  Neutron spherical polarimetry, which is directly sensitive to the absolute
magnetic configuration and domain population, has been used in this work to
unambiguously prove the multiferroicity of (ND4)2[FeCl5(D2O)]. We demonstrate
that the application of an electric field upon cooling results in the
stabilization of a single-cycloidal magnetic domain below 6.9 K, while poling
in the opposite electric field direction produces the full population of the
domain with opposite magnetic chirality. We prove the complete switchability of
the magnetic domains at low temperature by the applied electric field, which
constitutes a direct proof of the strong magnetoelectric coupling.
Additionally, we refine the magnetic structure of the ordered ground state,
determining the underlying magnetic space group consistent with the direction
of the ferroelectric polarization, and we provide evidence of a collinear
amplitude-modulated state with magnetic moments along the a-axis in the
temperature region between 6.9 and 7.2 K.
