  (NH$_4$)$_2$[FeCl$_5$(H$_2$O)], a member of the family of antiferromagnetic
$A_2$[Fe$X_5$(H$_2$O)] compounds ($X$ = halide ion, $A$ = alkali metal or
ammonium ion) is classified as a new multiferroic material. We report the onset
of ferroelectricity below ~6.9 K within an antiferromagnetically ordered state
($T_N \sim 7.25 K$). The corresponding electric polarization can drastically be
influenced by applying magnetic fields. Based on measurements of pyroelectric
currents, dielectric constants and magnetization we characterize the
magnetoelectric, dielectric and magnetic properties of
(NH$_4$)$_2$[FeCl$_5$(H$_2$O)]. Combining these data with measurements of
thermal expansion, magnetostriction and specific heat, we derive detailed
magnetic field versus temperature phase diagrams. Depending on the direction of
the magnetic field up to three different multiferroic phases are identified,
which are separated by a magnetically ordered, but non-ferroelectric phase from
the paramagnetic phase. Besides these low-temperature transitions, we observe
an additional phase transition at ~79 K, which we suspect to be of structural
origin.
