  We have investigated the Co-doping dependence of the structural, transport,
and magnetic properties of \epsilon-FeCoSi epilayers grown by molecular beam
epitaxy on silicon (111) substrates. Low energy electron diffraction, atomic
force microscopy, X-ray diffraction, and high resolution transmission electron
microscopy studies have confirmed the growth of phase-pure, defect-free
\epsilon-FeCoSi epitaxial films with a surface roughness of ~1 nm. These
epilayers are strained due to lattice mismatch with the substrate, deforming
the cubic B20 lattice so that it becomes rhombohedral. The temperature
dependence of the resistivity changes as the Co concentration is increased,
being semiconducting-like for low $x$ and metallic-like for x \gtrsim 0.3. The
films exhibit the positive linear magnetoresistance that is characteristic of
\epsilon-FeCoSi below their magnetic ordering temperatures $T_\mathrm{ord}$, as
well as the huge anomalous Hall effect of order several \mu\Omega cm. The
ordering temperatures are higher than those observed in bulk, up to 77 K for x
= 0.4. The saturation magnetic moment of the films varies as a function of Co
doping, with a contribution of ~1 \mu_{B}/ Co atom for x \lesssim 0.25. When
taken in combination with the carrier density derived from the ordinary Hall
effect, this signifies a highly spin-polarised electron gas in the low x,
semiconducting regime.
