Unified explanation of chemical ordering, the Slater-Pauling rule, and half-metallicity in full Heusler compounds

In the present work we developed an orbital coupling model for cubic full Heusler compounds that provides a unified set of rules that account for the chemical ordering, magnetic moment, and composition of the most promising candidates for half-metallicity. The origin and limitations of the rules are clearly described. To the best of our knowledge all of the several dozen half-metallic Heusler compounds known in the literature that follow the $M_t=N_t-24$ or $M_t=N_t-28$ generalized Slater-Pauling behavior satisfy the derived half-metallicity rule. Calculations performed by using density functional theory—performed for 259 compounds—confirm the validity of our model and derived rules for broad classes of Heusler compounds.

Figure 1

(a) Crystal structure of cubic Heusler compound, (b) DOS for majority $(\text{DOS}>0)$ and minority $(\text{DOS}<0)$ bands of regular ${\mathrm{Co}}_2\mathrm{MnGe}$. Minority bands of regular (c) and inverse (d) ${\mathrm{Co}}_2\mathrm{MnGe}$ and inverse (e) and regular (f) ${\mathrm{Mn}}_2\mathrm{CoGe}$. See text for details.

Figure 2

$\mathrm{\Delta }E$ for ${\mathrm{X}}_2\mathrm{YZ}$ compounds with X = Mn (a), Fe (b), Co (c), and X = Ru, Rh, Pd, Ni (d); see text for details.

Figure 3

(a)–(g) DOS averaged over Z and ${\mathrm{Y}}^{(\pm )}$ for sets of ${\mathrm{X}}_2{\mathrm{Y}}^{(\pm )}\mathrm{Z}$ compounds where X = Mn, Fe, Co for phases that satisfy the “lightest atom” rule. (h)–(n) Same as (a)–(g) for the corresponding phase that does not satisfy the “lightest atom” rule.

Figure 4

Minority bands of the stable phase (inverse for X = Fe and regular for X = Co) of 6 Heusler compounds that are not half-metallic exclusively due to the drop of a (green) band that includes the (15r/i) state at the $X$ point below the Fermi energy.

Figure 5

Minority bands of the stable phase (inverse for X = Mn and regular for X = Fe, Co) of 12 half-metallic Heusler compounds that have the Slater-Pauling behavior.

Figure 6

Minority bands of the half-metallic inverse phase of ${\mathrm{Mn}}_2\mathrm{CuSi}$.