Volume magnetostriction of $\mathrm{Fe}$-$\mathrm{Ga}$ alloys: calculation from first principles

In this paper, with the help of the density functional theory, the magnetic and magnetoelastic properties of the crystal structures $\mathrm{A2}$ and $\mathrm{D}0_3$ of $\mathrm{Fe}_{100-x}\mathrm{Ga}_{x}$ alloys ($x = 18{-}22$ at.$\%$) have been studied. The calculations were performed using the SPR-KKR software package. The exchange integrals, the values of the volume magnetoelastic constant $\mathrm{B}_0$, and the volume magnetostriction $\Delta V/V$ have been calculated. The obtained dependence of the exchange interaction constants on the crystal lattice parameter is a decreasing function for both $\mathrm{A2}$ and $\mathrm{D}0_3$ structures. It has been shown that the ferromagnetic interaction between iron atoms in the first coordination sphere increases with increasing $\mathrm{Ga}$ concentration in the fully disordered $\mathrm{A2}$ phase, while this interaction weakens in the ordered crystal structure $\mathrm{D}0_3$. The obtained values of $\Delta V/V$ for various compositions of $\mathrm{Fe}_{100-x}\mathrm{Ga}_{x}$ alloys are negative. It is shown that an increase in the $\mathrm{Ga}$ content leads to an increase in volume magnetostriction for the $\mathrm{A2}$ structure and a decrease in $\Delta V/V$ for the $\mathrm{D}0_3$ phase. The character of the volume magnetostriction dependence on the concentration of Ga for structure $\mathrm{A2}$ is consistent with the experimental data and with the results obtained for compounds based on $\mathrm{Ni}$.