The role of N defects in paramagnetic CrN at finite temperatures from first-principles

Simulations of defects in paramagnetic materials at high temperature constitute a formidable challenge to solid state theory due to the interaction of magnetic disorder, vibrations, and structural relaxations. CrN is a material where these effects are particularly large due to a strong magneto-lattice coupling and a tendency for deviations from the nominal 1:1 stoichiometry. In this work we present a first-principles study of nitrogen vacancies and nitrogen interstitals in CrN at elevated temperature. We report on formation energetics, the geometry of interstital nitrogen dimers, and impact on the electronic structure caused by the defects. We find a vacancy formation energy of 2.28 eV with a small effect of temperature, a formation energy for N interstitial in the form of a $\big<111\big>$ oriented split-bond of 3.77 eV with an increase to 3.97 at 1000 K. Vacancies are found to add three electrons while split bond interstitial adds one electron to the conduction band. The band gap of defect-free CrN is smeared out due to vibrations, though it is difficult to draw conclusion about the exact temperature at which the band gap closes from our calculations. However, it is clear that at 900 K there is a non-zero density of electronic states at the Fermi level. At 300 K our results indicate a boarder case were the band-gap is about to close.