First-principles study of ferromagnetic coupling in Zn$_{1-x}$Cr$_x$Te thin film

Using gradient corrected density functional theory and supercell technique, we have calculated total energies, electronic structure, and magnetic properties of Cr doped ZnTe in both bulk and thin film configurations. Calculations with full geometry optimization for Zn$_{1-x}$Cr$_{x}$Te supercell were carried out for different Cr concentrations (x=0.095, 0.143, and 0.19) and by varying the sites Cr atoms occupy. We show that the ferromagnetic phase of Zn$_{1-x}$Cr$_{x}$Te in both bulk and thin film is energetically the most preferable state irrespective of the concentration and/or site occupation of Cr atom. The strong hybridization between Cr-3$d$ and Te-5$p$ states is found to be responsible for the ferromagnetic coupling - in agreement with recent experiments.