Structural and electronic origin of large magnetostrictive $Fe_{1-x}Ga_x$ alloys*

$Fe_{1-x}Ga_x$ binary alloys exhibiting large magnetostriction and excellent ductility have great potentials for various applications. The origin of large magnetostriction has not been thoroughly studied, especially at high Ga concentration ($x > 18.75 \%$). We conduct extensive ab initio molecular dynamics simulation of $Fe_{1-x}Ga_x$ alloys to generate atomic structures; and find that the alloys adopt the disordered A2 structure for $x < 18.75 \%$ and the A2+$D0_3$ mixed structures for $18.75 \% < x < 23.4 \%$, respectively. The formation of $D0_3$-like structure play a key role for the decrease of magnetostriction beyond $x = 19\%$. Interestingly, the magnetostriction may greatly enhance, up to $\lambda_{001} = 850$ ppm in ternary alloys with incorporation of $3 - 5 \%$ Cu and Zn.