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 ${\text{Co}}_{2-x}{\text{Mn}}_{1+x}\text{Si}\left(-1\le x\le 2\right)$ 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 a position to determine the stability of different configurations, to detect (also half-metallic) ground states and to extend the known Slater-Pauling rule for ideally stoichiometric Heusler alloys to nonstoichiometric, 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 ${\text{Co}}_{2-x}{\text{Mn}}_{1+x}\text{Si}$ 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 ${\text{Co}}_2\text{MnSi}$ allows suppression of the thermally activated formation of detrimental Co antisites. At Mn-rich compositions $\left(x>1\right)$, the ordered ground-state structures predicted for zero temperature are found to be thermally unstable and to decompose into ${\text{Co}}_2\text{MnSi}$ and ${\text{Mn}}_3\text{Si}$ above room temperature.

• Received 24 October 2008

DOI:https://doi.org/10.1103/PhysRevB.79.094407

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