Candidate Quantum Spin Liquid in the ${\mathrm{Ce}}^{3+}$ Pyrochlore Stannate ${\mathrm{Ce}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$

We report the low-temperature magnetic properties of ${\mathrm{Ce}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$, a rare-earth pyrochlore. Our susceptibility and magnetization measurements show that due to the thermal isolation of a Kramers doublet ground state, ${\mathrm{Ce}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ has Ising-like magnetic moments of $\sim 1.18{\mu }_B$. The magnetic moments are confined to the local trigonal axes, as in a spin ice, but the exchange interactions are antiferromagnetic. Below 1 K, the system enters a regime with antiferromagnetic correlations. In contrast to predictions for classical $⟨111⟩$-Ising spins on the pyrochlore lattice, there is no sign of long-range ordering down to 0.02 K. Our results suggest that ${\mathrm{Ce}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ features an antiferromagnetic liquid ground state with strong quantum fluctuations.

Figure 1

Rietveld refinement of neutron powder diffraction data (HRPT instrument at PSI) collected at 1.5 K using an incident wavelength of 1.49 Å. Fitted isotropic displacement parameters: $B_{\mathrm{Ce}}=0.87(4){\AA }^2$; $B_{\mathrm{Sn}}=0.79(3){\AA }^2$; $B_{\mathrm{O}(48f)}=1.08(2){\AA }^2$; $B_{{\mathrm{O}}^{\prime }(8b)}=0.87(5){\AA }^2$. Conventional Rietveld factors (%): $R_P=4.10$; $R_{WP}=5.19$; $R_{\text{Bragg}}=5.52$; $R_F=4.25$.

Figure 2

(a) Magnetization $M$ as a function of temperature $T$ in a magnetic field $H=1000$ Oe, plotted as the susceptibility $\chi (T)\sim M(T)/H$. The inset shows $M/H$ at several applied fields. (b) The temperature dependence of the inverse susceptibility ${\chi }^{-1}(T)$ exhibits two Curie-Weiss regimes (red lines) at high ($T>130\mathrm{K}$) and moderate ($1\mathrm{K}<T<10\mathrm{K}$) temperatures, and, in between, a regime which shows a curvature due to crystal field effects. The inset shows an enlargement of the moderate temperature Curie-Weiss regime; open and solid symbols refer to data points from the high- and low-temperature magnetometers, respectively. (c) Effective moment ${\mu }_{\mathrm{eff}}=[(3k_B/N_A{\mu }_B^2)\chi T{]}^{1/2}\sim 2.828\sqrt{\chi T}$ vs $T$. The red line is the fit, above 2 K, to the crystal field Hamiltonian. The inset in (c) shows the heat capacity on the same temperature scale as for the main panel.

Figure 3

Magnetization ($M$) recorded as a function of magnetic field ($H$). (a) Data in the form $M(H)$; lines are calculations for effective $S_{\mathrm{eff}}=1/2$ spins with $⟨111⟩$ easy-axis anisotropy and parametrized $g$ factor [42]. (b) Data in the form $M(H/T)$, so that they collapse in the uncorrelated regime. The inset shows linear fits to low-field $M(H)$ data, enabling comparison to the effective moments in Fig. 2.

Figure 4

Muon spin relaxation ($\mu \mathrm{SR}$) experiments. (a) Zero-field and longitudinal-field data in the usual histogram form $A(t)$; the blue line is a fit to the function $A(t)=A_0\exp [-(t/T_1{)}^{\beta }]+A_{bg}$. (b) Frequency shift ($K$) between the external field ($B_{\mathrm{ext}}$) and the local field at the muon site ($B_{{\mu }^{+}}$) plotted at 0.1 K as a function of the external transverse field and scaled to the derivative of $M(H)$ at 0.09 K.