Understanding the intrinsic mechanism of the giant magnetostriction in binary and alloyed FeGa solid solutions

Doping nonmagnetic Ga atoms into Fe leads to the enhancement in magnetostriction by \ensuremath{\sim}10 times in the FeGa solid solutions; the fundamental mechanism of the anomalous enhancement has attracted substantial attention. However, current experimental methods are difficult to reveal the origin because of their inability in the electronic and atomic scales. In this work, we utilized first-principles calculations to unveil the origin of giant magnetostriction in FeGa solid solutions. Ga doping results in the random substitution of Fe by Ga in the disordered $A2$ matrix and the formation of $L{6}_{0}$ nanoheterogeneities simultaneously. The former weakens the strength of Fe--Fe metallic bonding framework, thus leading to the lattice softening as presented by the sharp reduction in elastic constant ${c}^{\ensuremath{'}} [{c}^{\ensuremath{'}}=({c}_{11}\ensuremath{-}{c}_{12})/2$]. The latter strengthens the magnetoelastic coupling effect by regulating the density of states of $3d$ orbits of Fe atoms inside and adjacent to the nanoheterogeneities, resulting in the 3 times larger magnetoelastic coupling coefficient $\ensuremath{-}{b}_{1}$. The two effects synergistically offer the giant magnetostriction in FeGa solid solutions based on the relationship of ${\ensuremath{\lambda}}_{001}=\phantom{\rule{4pt}{0ex}}\ensuremath{-}({b}_{1}/3{c}^{\ensuremath{'}})$. Furthermore, the influence of elemental doping, including Co, Ni, P, and Tb, on magnetostriction is systematically studied. It is demonstrated that Tb is the sole alloying element which can enhance the magnetoelastic coupling effect strongly, allowing FeGa-Tb supercell to present an ultrahigh magnetostriction of 738 ppm, which is over 2 times larger than that of the FeGa supercells. This work offers insights into the origin of giant heterogeneous magnetostriction in Fe-based solid solutions, which benefits the development of high-performance FeGa-based magnetostrictive materials.