The Failure of LDA and GGA to describe Relative Stability, Electronic Structure and Magnetism of MnN and (Ga,Mn)N Alloys*

Pure MnN and (Ga,Mn)N alloys are studied using {\it ab initio} generalised gradient approximation +$U$ (GGA+$U$) or hybrid-exchange density functional (B3LYP) methods which predict dramatically different electronic structure, magnetic behavior and relative stabilities compared to local-density calculations. A unique structural anomaly of MnN, in which local-density calculations fail to predict the experimentally observed rocksalt as the ground state, is resolved with GGA+U and B3LYP. The phase-separation of zinc-blende (Ga,Mn)N alloys is examined using a mixed-basis cluster expansion based on the corrected GGA total energies. The predicted asymmetric spinodal phase diagram indicates that (Ga,Mn)N precipitates contain $\sim$5\% or $\sim$50\% Mn at typical growth temperatures. Thus, 100\% pure MnN, that suppresses the Curie temperature, will not be formed. The Curie temperature for the x$_{Mn}$=50\% phase is estimated to be T$_C$=$\sim$300~K indicating that high T$_C$ ferromagnetism in zinc-blende (Ga,Mn)N alloys is due to precipitates. \\ Chan {\it et al.} Phys. Rev. B {\bf 78}, 184109 (2008).