  The electronic structure, magnetic properties and phase formation of
hexagonal ferromagnetic Fe$_{3}$Sn-based alloys have been studied from first
principles and by experiment. The pristine Fe$_{3}$Sn compound is known to
fulfill all the requirements for a good permanent magnet, except for the
magnetocrystalline anisotropy energy (MAE). The latter is large, but planar,
i.e. the easy magnetization axis is not along the hexagonal c direction,
whereas a good permanent magnet requires the MAE to be uniaxial. Here we
consider Fe$_{3}$Sn$_{0.75}$M$_{0.25}$, where M= Si, P, Ga, Ge, As, Se, In, Sb,
Te and Bi, and show how different dopants on the Sn sublattice affect the MAE
and can alter it from planar to uniaxial. The stability of the doped Fe$_{3}$Sn
phases is elucidated theoretically via the calculations of their formation
enthalpies. A micromagnetic model is developed in order to estimate the energy
density product (BH)max and coercive field $\mu_{0}$H$_{c}$ of a potential
magnet made of Fe$_{3}$Sn$_{0.75}$Sb$_{0.25}$, the most promising candidate
from theoretical studies. The phase stability and magnetic properties of the
Fe$_{3}$Sn compound doped with Sb and Mn has been checked experimentally on the
samples synthesised using the reactive crucible melting technique as well as by
solid state reaction. The Fe$_{3}$Sn-Sb compound is found to be stable when
alloyed with Mn. It is shown that even small structural changes, such as a
change of the c/a ratio or volume, that can be induced by, e.g., alloying with
Mn, can influence anisotropy and reverse it from planar to uniaxial and back.
