Microscopic Properties of the Pinwheel Kagome Compound ${\mathrm{Rb}}_2{\mathrm{Cu}}_3{\mathrm{SnF}}_{12}$

Using ${}^{63,65}\mathrm{Cu}$ nuclear magnetic resonance in magnetic fields up to 30 T, we study the microscopic properties of the 12-site valence-bond-solid ground state in the “pinwheel” kagome compound ${\mathrm{Rb}}_2{\mathrm{Cu}}_3{\mathrm{SnF}}_{12}$. We find that the ground state is characterized by a strong transverse staggered spin polarization whose temperature and field dependence points to a mixing of the singlet and triplet states. This is further corroborated by the field dependence of the gap $\Delta (H)$, which has a level anticrossing with a large minimum gap value of $\approx \Delta (0)/2$, with no evidence of a phase transition down to 1.5 K. By the exact diagonalization of small clusters, we show that the observed anticrossing is mainly due to staggered tilts of the $g$ tensors defined by the crystal structure and reveal symmetry properties of the low-energy excitation spectrum compatible with the absence of level crossing.

Figure 1

${}^{63,65}\mathrm{Cu}$ spectrum of ${\mathrm{Rb}}_2{\mathrm{Cu}}_3{\mathrm{SnF}}_{12}$ measured at 2.6 K and 11.568 T for the magnetic field parallel to the $c$ axis of the crystal. Colors and their hues are used to distinguish positively (red hatched) and negatively (blue) polarized sites as well as the central lines (dark color) and satellites (light color). Additional lines of ${}^{87}\mathrm{Rb}$ and ${}^{27}\mathrm{Al}$ (used for magnetic field calibration) are marked in gray. The inset shows the exchange couplings structure of a pinwheel cluster.

Figure 2

(a) Temperature dependence of the local fields at 13.0 T. Two groups of sites are marked by the green ($A$) and orange ($B$) symbols, as defined in the legend. Circles (diamonds and squares) show the values obtained for ${}^{63}\mathrm{Cu}$ (${}^{65}\mathrm{Cu}$) isotope. The dashed line marks the estimated orbital contribution ($K_{\mathrm{orb}}\approx 1.5\%$). (b) The average local staggered field at sites $A$ (diamonds, left scale) and $B$ (squares, right scale). (c) The uniform hyperfine field averaged over the $A$, $B$ and all sites (up triangles, down triangles, and solid circles, respectively).

Figure 3

(a) Magnetic field dependence of the local fields at 3.9 K, with the same symbol and color code as in Fig. 2. (b) The average local staggered field. The thick line is a guide for the eye showing approximately a square-root dependence, whereas the dotted line shows an expected qualitative behavior for lower magnetic fields.

Figure 4

$H$ dependence of the singlet-triplet energy gap measured by $T_1^{-1}$ (red-yellow circles) and by neutron scattering (black-gray squares, from Ref. 7). Insets: (top) Arrhenius plot of the measured $T_1^{-1}(T)$ dependence (symbols) and the fit (lines) used to extract the gap values shown in the main figure. Only selected, representative data sets are shown. (bottom right) Two neighboring ${\mathrm{CuF}}_6$ octahedra.