Evidence from thermodynamic measurements for a singlet crystal-field ground state in pyrochlore ${\text{Tb}}_2{\text{Sn}}_2{\text{O}}_7$ and ${\text{Tb}}_2{\text{Ti}}_2{\text{O}}_7$

The magnetic entropy variation for the ordered spin-ice ${\text{Tb}}_2{\text{Sn}}_2{\text{O}}_7$ and the spin-liquid ${\text{Tb}}_2{\text{Ti}}_2{\text{O}}_7$ measured up to $\sim 20\text{K}$ shows that the crystal-field ground state for both systems is a singlet split from the first excited level by a thermal energy of $\sim 2\text{K}$. It is the superexchange interactions between the ${\text{Tb}}^{3+}$ spins which induce the terbium magnetic moments. Our results are analyzed in terms of a tetragonal perturbation for ${\text{Tb}}_2{\text{Ti}}_2{\text{O}}_7$ and this perturbation plus a molecular field for ${\text{Tb}}_2{\text{Sn}}_2{\text{O}}_7$.

Figure 1

(Color online) Total specific heat $C_{\text{tot}}$ versus temperature measured for a powder sample of ${\text{Tb}}_2{\text{Sn}}_2{\text{O}}_7$. The contribution $C_{\text{lat}}$ from the phonons, i.e., the lattice, is deduced from measurements on the isostructural diamagnetic compound ${\text{Lu}}_2{\text{Sn}}_2{\text{O}}_7$ using a scaling law as explained in the main text. The nuclear contribution $C_{\text{nuc}}$ is directly taken from the estimation of Mirebeau et al. (Ref. 4).

Figure 2

(Color online) Magnetic specific heat (left scale) and magnetic entropy variation (right scale) versus temperature measured in zero field for ${\text{Tb}}_2{\text{Sn}}_2{\text{O}}_7$. The dotted line is the result from a fit with the crystal-field level scheme indicated in the figure.

Figure 3

(Color online) Temperature dependence of the absolute entropy $S_{\text{mag}}$ associated with four crystal-field levels: a nondegenerate ground state, an excited single level located at $\delta$, and a doublet at 17 K. The curves are drawn for five values of $\delta$ (0.0, 0.1, 0.3, 1.0, and 1.8 K). The crystal-field energies are given in temperature scale. $S_{\text{mag}}$ is plotted for temperatures ranging from 0.13 to 20 K. This covers the whole temperature range probed by our measurements.

Figure 4

(Color online) Magnetic entropy variation versus temperature measured in zero field for three differently prepared crystals of ${\text{Tb}}_2{\text{Ti}}_2{\text{O}}_7$ (Ref. 18). The dotted line is the result of a fit with the crystal-field level scheme indicated in the figure.