  Frustrated magnetism plays a central role in the phenomenology of exotic
quantum states. However, because the magnetic structures of frustrated systems
are aperiodic, there has always been the problem that they cannot be determined
using traditional crystallographic techniques. Here we show that the magnetic
component of powder neutron scattering data is actually sufficiently
information-rich to drive magnetic structure solution for frustrated systems,
including spin ices, spin liquids, and molecular magnets. Consequently,
single-crystal samples are not prerequisite for detailed characterisation of
exotic magnetic states. Our methodology employs ab initio reverse Monte Carlo
refinement, making informed use of an additional constraint that minimises
variance in local spin environments. By refining atomistic spin configurations,
we obtain at once (i) a magnetic structure "solution" - i.e. the orientation of
classical spin vectors - (ii) the spin correlation functions, and (iii) the
full three-dimensional magnetic scattering pattern.
