## ABSTRACT

The design of alkali-metal-based half-Heusler alloys in C1b structures of the alpha (α), beta (β) and gamma (γ) phases, respectively, based on first-principles calculations is reviewed. Each phase is characterized by atomic arrangements of three elements in a primitive face-centered-cubic unit cell. In this review, the focus is on the β and γ phases that consist of three elements: an alkali-metal element, a 3d transition metal element (Cr), and a Group VI, non-metal element. The design principles of alkali-metal-based half-Heusler alloys were guided by three criteria: (a) the nearest-neighbor configurations of the non-metal atom with the 3d transition metal element should be under the tetrahedral environment; (b) the strength of the electro-negativity of the Group VI elements, the non-metal atoms, on the alkali-metal elements should be strong; and (c) the Pauli principle should be considered to align spins at transition-metal element sites. Two required conditions were imposed to be satisfied for possible spintronic materials: (a) half-metallic properties at some lattice constants; and (b) the largest magnetic moment possible for the 3d transition-metal element. Furthermore, based on the stability consideration, a third criterion was imposed: (c) alloys should have the largest moment at the optimized lattice constants at T = 0 K. Out of 30 alloys in this study, nine crystals were found to satisfy all three criteria; four cases satisfy the first two criteria (a) and (b); and 17 alloys do not satisfy any of the criteria. Among the nine alloys, two of them are in the β-phase. In particular, β-CsCrS is the best candidate because it has the lowest free energy among the nine alloys and a negligible spin–orbit interaction.