How many spin liquids are there in Ca${}_{10}$Cr${}_7$O${}_{28}$?

The search for novel phases of matter is a central theme of modern physics, with some of the most intriguing examples provided by the spin liquids found in magnets with competing, or “frustrated” interactions. Ca${}_{10}$Cr${}_7$O${}_{28}$, a novel spin-$1\mathrm{/}2$ magnet with a bilayer breathing-kagome lattice, has properties which differ from from any known spin liquid. However, understanding Ca${}_{10}$Cr${}_7$O${}_{28}$ presents a significant challenge, because of its complex frustration. Here we use large-scale molecular-dynamics simulation to explore the origin of spin-liquid behaviour in Ca${}_{10}$Cr${}_7$O${}_{28}$. We uncover qualitatively different behaviour on different timescales, and argue that ground state of Ca${}_{10}$Cr${}_7$O${}_{28}$ is born out of a slowly-fluctuating “spiral spin liquid”, while faster fluctuations echo the U(1) spin liquid found in the kagome antiferromagnet. These results provide a concrete scenario for spin-liquid behaviour in Ca${}_{10}$Cr${}_7$O${}_{28}$, and highlight the possibility of spin liquids existing on multiple timescales.