Dimensional evolution of spin correlations in the magnetic pyrochlore Yb${}_2$Ti${}_2$O${}_7$

The pyrochlore material Yb${}_2$Ti${}_2$O${}_7$ displays unexpected quasi-two-dimensional (2D) magnetic correlations within a cubic lattice environment at low temperatures, before entering an exotic disordered ground state below $T=265$ mK. We report neutron scattering measurements of the thermal evolution of the 2D spin correlations in space and time. Short-range three-dimensional (3D) spin correlations develop below 400 mK, accompanied by a suppression in the quasielastic (QE) scattering below $\sim$0.2 meV. These show a slowly fluctuating ground state with spins correlated over short distances within a kagome-triangular-kagome (KTK) stack along [111], which evolves to isolated kagome spin stars at higher temperatures. Furthermore, low-temperature specific heat results indicate a sample dependence to the putative transition temperature that is bounded by 265 mK, which we discuss in the context of recent mean field theoretical analysis.

Figure 1

(a) The temperature dependence of neutron scattering intensity at two Q points that lie on the rod of scattering, Q${}_{1.54}$ (red crosses) and Q${}_{1.07}$ (blue circles) (10 K background subtracted). Bottom inset: the position of the two Q points is shown relative to the fcc Brillouin zone boundaries in the (HHL) plane. Top inset: the difference of intensities, $I_{1.07}-I_{1.54}$, with the solid line as a guide to the eye. (b) Elastic time-of-flight neutron scattering data at 30 and 500 mK (reproduced from Ref. 21). Error bars represent $\pm$1$\sigma$.

Figure 2

(a) (10 K background subtracted) Longitudinal rod scans at $T=60$ and 300 mK. Data points at 540 mK are consistent with a Q dependence that follows the Yb${}^{3+}$ magnetic form factor (black solid line). (b) Examples of transverse scans across the rod, centered at Q${}_{1.07}$ and Q${}_{1.54}$. The insets show the positions of the scans in reciprocal space.

Figure 3

(a) Full width at half maxima (FWHM) and (b) integrated area extracted from the Lorentzian fits to the transverse scans shown in Fig. 2a. (c) The range of ${\xi }_T$ within the kagome layer. Above 400 mK (black), the correlations are restricted to a single kagome star unit. Below 265 mK (blue), the transverse correlations grow only to encompass the next-near neighbors in the kagome layer. (d) The pyrochlore lattice decomposed into kagome and interleaved triangular layers. Below 400 mK, the longitudinal correlations extend only between a single KTK unit.

Figure 4

Energy dependence of the diffuse scattering above and below $T_c$, both on and off the rod of scattering. Thick lines are guides to the eye. Inset: range of binning for the on- and off-rod positions. On-rod: HHH $=$ [1.2,1.6], HH-2H$=[-0.1,0.1]$. Off-rod: HHH $=$ [1.2,1.6], HH-2H = [0.3,0.5].

Figure 5

Examples of low-temperature specific heat in Yb${}_2$Ti${}_2$O${}_7$. Significant sample dependence is observed in both powders and single crystals. The powder sample prepared at McMaster University shows the highest temperature (265 mK) and sharpest anomaly. The neutron scattering sample, B, shows a sharp peak at 265 mK similar to the powder, and a broad, low-temperature feature similar to crystal A. None of the samples studied had any feature at 400 mK.

Figure 6

Neutron diffraction data from two samples of Yb${}_2$Ti${}_2$O${}_7$ taken at 250 K: a sintered powder (top) and a crushed single crystal (bottom). The result of Rietveld analysis, using a fully ordered model for Yb${}_2$Ti${}_2$O${}_7$, is shown in red. The difference between the measured and calculated profiles is in black.