The breaking of chiral and time-reversal symmetries provides a pathway to exotic quantum phenomena and topological phases. Recent work has extensively explored the resulting emergence of chiral charge orders and chiral spin liquids (CSLs) on the kagome lattice. Such CSLs are closely tied to bosonic fractional quantum Hall states with anyonic quasiparticles; however, their connection to nearby ordered states has remained a mystery. Here, we use spin-wave theory, parton Gutzwiller wave functions, and exact diagonalization to show that two distinct magnetic orders with uniform scalar chirality—the XYZ umbrella state and the octahedral spin crystal–emerge as competing orders in close proximity to the CSL. In this letter, we highlight the intimate link between a topologically ordered liquid and broken symmetry states with nontrivial real-space topology.

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• Magnetism
• Quantum phase transitions
• Quantum spin liquid
• Spin liquid
• Topological order
• Chiral magnets
• Kagome lattice
• Exact diagonalization
• Linear spin wave theory
• Monte Carlo methods
• Variational approach