L2₁ and XA Ordering Competition in Hafnium-Based Full-Heusler Alloys Hf₂VZ (Z = Al, Ga, In, Tl, Si, Ge, Sn, Pb).

For theoretical designing of full-Heusler based spintroinc materials, people have long believed in the so-called Site Preference Rule (SPR). Very recently, according to the SPR, there are several studies on XA-type Hafnium-based Heusler alloys X₂YZ, i.e., Hf₂VAl, Hf₂CoZ (Z = Ga, In) and Hf₂CrZ (Z = Al, Ga, In). In this work, a series of Hf₂-based Heusler alloys, Hf₂VZ (Z = Al, Ga, In, Tl, Si, Ge, Sn, Pb), were selected as targets to study the site preferences of their atoms by first-principle calculations. It has been found that all of them are likely to exhibit the L2₁-type structure instead of the XA one. Furthermore, we reveal that the high values of spin-polarization of XA-type Hf₂VZ (Z = Al, Ga, In, Tl, Si, Ge, Sn, Pb) alloys have dropped dramatically when they form the L2₁-type structure. Also, we prove that the electronic, magnetic, and physics nature of these alloys are quite different, depending on the L2₁-type or XA-type structures.