Analysis of the co-doping effect of manganese and lanthanide elements in SrGa₂S₄ by the relativistic DV-Xα calculation

The electronic states of manganese and lanthanide elements in SrGa ₂S₄ are calculated by the relativistic discrete varia-tional Xα method using a FORTRAN program of DVSCATR in order to investigate the mechanism allowing the 3d-3d transition of Mn in SrGa ₂S₄ by co-doping a lanthanide element. We use a spherical cluster model of the D₂ symmetry which consists of 45 atoms of Sr₉Ga₁₂S₂₄, representing SrGa₂S ₄, in our calculation. Doping a lanthanide to SrGa₂S ₄ is represented by substituting a Sr atom with a lanthanide atom (indicated by 'Ln') at the cluster centre as (LnSr₈)Ga ₁₂S₂₄. Two types of co-doping models are prepared as (LnMn₂Sr₆)Ga₁₂S₂₄ for Mn _Sr and (LnSr₈)(Mn₄Ga₈)S₂₄ for Mn_Ga with keeping the D₂ symmetry. As a result of the self-consistent charge (SCC) calculation, the averaged distance between a lanthanide atom at the cluster centre and surrounding eight sulphur atoms has to be set as 70 to 80% of that between the original Sr-S combinations. Calculated electronic states show that the Ln(5d) and Mn(4s, 4p) atomic orbitals are highly mixed, and in the lower energy range, the Mn(4s, 4p) and Mn(3d) are also highly mixed. This hybridization cascade can explain the co-doping effect as that the electrons optically excited to the unoccupied states relating to the Ln(5d) would finaly relax to the 3d-3d transition of Mn.