  The significance of the spin-orbit interaction is very well known in
compounds containing heavier elements such as the rare-earth Eu ion. Here,
through density functional calculations, we investigated the effect of the
spin-orbit interaction on the magnetic ground state of Eu doped magnetite
($\mathrm{Fe_3O_4:Eu_{Fe}}$). By examining all possible spin alignments between
Eu and magnetite's Fe, we demonstrate that Eu, which is most stable when doped
at the tetrahedral site, adapts a spin almost opposite the substituted Fe.
Consequently, because of smaller spin cancellation between the cations on the
tetrahedral site ($\mathrm{Fe_{Tet}}$ and $\mathrm{Eu_{Tet}}$) and the cations
on the octahedral sites ($\mathrm{Fe_{Oct}}$), $\mathrm{Fe_3O_4:Eu_{Fe}}$
exhibits a maximum saturation magnetisation of 9.451 $\mu_B/$f.u. which is
significantly larger than that of undoped magnetite (calculated to be 3.929
$\mu_B/$f.u.). We further show that this large magnetisation persists through
additional electron doping. However, additional hole doping, which may
unintentionally occur in Fe deficient magnetite, can reduce the magnetisation
to values smaller than that of the undoped magnetite. The results presented
here can aid in designing highly efficient magnetically recoverable catalysts
for which both magnetite and rare earth dopants are common materials.
