  Investigations into the magnetic properties of sputtered Mn$_{x}$CoGe films
in the range $0.8 \leq x \leq 2.5$ uncovered ferrimagnetic order, unlike the
ferromagnetic order reported in bulk samples. These films formed hexagonal
Ni$_{2}$In-type structures when annealed at temperatures below 600$^{\circ}$C.
While the Curie temperatures of the films are comparable to those of hexagonal
bulk MnCoGe, there is a reduction in the magnetization of the Mn$_{x}$CoGe
films relative to bulk MnCoGe, and a magnetization compensation point is
observed in the $x<1$ samples. To understand the behavior, we calculated the
magnetic moments of Mn-antisite defects in MnCoGe with density-function theory
(DFT) calculations. Models constructed from the calculation suggest that films
become ferrimagnetic due to the presence of Mn on the Co and Ge sites. In the
$x<1$ samples, these defects arose from the disorder in the films, whereas for
$x>1$, the excess Mn was driven onto the antisites. Mean field modeling of the
temperature dependence of the magnetization provides additional evidence for
ferrimagnetism. Our mean field and DFT models provide a description of how the
variation in film defects with composition will transition the magnetic
behavior from a compensated (V-type) to an uncompensated (Q-type) ferrimagnet.
