Yb${}_2$Sn${}_2$O${}_7$: A magnetic Coulomb liquid at a quantum critical point

We report neutron scattering and ac susceptibility measurements on the pyrochlore Yb${}_2$Sn${}_2$O${}_7$. The appearance of magnetic diffuse scattering, low-energy spin excitations, and a nearly temperature-independent relaxation time are signatures that the system enters a short-range-ordered regime with quantum dynamics beneath 2 K. ac susceptibility data further suggest that Yb${}_2$Sn${}_2$O${}_7$ enters a long-range magnetically ordered state below 0.11 K. These results suggest that Yb${}_2$Sn${}_2$O${}_7$ is a ferromagnet with persistent spin dynamics down to 0.05 K. Referencing the phase diagram for Yb pyrochlores, Yb${}_2$Sn${}_2$O${}_7$ is approaching a quantum phase transition near the ferromagnetic ordered critical point.

Figure 1

(a) The inverse of the temperature dependence of susceptibility of Yb${}_2$Sn${}_2$O${}_7$ measured at ${\mu }_{0}H=0.001$ T. The symbols are experimental data and the solid line is the Curie-Weiss fitting. (b) The temperature dependence of specific heat and calculated variation of magnetic entropy for Yb${}_2$Sn${}_2$O${}_7$. (c) The real (${\chi }^{\prime }$) and (d) imaginary (${\chi }^{\prime \prime }$) parts of the ac susceptibility at different magnetic fields.

Figure 2

Neutron scattering patterns ($\lambda =5.0$ Å) for Yb${}_2$Sn${}_2$O${}_7$ at 0.05 (a), 1.0 (b), 2.0 (c), 3.0 (d), 5.0 (e), and 10 K(f). The 100 K data have been subtracted as a lattice background.

Figure 3

(a) The elastic diffuse scattering at different temperatures, which were obtained by cuts with $-0.02\le E\le 0.02\text{meV}$ from Fig. 2. Inset: The temperature dependence of the integration of diffuse scattering within $0.1\le Q\le 0.12{\text{Å}}^{-1}$. (b) Schematic phase diagram as a function of temperature $T$ and the relative strength $\delta$ of the U(1)-symmetric planar exchange interaction and the Ising exchange for Yb pyrochlores, adopted from Ref. 25. The question mark for Yb${}_2$Ti${}_2$O${}_7$ represents that the ground state of this material is still under debate.

Figure 4

(a) Inelastic spectra obtained by cuts within $0\le Q\le 0.5$ Å${}^{-1}$ ($\lambda =5.0$ Å) at (a) 100 and (b) 0.05 K. Open circles are experimental data, the dash-dotted (red) lines are the fits described in the text, and the solid (blue) lines show the magnetic contribution. Here the empty-can data are subtracted as background. (b) The temperature dependence of the relaxation time extracted from the neutron data via $\tau \text{(ns})=1.31/\mathcal{W}(\mu \text{eV})$ where $\mathcal{W}$ is the FWHM.[31] The energy barrier extracted from an Arrhenius fit, shown as the solid (blue) line, is 2.4 K.