Abstract
Being a wide band gap system GaMnN attracted considerable interest after the discovery of highest reported ferromagnetic transition temperature ${T}_{C}\ensuremath{\sim}940$ K among all diluted magnetic semiconductors. Later, it became a debate due to the observation of either very low ${T}_{C}\ensuremath{\sim}8$ K or sometimes the absence of ferromagnetism. We address these issues by calculating the ferromagnetic window ${T}_{C}$ vs $p$, within the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}$ Kondo lattice model using a spin-fermion Monte Carlo method on a simple cubic lattice. The next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$ is exploited to tune the degree of delocalization of the free carriers to show that the carrier localization (delocalization) significantly widens (shrinks) the ferromagnetic window with a reduction (enhancement) of the optimum ${T}_{C}$ value. We correlate our results with the experimental findings and explain the ambiguities in ferromagnetism in GaMnN.
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