Abstract
Using the first-principles density-functional approaches, impurity distributions and magnetic properties of Co-doped anatase ${\mathrm{TiO}}_{2}$ were investigated. From the total energies calculated for various possible configurations, Co atoms were found to prefer the non-uniform doping mode with short Co-Co distances. This non-uniform distribution furthermore is crucial for the ferromagnetic ordering observed in ${\mathrm{Co}}_{x}{\mathrm{Ti}}_{1\ensuremath{-}x}{\mathrm{O}}_{2},$ whereas the antiferromagnetic state prevails in uniformly doped cases investigated $(x=0.0625).$ Large exchange parameters appear to explain high ${T}_{c}.$
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