Unified approach to electronic, thermodynamical, and transport properties of ${\mathrm{Fe}}_3\mathrm{Si}$ and ${\mathrm{Fe}}_3\mathrm{Al}$ alloys

The electronic, thermodynamical, and transport properties of ordered ${\mathrm{Fe}}_{3}X$ ($X=\text{Al},\mathrm{Si}$) alloys are studied from first principles. We present here a unified approach to the phase stability, the estimate of the Curie temperature, the temperature dependence of sublattice magnetizations, magnon spectra, the spin-stiffnesses, and residual resistivities. An important feature of the present study is that all calculated physical properties are determined in the framework of the same first-principles electronic structure model combined with the effective Ising and Heisenberg Hamiltonians used for study of the thermodynamical properties of alloys. Curie temperatures, spin-stiffnesses, and magnon spectra are determined using the same calculated exchange integrals. Finally, the transport properties are calculated using the linear-response theory. Our theoretical estimates compare well with available experimental data. In particular, calculations predict (in agreement with experiment) the ordered $D{0}_3$ phase as the ground-state alloy structure, demonstrate that a correct relation of Curie temperatures of ${\mathrm{Fe}}_3\mathrm{Al}/{\mathrm{Fe}}_3\mathrm{Si}$ alloys can be obtained only by going beyond a simple mean-field approximation, provide reasonable estimates of spin-stiffnesses, and give resistivities compatible with structural disorder observed in the experiment. Although the calculated temperature dependences of the Fe magnetization on different sublattices are similar, they nevertheless deviate more than in the experiment, and we discuss a possible origin.

Figure 1

The sublattice-resolved exchange interactions among various Fe sites for the ordered ${\mathrm{Fe}}_3\mathrm{Al}$ alloy on the ${D0}_3$ lattice as a function of the distance ($d$) in units of the lattice constant ($a$). Four fcc sublattices along the [111] direction have the structural formula Fe[A]-Fe[B]-Fe[C]-Al[D]. Very small interactions involving Al sites are not shown.

Figure 2

The same as in Fig. 1, but for the ordered ${\mathrm{Fe}}_3\mathrm{Si}$ alloy.

Figure 3

The exchange interactions between Fe sites in the ${D0}_3$ structure for all sites occupied by iron with the formula Fe[A]-Fe[B]-Fe[C]-Fe[D] plotted as a function of the distance ($d$) in units of the lattice constant ($a$). The calculations were done for the lattice constant of ${\mathrm{Fe}}_3\mathrm{Si}$.

Figure 4

The MFA (circles) and RPA (squares) Curie temperatures as a function of the cutoff distance of exchange integrals included in calculations. The cutoff distance is in units of the lattice constant ($a$). Full and empty symbols correspond to ${\mathrm{Fe}}_3\mathrm{Si}$ and ${\mathrm{Fe}}_3\mathrm{Al}$ alloys, respectively.

Figure 5

(a) The relative sublattice magnetizations $m_{\alpha }\left(T\right)=M_{\alpha }\left(T\right)/M_{\alpha }(T=0)$ ($\alpha =\text{A/C}$ or B) plotted as a function of relative temperatures $T/T_c$ for ${\mathrm{Fe}}_3\mathrm{Si}$ (see text for definitions). Magnetizations are nonzero at $T/T_c=1$ due to the finite-size effects close to $T_c$. The dotted line shows the ratio of relative sublattice magnetizations $m^{\mathrm{A}/\mathrm{C}}/m^{\mathrm{B}}$. (b) The same but for relative sublattice hyperfine fields $h_{\alpha }\left(T\right)=H_{\alpha }\left(T\right)/H_{\alpha }(T=0)$ ($\alpha =\text{A/C}$ or B) as obtained from the experiment [36]. The dotted line shows the ratio of relative sublattice hyperfine fields $h^{\mathrm{A}/\mathrm{C}}/h^{\mathrm{B}}$. The quantities $M\left(0\right)$ and $H\left(0\right)$ relate to $T=0$.

Figure 6

Calculated magnon dispersion of ${\mathrm{Fe}}_3\mathrm{Al}$ at $T=300$ K.

Figure 7

Calculated magnon dispersion of ${\mathrm{Fe}}_3\mathrm{Si}$ at $T=300$ K.

Figure 8

The concentration dependence of the reduced sublattice-resolved hyperfine fields, $h_{\alpha }\left(z\right)$, and magnetizations, $m_{\alpha }\left(z\right)$, in the DLM model on the Fe[B] sublattice: (a) for the ${\mathrm{Fe}}_3\mathrm{Si}$ compound and (b) for the ${\mathrm{Fe}}_3\mathrm{Al}$ compound.