We performed first-principles calculations at finite temperatures to investigate the temperature dependence of the magnetic properties, such as exchange stiffness constants and Curie temperatures, of ${\text{Co}}_2\text{Mn}Z$ ($Z$ = Si, Al) assuming $L{2}_1$ and $B2$ structures. In $L{2}_1$ structures, we confirmed a relatively high Curie temperature for ${\text{Co}}_2\text{MnAl}$, comparable with that of ${\text{Co}}_2\text{MnSi}$; however, its exchange stiffness constant and single-site magnetic excitation energy at zero temperature are much smaller than those of ${\text{Co}}_2\text{MnSi}$. This might indicate that the Curie temperature of itinerant magnets cannot be determined by the exchange interaction at zero temperature. We also investigated the temperature dependence of the exchange stiffness constants of both alloys, and we found robustness in the temperature dependence of the exchange stiffness constant for ${\text{Co}}_2\text{MnAl}$, assuming an $L{2}_1$ structure. This might lead to a high Curie temperature, contrary to its small exchange stiffness constant. Meanwhile, for the results of the $B2$ structures, the exchange stiffness constants monotonically decrease with increasing temperatures for both alloys. In addition, we found that the behavior of the temperature dependences of the exchange stiffness constant can be controlled by the electron filling for both structures. Finally, we examined the temperature dependence of the electronic structure and how spin disorder alters the electronic structure. We also confirmed that the spin polarization at the chemical potential effectively increases and half metallicity is effectively induced with increasing temperature due to the altered electronic structure induced by the spin disorder of ${\text{Co}}_2\text{MnAl}$ with the $L{2}_1$ structure. Our results might indicate that renormalization of the electronic structure due to spin disorder at finite temperature influences the robustness of the exchange interactions and half-metallic properties of ${\text{Co}}_2\text{MnAl}$ with $L{2}_1$ structure.

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• Electronic structure
• First-principles calculations
• Magnetic interactions
• Magnetism
• Spintronics
• Heusler alloy
• Coherent potential approximation
• Density functional theory