Lack of evidence for a singlet crystal-field ground state in the magnetic pyrochlore Tb${}_2$Ti${}_2$O${}_7$

We present high-resolution inelastic neutron scattering data on the candidate spin liquid Tb${}_2$Ti${}_2$O${}_7$. We find that there is no evidence for a zero-field splitting of the ground-state doublet within the $0.2$ K resolution of the instrument. This result contrasts with a pair of recent works claiming that the spin-liquid behavior of Tb${}_2$Ti${}_2$O${}_7$ can be attributed to a 2 K split singlet-singlet single-ion spectrum at low energies. We also reconsider the entropy argument presented by Chapuis et al. [Phys. Rev. B 82, 100420 (2010)] as further evidence of a singlet-singlet crystal-field spectrum. We argue that estimates of the low-temperature residual entropy drawn from specific heat measurements are a poor guide to the single-ion spectrum without a proper understanding of the nature of the correlations in the spin-liquid regime.

Figure 1

Inelastic neutron scattering data taken with $\lambda =5$ Å neutrons on DCS (Ref.21). (a) False color map of the 400 mK, ${\mu }_{0}H=0$ data integrated over a wide range of $\left[HH0\right]$. (b) Magnetic scattering for ${\mu }_{0}H=0$, 400 mK, which is well described by a sharp elastic and a broad quasielastic component (solid line; see text). These data result from subtracting the incoherent nuclear scattering from the ${\mu }_{0}H=3$ T data (open red symbols) from the ${\mu }_{0}H$ $=$ 0 data (solid blue symbols in inset). Error bars are $\pm$1 $\sigma$.

Figure 2

Very high energy-resolution INS data employing $\lambda =9$ Å incident neutrons with DCS, as described in the text. The zero field measurement shows the quasielastic magnetic distribution of scattering to extend down to at least 0.02 meV.

Figure 3

Panel (a) shows the specific heat, $C$ (black, arrow to leftaxis) and entropy, $S$ (red, arrow to right axis), for a one-dimensional spin-$3/2$ Ising model with $J=0$ (solid lines) and $J/\Delta =0.05$ (dashed lines). The $S$ plateau in panel (a) at low temperature is at $\ln 2$. Panel (b) shows the entropy for a one-dimensional spin-$3/2$ Ising model with $J/\Delta$ from 0 to $0.10$. The plateau gradually disappears as $J/\Delta$ increases (illustrated by the direction of the downward arrow).