Fig. 1: Crystalline structures of both (a) half and (b) full Heusler alloys; C1b and L21 structures, respectively. Atomically disordered structures, (c) B2 and (d) A2, are also shown .
Among proposed half-metallic ferromagnets (HMFs), the Heusler alloys holds the greatest potential to realize the half-metallicity at room temperature (RT) due to their lattice constant matching with the III-V semiconductors, high Curie temperature above RT and large bandgap at EF in general. The Heusler alloys are categorized into two distinct groups by their crystalline structures; half Heusler alloys with the form of XYZ in the C1b structure and full Heusler alloys with the form of X2YZ in the L21 structure as schematically drawn in Figs. 1(a) and (b), respectively, where X and Y atoms are transition metals, while Z is either a semiconductor or a non-magnetic metal (see Fig. 2) . The unit cell of the L21 structure consists of four face-centered cubic (fcc) sublattices, while that of the C1b structure is formed by removing one of the X sites. In the Heusler alloys, the half-metallicity is known to be fragile against atomic disorder. For the L21 structure, when the Y and Z atoms replace their sites (Y-Z disorder) and eventually occupy their sites absolutely at random, the alloy transforms into the B2 structure (Fig. 1(c)). In addition, X-Y and X-Z disorder finally forms the A2 structure (Fig. 1(d)).
Fig. 2: Major combinations of Heusler alloy formation .
 P. J. Webster and K. R. A. Ziebeck, "Heusler Alloys," in Landolt-B_rnstein New Series Group III, Vol. 19C, H. R. J. Wijn (Ed.) (Springer, Berlin, 1988) p. 75.