Microscopic properties of the "pinwheel" kagome compound Rb₂Cu₃SnF₁₂

Using $^{63,65}$Cu nuclear magnetic resonance (NMR) 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 Rb$_2$Cu$_3$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.