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Ca$_{10}$Cr$_7$O$_{28}$ is a novel spin-$1/2$ magnet exhibiting spin liquidbehaviour which sets it apart from any previously studied model or material.However, understanding Ca$_{10}$Cr$_7$O$_{28}$ presents a significantchallenge, because the low symmetry of the crystal structure leads to verycomplex interactions, with up to seven inequivalent coupling parameters in theunit cell. Here we explore the origin of the spin-liquid behaviour inCa$_{10}$Cr$_7$O$_{28}$, starting from the simplest microscopic modelconsistent with experiment - a Heisenberg model on a single bilayer of thebreathing-kagome (BBK) lattice. We use a combination of classical Monte Carlo(MC) simulation and (semi-)classical Molecular Dynamics (MD) simulation toexplore the thermodynamic and dynamic properties of this model, and comparethese with experimental results for Ca$_{10}$Cr$_7$O$_{28}$. We uncoverqualitatively different behaviours on different timescales, and argue that theground 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 foundin the kagome antiferromagnet. We also identify key differences betweenlongitudinal and transverse spin excitations in applied magnetic field, andargue that these are a distinguishing feature of the spin liquid in the BBKmodel.

Theory of Ca$_{10}$Cr$_7$O$_{28}$ as a bilayer breathing-kagome magnet: Classical thermodynamics and semi-classical dynamics