Magnetic ordering and exchange interactions in structural modifications ofMn3Gaalloys: Interplay of frustration, atomic order, and off-stoichiometry

Mn-Ga alloys close to the $\mathrm{M}{\mathrm{n}}_{3}\mathrm{Ga}$ stoichiometry can be synthesized in three different crystal modifications: hexagonal, tetragonal, and face-centered cubic, both in bulk and in thin-film forms. The magnetic ordering of these modifications is varying from noncollinear antiferromagnetic in the hexagonal case to ferrimagnetic order in the tetragonal one, whereas it is still unknown for the atomically disordered fcc structure. Here we study the onset of magnetic order at finite temperatures in these systems on a first-principles basis calculating the interatomic magnetic exchange interactions in the high-temperature paramagnetic regime. We employ the disordered local moment formalism and the magnetic force theorem within the framework of the local spin-density approximation and Monte Carlo simulations taking also the effects of atomic disorder in fcc alloys into account. In particular we find the origin of the stabilization of the noncollinear $3k$ structure in competition between antiferromagnetic inter- and in-plane couplings of frustrated kagome planes in hexagonal $\mathrm{M}{\mathrm{n}}_{3}\mathrm{Ga}$ and predict the antiferromagnetic-1 collinear order due to frustration in fcc alloys. Special attention is paid to the effects of the off-stoichiometry and the consequences of atomic disorder. We calculate the site-preference energy of Ga antisite atoms in the tetragonal structures in the range of the compositions from $\mathrm{M}{\mathrm{n}}_{3}\mathrm{Ga}$ to $\mathrm{M}{\mathrm{n}}_{2}\mathrm{Ga}$ and slightly beyond and confirm the earlier explanation of the effect of magnetization increase due to Ga preferentially occupying one of the Mn sites.