  Erythrosiderites with the formula A2FeX5H2O, where A = Rb, K, and (NH4) and X
= Cl and Br are intriguing systems that possess various magnetic and electric
phases, as well as multiferroic phases in which magnetism and ferroelectricity
are coupled. In this report, we study the magnetic phase diagram of
erythrosiderites as a function of superexchange interactions. To this end, we
perform classical Monte Carlo simulations on magnetic Hamiltonians that contain
five different superexchange interactions with single-ion anisotropies. Our
phase diagram contains all magnetic ground states that have been experimentally
observed in these materials. We argue that the ground states can be explained
by varying the ratio of J4/J2. For J4/J2 > 0.95 a cycloidal spins structure is
stabilized as observed in (NH4)2FeCl5H2O and otherwise, a collinear spin
structure is stabilized as observed in (K,Rb)2FeCl5H2O. We also show that the
difference in the single-ion anisotropy along a- and c- axes is essential to
stabilize the intermediate state observed in (NH)2FeCl5H2O.
