On the possible magnetic properties of ultrathin Mn$_2$GaC films on Al$_2$O$_3$ substrates

The possibility of growth of thin Mn$_2$GaC MAX phase films on Al$_2$O$_3$ substrates with various orientations and their magnetic properties have been studied. The most favorable orientation relationships and interface planes in the Mn$_2$GaC//Al$_2$O$_3$ system, which indicate the possibility of growth on C-face (0001), S-face $(01\bar {1}\bar {1})$, N-face $(11\bar {2}\bar {3})$, and R-face $(0\bar {1}1\bar {2})$ sapphire substrates, have been predicted within a geometric approach. Using the electron density functional method, the possible magnetic properties of continuous ultrathin Mn$_2$GaC films have been calculated under the condition of conservation of uniform expansions/compressions of the MAX phase lattice, which are induced by growth on the predicted substrates. The effect of the deformation of the Mn2GaC lattice on magnetic ordering and magnetic moments has been determined, and the possibility of a transition from an antiferromagnetic to a ferromagnetic state under the action of external magnetic fields has been evaluated. It has been shown that the growth of the ferromagnetic film of the Mn$_2$GaC MAX phase is the most probable on the Al$_2$O$_3$ (0001), Al$_2$O$_3$ $(11\bar {2}\bar {3})$, and Al$_2$O$_3$ $(0\bar {1}1\bar {2})$ substrates.