First principles determination of the rhombohedral magnetostriction of $Fe_{100-x}Ga_x$ and $Fe_{100-x}Al_x$ ($x<20$) alloys

Extensive efforts have been dedicated to investigate the extraordinary magnetostriction of Galfenol (Fe$_{100-x}Ga_x$) and Alfenal (Fe$_{100-x}Al_x$) alloys, which are very promising magnetostrictive materials for various applications such as sensors, transducers and spintronic devices. In contrast to the strong response of the tetragonal magnetostriction ($\lambda_{100}$) to the Ga/Al concentration (x), the rhombohedral magnetostriction,$\lambda_{111}$, vs. x curves for both FeGa and FeAl alloys show negative and steady values for $0