Summary: | Fully compensated ferrimagnets do not create any magnetic stray field and allow for a completely polarized current of charges. As a result, these alloys show promising prospects for applications as spintronic devices. In this paper, we investigated the phase stability, the site preference, the tetragonal distortion and the influence of symmetry from the crystal structure and chemical environments of magnetic ions on the magnetic properties of Cr<sub>2</sub><i>YZ</i> and Mn<sub>2</sub><i>YZ</i> (<i>Y</i> = void, Ni, Cu, and Zn; <i>Z</i> = Ga, Ge, and As) full Heusler alloys by first-principles calculations. We found that the selected Cr<sub>2</sub>-based alloys, except for Cr<sub>2</sub>NiGa and Cr<sub>2</sub>NiGe, prefer to crystallize in the centrosymmetric <i>L</i>2<sub>1</sub>-type structure, while the selected Mn<sub>2</sub>-based alloys, except for Mn<sub>2</sub>CuAs, Mn<sub>2</sub>ZnGe and Mn<sub>2</sub>ZnAs, tend to crystallize in the non-centrosymmetric XA-type structure. Due to the symmetry, the antiferromagnetism of the selected <i>L</i>2<sub>1</sub>-type alloys is very stable, and no spin-polarized density of states could be generated. In contrast, the magnetic moment of the selected XA-type alloys depends heavily on the number of valence electrons and tetragonal distortion, and spin-polarized density of states is generated. Therefore, the selected alloys with <i>L</i>2<sub>1</sub>-type structures and their tetragonal-distorted structure are potential candidates for conventional antiferromagnets, while those with XA-type structure and their tetragonal-distorted structure are promising candidates for (fully) compensated ferrimagnets.
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