Magnetostrictive Fe_1-xGa_x alloys, as a new class of smart materials, have great potential in sensing and actuator applications. However, the fundamental understanding of the anisotropic elastic responses and micro mechanism at high Ga concentration remains one of the most challenging problems for the binary alloys. Here, we apply the density functional theory and large scale ab initio molecular dynamics simulation to investigate the effect of high Ga concentration on the elastic anisotropy of the Fe-Ga alloys with supercell models obtained by non-linear and non-uniform annealing processes. It is demonstrated that the formation of D0₃-like structures have an important effect on the softness of tetragonal shear modulus and a negligible influence on rhombohedra shear modulus. Meanwhile, the Fe dangling bond to its nearest Ga atoms results in the decrease of the Young’s modulus and the negative Poisson's ratio in [110] direction. The improved Young’s modulus in [110] direction than that in [100] direction is attributed to the different arrangement of pure Fe layer and Fe-Ga mixed layer along [110] and [100] axes. Furthermore, the ductility of Fe_1-xGa_x alloys is enhanced at high Ga content, playing a key role for the enhanced magnetostriction. We established the atomic mechanism for the first time that leads to the sudden drop of tetragonal magnetostriction at x～0.19. Based on rigid band analysis, we propose possible ways to further optimize the performance of Galfenol for device applications.

(a) Calculated E_MCA with εz=±1% for Fe_79.7Ga_20.3 (black dash line) and Fe_79.9Ga_18.7Cu_1.6 (red solid line) versus the number of valence electrons in the unit cell. The two vertical lines show positions of their actual N_e, black for Fe_79.7Ga_20.3 and red for Fe_79.9Ga_18.7Cu_1.6. (b) Strain dependent EMCA of Fe_79.7Ga_20.3 (black open triangle) and Fe_79.9Ga_18.7Cu_1.6 (red open circle); the inset shows the atomic configuration of Fe_79.9Ga_18.7Cu_1.6, where golden, green and blue balls represent Fe, Ga and Cu atoms, respectively. (c) Charge difference between Fe_79.9Ga_18.7Cu_1.6 and Fe_79.7Ga_20.3, in a range of ±0.008 eV/?³. (d) Partial density of states of Fe₂, Fe₁,Ga, Fe₁,Cu and Cu atoms in Fe_79.9Ga_18.7Cu_1.6, the purple arrow highlights the nonbonding states of Fe_1,Ga and Fe_1,Cu atoms.

Calculated (red filled circles) x-dependent of 3/2<λ001>, along with the experimental data measured for the quenched samples at room temperature (dark cyan open circle).6 The golden filled circle at x=20.3 represents result for a metastable structure of Fe79.7Ga18.7Cu1.6. The inset shows the strain-dependent total energy and magnetocrystalline anisotropy energy for one configuration of Fe81.25Ga18.75. (b) Calculated x-dependent <c'> (red filled circles) and <b₁> (blue filled circles), along with experimental data of c'(red open circles and triangles) and b₁ (blue open circles).The golden filled circle represents the calculated b1 of a metastable structure of Fe_7.97Ga_18.7Cu_1.6. (c) Calculated x-dependent number of electronic states at the Fermi level in the minority spin channel, N(E_F,↓). The inset shows the projected density of states (PDOS) of Fe₁, Fe₂ atoms in Fe_81.25Ga_18.75, along with the shaded region for the PDOS of the bcc bulk Fe. (d) Number of D0₃ (black open circles) and B₂ (×30, purple filled circles) pairs. The insets show Fe (golden balls) and Ga (green balls) atoms in the D0₃ and B2 structures.