Spin Liquid State in the $S=1/2$ Triangular Lattice ${\mathrm{Ba}}_3{\mathrm{CuSb}}_2{\mathrm{O}}_9$

The synthesis and characterization of ${\mathrm{Ba}}_3{\mathrm{CuSb}}_2{\mathrm{O}}_9$, which has a layered array of ${\mathrm{Cu}}^{2+}$ spins in a triangular lattice, are reported. The magnetic susceptibility and neutron scattering experiments of this material show no magnetic ordering down to 0.2 K with a ${\theta }_{\mathrm{CW}}=-55\mathrm{K}$. The magnetic specific heat reveals a $T$-linear dependence with a $\gamma =43.4\mathrm{mJ}{\mathrm{K}}^{-2}{\mathrm{mol}}^{-1}$ below 1.4 K. These observations suggest that ${\mathrm{Ba}}_3{\mathrm{CuSb}}_2{\mathrm{O}}_9$ is a new quantum spin liquid candidate with a $S=1/2$ triangular lattice.

Figure 1

(a) Schematic crystal structure for ${\mathrm{Ba}}_3{\mathrm{CuSb}}_2{\mathrm{O}}_9$; (b) The layer structure along the $c$ axis; (c) The triangular lattice of ${\mathrm{Cu}}^{2+}$ in the $ab$ plane.

Figure 2

(a) The temperature dependencies of the dc magnetic susceptibility ($\chi$). The open squares, dashed line, and open circles represent $\chi$ as measured, $\chi$-orphan spins, and $\chi$ after deleting orphan spins, respectively. The solid curve on $\chi$ data above 150 K represents a fit to the HTSE. Inset: $1/\chi$ after deleting the orphan spin contribution (open triangles). The solid line on the $1/\chi$ data represents a Curie-Weiss fit. (b) The temperature dependence of the real part of the ac magnetic susceptibility (${\chi }^{\prime }$). (c) Neutron diffraction pattern (crosses) for ${\mathrm{Ba}}_3{\mathrm{CuSb}}_2{\mathrm{O}}_9$ at 0.2 K. The solid curve is the best fit from the Rietveld refinement using FullProf. The vertical marks indicate the position of Bragg peaks, and the bottom curve shows the difference between the observed and calculated intensities.

Figure 3

(a) The temperature dependencies of specific heat at different fields for ${\mathrm{Ba}}_3{\mathrm{CuSb}}_2{\mathrm{O}}_9$ and ${\mathrm{Ba}}_3{\mathrm{ZnSb}}_2{\mathrm{O}}_9$. (b) Open squares are $\Delta C_{P\mathrm{\text{−}}\mathrm{Cu}}/T=[C_{P\mathrm{\text{−}}\mathrm{Cu}}(0\mathrm{T})–C_{P\mathrm{\text{−}}\mathrm{Cu}}(9\mathrm{T})]/T$. The solid line is a fit as described in the text. Inset: $\Delta E_H$ as a function of ${\mu }_{0}H$ between 0 and 9 T. The solid line represents a fit to Zeeman splitting. Inelastic neutron scattering spectra ($\lambda =4.8\AA$) for ${\mathrm{Ba}}_3{\mathrm{CuSb}}_2{\mathrm{O}}_9$ at 0.2 K with applied magnetic field 0 T (c) and 2 T (d). Open squares are experimental data, the dash-dotted lines are the fits described in the text, the solid lines show the magnetic contribution.

Figure 4

(a) The temperature dependencies of $C_M/T$ and the magnetic entropy variation $S_M$. (b) The temperature dependence of $C_M$ (open symbols). The solid lines are fits as described in the text.