Vindication of ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ as a Model Exchange Quantum Spin Ice

We use numerical linked-cluster expansions to compute the specific heat $C(T)$ and entropy $S(T)$ of a quantum spin ice Hamiltonian for ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ using anisotropic exchange interactions, recently determined from inelastic neutron scattering measurements, and find good agreement with experimental calorimetric data. This vindicates ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ as a model quantum spin ice. We find that in the perturbative weak quantum regime, such a system has a ferrimagnetic ordered ground state, with two peaks in $C(T)$: a Schottky anomaly signaling the paramagnetic to spin ice crossover, followed at a lower temperature by a sharp peak accompanying a first-order phase transition to the ordered state. We suggest that the two $C(T)$ features observed in ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ are associated with the same physics. Spin excitations in this regime consist of weakly confined spinon-antispinon pairs. We anticipate that the conventional ground state with exotic quantum dynamics will prove a prevalent characteristic of many real quantum spin ice materials.

Figure 1

(a) Two neighboring tetrahedra with spins in their two-in–two-out ground state, (b) spinon-antispinon pair, and (c) spinon-antispinon pair separated by a (green) string of misaligned spins in the pyrochlore lattice.

Figure 2

Heat capacity $C(T)$ per mole of Yb for the model parameters in Ref. 16, in units of the Boltzmann constant $k_{\mathrm{B}}$, calculated via NLC (up to the fourth order NLC together with Euler extrapolations) are compared with experimental data for ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. The filled small black circles are data from Ref. 25.

Figure 3

Entropy $S(T)$ per mole of Yb, in units of $k_{\mathrm{B}}$, following the methods described in the caption of Fig. 2. The black circles are obtained by integrating the data from Ref. 25 excluding the nuclear (hyperfine) contribution. The Pauling entropy $S_{\mathrm{P}}\sim \frac{k_{\mathrm{B}}}{2}\ln \frac{3}{2}$ is shown as a horizontal line. The inset shows $S(T)$ in the perturbative regime with $J_3/J_{zz}=-0.001$. A clear plateau at $S(T)\approx S_{\mathrm{P}}$ is seen, followed at lower $T$ by a precipitous drop of $S(T)$ (i.e., latent heat) accompanying the transition to long-range FM order [33].

Figure 4

Defect density $\rho (T)$ calculated using NLC, shown down to a temperature where the third- and fourth-order Euler transforms agree. Here, quantum exchanges are scaled with respect to the YbTO $\{J_e\}$ parameters by different values of $\lambda$.