Density functional theory study of vacancy induced magnetism in Li$_{3}$N

The effect of lithium vacancies in the hexagonal structure of $alpha-$Li$_3$N, is studied within the framework of density functional theory. Vacancies ($square$) substituting for lithium in $alpha-$Li$_2$(Li$_{1-x}square_x$)N are treated within the coherent potential approximation as alloy components. According to our results long range N($p$)-ferromagnetism ($sim 1$ $mu_B$) sets in for vacancy substitution within the [Li$_2$N] layers ($x ge 0.7$) with no significant change in unit cell dimensions. By total energies differences we established that in-plane exchange couplings are dominant. Vacancies substituting inter-plane Li, leads to a considerable structural collapse ($c/a approx 0.7$) and no magnetic moment formation.