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Register a new userSpin correlations of quantum-spin-liquid and quadrupole-ordered states of Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$
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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.
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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.
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.
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.
The pyrochlore material $rm Ho_{2}Ti_{2}O_{7}$ has been suggested to show ``spin ice behaviour. We present neutron scattering and specific heat results that establish unambiguously that Ho$_2$Ti$_2$O$_7$ exhibits spin ice correlations at low temperature. Diffuse magnetic neutron scattering from Ho$_2$Ti$_2$O$_7$ is found to be quite well described by a near neighbour spin ice model and very accurately described by a dipolar spin ice model. The heat capacity is well accounted for by the sum of a dipolar spin ice contribution and an expected nuclear spin contribution, known to exist in other Ho$^{3+}$ salts. These results settle the question of the nature of the low temperature spin correlations in $rm Ho_{2}Ti_{2}O_{7}$ for which contradictory claims have been made.
The pyrochlore magnet Tb$_{2}$Ti$_{2}$O$_{7}$ shows a lack of magnetic order to low temperatures and is considered to be a quantum spin liquid candidate. We perform time-domain THz spectroscopy on high quality Tb$_{2}$Ti$_{2}$O$_{7}$ crystal and study the low energy excitations as a function of [111] magnetic field with high energy resolution. The low energy crystal field excitations change their energies anomalously under magnetic field. Despite several sharp field dependent changes, we show that the materials spectrum can be described not by a phase transitions, but by field dependent hybridization between the low energy crystal field levels. We highlight the strong coupling between spin and lattice degrees of freedom in Tb$_{2}$Ti$_{2}$O$_{7}$ as evidenced by the magnetic field tunable crystal field environment. Calculations based on single ion physics with field induced symmetry reduction of the crystal field environment can reproduce our data.
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