Gapless Quantum Spin Liquid in the Triangular System ${\mathrm{Sr}}_3{\mathrm{CuSb}}_2{\mathrm{O}}_9$

We report gapless quantum spin liquid behavior in the layered triangular ${\mathrm{Sr}}_3{\mathrm{CuSb}}_2{\mathrm{O}}_9$ system. X-ray diffraction shows superlattice reflections associated with atomic site ordering into triangular Cu planes well separated by Sb planes. Muon spin relaxation measurements show that the $S=\frac{1}{2}$ moments at the magnetically active Cu sites remain dynamic down to 65 mK in spite of a large antiferromagnetic exchange scale evidenced by a large Curie-Weiss temperature ${\theta }_{\mathrm{CW}}\simeq -143\mathrm{K}$ as extracted from the bulk susceptibility. Specific heat measurements also show no sign of long-range order down to 0.35 K. The magnetic specific heat ($C_m$) below 5 K reveals a $C_m=\gamma T+\alpha T^2$ behavior. The significant $T^2$ contribution to the magnetic specific heat invites a phenomenology in terms of the so-called Dirac spinon excitations with a linear dispersion. From the low-$T$ specific heat data, we estimate the dominant exchange scale to be $\sim 36\mathrm{K}$ using a Dirac spin liquid ansatz which is not far from the values inferred from microscopic density functional theory calculations ($\sim 45\mathrm{K}$) as well as high-temperature susceptibility analysis ($\sim 70\mathrm{K}$). The linear specific heat coefficient is about $18\mathrm{mJ}/\mathrm{mol}{\mathrm{K}}^2$ which is somewhat larger than for typical Fermi liquids.

Figure 1

(a) A schematic of the SCSO crystal structure is shown highlighting the individual planes of Cu (red) and Sb (blue) atoms. The Sr atoms are omitted for visual clarity. (b) The paths corresponding to different exchange couplings.

Figure 2

Rietveld refinement of ${\mathrm{Sr}}_3{\mathrm{CuSb}}_2{\mathrm{O}}_9$ is shown along with Bragg positions and corresponding Miller indices ($hkl$) with $K$ modulation ($\frac{1}{3}$, $\frac{1}{3}$, $\frac{1}{3}$) (referred to a pseudocubic cell) to fit the superlattice peaks.

Figure 3

The variation of $\chi (T)$ for SCSO in $H=1\mathrm{kOe}$ is shown in the main figure. The solid line is a theoretical TLAF fit for data in the range 150–300 K and then extrapolated down to 2 K. In the inset, no bifurcation is seen in the plot of $\chi (T)$ vs $T$ between ZFC and FC data in $H=50\mathrm{Oe}$.

Figure 4

The variation of the muon asymmetry with time is shown at various temperatures in zero field for ${\mathrm{Sr}}_3{\mathrm{CuSb}}_2{\mathrm{O}}_9$. On fitting these data as described in the text, the muon relaxation rate was obtained and is shown in the inset.

Figure 5

The heat capacity of SCSO is plotted as a function of temperature in various fields. The solid lines are fits as explained in the text. Dashed lines represent power law variations $T^1$ and $T^2$. Inset: The variation of the coefficients of the linear (blue diamonds; left $y$-axis) and quadratic (red triangles; right $y$-axis) terms is shown as a function of $H$.