, and is not obviously connected with conventional order of magnetic dipole degrees of freedom.
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