  Previous studies indicated that intrinsic point defects play a crucial role
for the density of states of ferromagnetic half-metals in the band gap region:
At large concentrations, defect-derived bands might close the gap at the Fermi
energy in the minority spin channel. In this work, structural disorder in the
Co- and Mn-sublattices of the full Heusler alloy Co_2-xMn_1+xSi (-1 < x < 2) is
investigated with a cluster expansion approach, parametrized using all-electron
density functional theory calculations. By establishing two separate cluster
expansions, one for the formation energy and one for the total spin moment, we
are in position to determine the stability of different configurations, to
predict new (also half-metallic) ground states and to extend the known
Slater-Pauling rule for ideally stoichiometric Heusler alloys to
non-stoichiometric, Mn-rich compositions. This enables us to identify
potentially half-metallic structures in the Mn-rich region. With the help of
Monte Carlo simulations based on the cluster expansion, we establish
theoretically that Co_2-xMn_1+xSi close to the stoichiometric composition ought
to show a high degree of structural order in thermodynamic equilibrium. Hence,
samples prepared with the correct stoichiometry should indeed be half-metallic
after thermal annealing. Moreover, we predict that adding a small amount of Mn
to stoichiometric Co_2MnSi allows to suppress the thermally activated formation
of detrimental Co antisites. At Mn-rich compositions (x>1), the ordered ground
state structures predicted for zero temperature are found to be thermally
unstable and to decompose into Co2MnSi and Mn3Si above room temperature.
