First-principles calculation of the effects of partial alloy disorder on the static and dynamic magnetic properties of ${\mathrm{Co}}_2\mathrm{MnSi}$

On the basis of fully relativistic Korringa-Kohn-Rostoker calculations and in conjunction with the coherent potential approximation and the linear response formalism, we present a complete ab initio study of the influence of alloy disorder on the static and dynamic (Gilbert damping) magnetic properties and on the electronic structure of the half-metallic full-Heusler alloy ${\mathrm{Co}}_2\mathrm{MnSi}$. We discuss in particular partial atomic disorders intermediate between the main crystal phases $\text{L}{2}_1$, B2, A2, and $\text{D}{0}_3$ of this alloy. We compare our results with homemade experiments and measurements from the literature, and conclude that the presence of a partial $\text{D}{0}_3$-like disorder could explain the relatively high value of the Gilbert damping parameter and the lack of half-metallicity measured in real samples, in which alloy disorder cannot be totally avoided.

Figure 1

${\mathrm{Co}}_2\mathrm{MnSi}$ total DOS and atomic- and site-dependent contributions, calculated with $a_0^{\exp }$ for (a) the $\text{L}{2}_1$, (b) the B2, (c) the $\text{D}{0}_3$, (d) the $\text{D}{0}_3$', and (e) the A2 phases. The upper and lower parts of each panel respectively show the majority and minority spin DOS.

Figure 2

Ground-state energy $E_0$ of ${\mathrm{Co}}_2\mathrm{MnSi}$ per f.u. as a function of the disorder rates $(x,y,z)$, for the atomic distributions described in Sec. 2 and for the two values of the lattice parameter $a_0^{\exp }$ and $a_0^{\mathrm{DFT}}$. The ground-state energy for $\text{D}{0}_3$'-like disorder is also plotted (with open squares) in panel a) for $z=0.02,1/3,\text{and}2/3$. The energy of the $\text{L}{2}_1$ phase $E_0(0,0,0)$ is taken as a reference.

Figure 3

Majority- and minority-spin DOS at the Fermi level $[n^{\uparrow }\left(E_F\right)$ and $n^{\downarrow }\left(E_F\right)$, respectively] as a function of the disorder rates $(x,y,z)$ for the two values of the lattice parameter.

Figure 4

Total magnetic moment $M_{\mathrm{tot}}$ per formula unit as a function of the disorder rates $(x,y,z)$ and calculated with the two values of the lattice parameter.

Figure 5

Averaged value of the spin magnetic moment $M_{\mathrm{spin}}$ of the different atoms, as a function of the disorder rates $(x,y,z)$ and calculated with the two values of the lattice parameter.

Figure 6

Averaged value of the orbital magnetic moment $M_{\mathrm{orb}}$ of the different atoms, as a function of the disorder rates $(x,y,z)$ and calculated with the two values of the lattice parameter.

Figure 7

Gilbert damping parameter $\alpha$ as a function of the disorder rates $(x,y,z)$ and calculated with the two values of the lattice parameter.

Figure 8

Total DOS of ${\mathrm{Co}}_2\mathrm{MnSi}$, calculated for the $\text{L}{2}_1$ phase with $a_0^{\exp }$ (red curve) and $a_0^{\mathrm{DFT}}$ (blue curve).

Figure 9

FMR linewidth of a ${\mathrm{Co}}_2\mathrm{MnSi}$ irradiated sample. Blue curve: $\text{L}{2}_1$ order and red curve: $\text{L}{2}_1$ including Mn/Co swaps $\left(x=0.09\right)$.