  We propose two new methods to calculate exactly the spectrum of two
spin-${1\over 2}$ charge carriers moving in a ferromagnetic background, at zero
temperature. We find that if the spins are located on a different sublattice
than that on which the fermions move, magnon-mediated effective interactions
are very strong and can bind the fermions into low-energy bipolarons with
triplet character. This never happens in models where spins and charge carriers
share the same lattice, whether they are in the same band or in different
bands. This proves that effective one-lattice models do not describe correctly
the low-energy part of the two-carrier spectrum of a two-sublattice model, even
though they may describe the low-energy single-carrier spectrum appropriately.
