First-Principles Study of Doped Half-Metallic Spinels: Cu_0.5Zn_0.5Cr₂S₄, Cu_0.5Cd_0.5Cr₂S₄, Li_0.5Zn_0.5Cr₂O₄ and Li_0.5Zn_0.5Cr₂S₄

Electronic structure and magnetic properties of Cu_0.5Zn_0.5Cr₂S₄, Cu_0.5Cd_0.5Cr₂S₄, Li_0.5Zn_0.5Cr₂O₄ and Li_0.5Zn_0.5 Cr₂S₄ are investigated using the first−principles calculation based on the density functional theory. GGA+U exchange correlation is used in the calculation to correct the effective Coulomb repulsion energy of Cr underestimated by LSDA or GGA. The calculation results reveal that half−metallic Cu_0.5Zn_0.5Cr₂S₄ and Cu_0.5Cd_0.5Cr₂S₄ can be achieved by doping CuCr₂S₄ with Zn or Cd, though CuCr₂S₄ is not half−metallic. Half-metallic LiCr₂O₄ is experimentally unstable, but half−metallic Li_0.5Zn_0.5Cr₂O₄ and Li_0.5Zn_0.5Cr₂S₄ can be achieved by doping Li into experimentally stable ZnCr₂O₄ and ZnCr₂S₄, though ZnCr₂O₄ and ZnCr₂S₄ are not half−metallic. The influence of +U on the electronic structure and half-metallicity of the doped systems is also presented.