  Spin ices are exotic phases of matter characterized by frustrated spins
obeying local ice rules, in analogy with the electric dipoles in water ice. In
two dimensions, one can similarly define ice rules for in-plane Ising-like
spins arranged on a kagome lattice. These ice rules require each triangle
plaquette to have a single monopole, and can lead to various unique orders and
excitations. Using experimental and theoretical approaches including
magnetometry, thermodynamic measurements, neutron scattering and Monte Carlo
simulations, we establish HoAgGe as a crystalline (i.e. non-artificial) system
that realizes the kagome spin ice state. The system features a variety of
partially and fully ordered states and a sequence of field-induced phases at
low temperatures, all consistent with the kagome ice rule.
