  Search for a new quantum state of matter emerging in a crystal is one of
recent trends in condensed matter physics. For magnetic materials, geometrical
frustration and high magnetic field are two key ingredients to realize it: a
conventional magnetic order is possibly destroyed by competing interactions
(frustration) and is replaced by an exotic state that is characterized in terms
of quasiparticles, that are magnons, and the magnetic field can control the
density and chemical potential of the magnons. Here we show that a synthetic
copper mineral, Cd-kapellasite, comprising a kagome lattice made of
corner-sharing triangles of Cu2+ ions carrying spin-1/2 exhibits an
unprecedented series of fractional magnetization plateaux in ultrahigh magnetic
fields up to 160 T, which may be interpreted as crystallizations of emergent
magnons localized on the hexagon of the kagome lattice. Our observation reveals
a novel type of particle physics realized in a highly frustrated magnet.
