Spin correlations in the geometrically frustrated pyrochlore ${\text{Tb}}_2{\text{Mo}}_2{\text{O}}_7$

We report neutron-scattering studies of the spin correlations of the geometrically frustrated pyrochlore ${\text{Tb}}_2{\text{Mo}}_2{\text{O}}_7$ using single-crystal samples. This material undergoes a spin-freezing transition below $T_g\simeq 24\text{K}$, similar to ${\text{Y}}_2{\text{Mo}}_2{\text{O}}_7$, and has little apparent chemical disorder. Diffuse elastic peaks are observed at low temperatures, indicating short-range ordering of the Tb moments in an arrangement where the Tb moments are slightly rotated from the preferred directions of the spin-ice structure. In addition, a $\vec{Q}$-independent signal is observed which likely originates from frozen but completely uncorrelated Tb moments. Inelastic measurements show the absence of sharp peaks due to crystal-field excitations. These data show how the physics of the Tb sublattice responds to the glassy behavior of the Mo sublattice with the associated effects of lattice disorder.

Figure 1

(Color online) Elastic scattering measured on SPINS spectrometer. (a) Intensity at the (002) diffuse magnetic peak position and the “background” signal measured at the (112) position as a function of temperature. Inset: Magnetic susceptibility measured with $H=10\text{Oe}$ along the [111] direction using a superconducting quantum interference device (SQUID) magnetometer. Scans through the (b) (002) position and the (c) (111) position at various temperatures. The horizontal bar indicates the instrumental resolution.

Figure 2

(Color online) (a) Correlation lengths of the short-range order along different symmetry directions as a function of temperature. Inset: Representative scans through the (111) position measured on the BT9 spectrometer, where the horizontal bar indicates the instrumental resolution. (b) Temperature dependence of the diffuse peak intensities.

Figure 3

(Color online) (a) Pattern of the elastic-scattering intensity at $T=1.5\text{K}$ measured on BT9 in the $\left(HHL\right)$ zone. Data points due to scattering from nuclear Bragg peaks and Al powder lines (indicated by white regions) were removed in order to emphasize the diffuse magnetic scattering. (b) Calculated scattering pattern for short-range-ordered regions with the spin structure shown in the inset, which are domain averaged as described in the text. A constant background of 60 counts (which approximates the average background in the data) was added to the calculation.

Figure 4

(Color online) Inelastic-scattering data. (a) High-resolution measurements taken on SPINS at the (1.1, 1.1, 1) position in a single crystal. (b) Higher-energy data taken on the BT7 spectrometer (with $E_f=14.7\text{meV}$ and horizontally focused analyzer) on a powder sample at $\left|\vec{Q}\right|=3{\text{Å}}^{-1}$. Inset: Temperature dependence of the scattering at $\hslash \omega =4.5\text{meV}$.