The copper spins in Cs₂Cu₃SnF₁₂ sit on a triangular lattice that resembles the Japanese woven kagome pattern. When cooled below 20 K, these spins align into a pattern with negative vector chirality, as if all the whirlpools in a river spun in the same direction, but with a specific sign of twist.
Above 20 K, up to 150 K, the spins are not completely disordered: they retain two-dimensional Berezinskii–Kosterlitz–Thouless correlations. This is like a thin film of water where vortices and antivortices exist in pairs but never freeze into a crystal. Such behavior is typically seen in superfluid helium or superconducting films, yet here it emerges in a magnetic material.
The authors used nuclear quadrupole resonance — a technique where copper nuclei act as tiny magnetic compasses, revealing the local spin direction. Measurements of the relaxation rate T₁⁻¹ indicated a gapless ground state, while the broadening of the resonance line confirmed the short-range chiral order previously observed in neutron experiments.
The kagome lattice is named after a traditional Japanese basket weave where triangles form a pattern with hexagonal gaps.
In Greg Egan's novel "Schild's Ladder," physicists explore exotic states of matter, including vortex structures reminiscent of BKT correlations in quantum systems.