Intrinsic long range antiferromagnetic coupling in dilutely V doped CuInTe$_2$

Despite the various magnetic orders mediated by superexchange mechanism, the existence of a long range antiferromagnetic (AFM) coupling is unknown. Based on DFT calculations, we discovered an intrinsic long range AFM coupling in V doped CuInTe$_2$. The AFM coupling is mainly due to the $p-d$ coupling and electron redistribution along the interacting chains. The relatively small energy difference between $p$ and $d$ orbitals and the small energy difference between d orbitals of the dopants and that of stepping stone sites can enhance the stability of this AFM configuration. A multi-bands Hubbard model was proposed to provide fundamental understanding to the long range AFM coupling in chalcopyrite diluted magnetic semiconductors(DMS).