  The generalized Heusler compounds Mn2CoZ (Z = Al, Ga, In, Si, Ge, Sn, Sb)
with the Hg2CuTi structure are of large interest due to their half-metallic
ferrimagnetism. The complex magnetic interactions between the constituents are
studied by first principles calculations of the Heisenberg exchange coupling
parameters, and Curie temperatures are calculated from those. Due to the direct
Mn-Mn exchange interaction in Mn2CoZ, the Curie temperature decreases, while
the total moment increases when changing Z from one group to another. The
exchange interactions are dominated by a strong direct exchange between Co and
its nearest neighbor Mn on the B site, which is nearly constant. The coupling
between the nearest-neighbor Mn atoms scales with the magnetic moment of the Mn
atom on the C site. Calculations with different lattice parameters suggest a
negative pressure dependence of the Curie temperature, which follows from
decreasing magnetic moments. Curie temperatures of more than 800 K are
predicted for Mn2CoAl (890 K), Mn2CoGa (886 K), and Mn2CoIn (845 K).
