Large perpendicular magnetic anisotropy in magnetostrictive Fe$_{1-x}$Ga$_x$ thin films

In this work we report the appearence of a large perpendicular magnetic anisotropy (PMA) in Fe$_{1-x}$Ga$_x$ thin films grown onto ZnSe/GaAs(100). This arising anisotropy is related to the tetragonal metastable phase in as-grown samples recently reported [M. Eddrief {it et al.}, Phys. Rev. B {bf 84}, 161410 (2011)]. By means of ferromagnetic resonance studies we measured PMA values up to $sim$ 5$times$10$^5$ J/m$^3$. PMA vanishes when the cubic structure is recovered upon annealing at 300$^{circ}$C. Despite the important values of the magnetoelastic constants measured via the cantilever method, the consequent magnetoelastic contribution to PMA is not enough to explain the observed anisotropy values in the distorted state. {it Ab initio} calculations show that the chemical ordering plays a crucial role in the appearance of PMA. Through a phenomenological model we are able to explain that an excess of next nearest neighbour Ga pairs (B$_2$-like ordering) along the perpendicular direction arises as the source of PMA in Fe$_{1-x}$Ga$_x$ thin films.