Ab Initio Construction of Magnetic Phase Diagrams in Alloys: The Case of ${\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x\mathrm{Pt}$

A first-principles approach to the construction of concentration-temperature magnetic phase diagrams of metallic alloys is presented. The method employs self-consistent total energy calculations based on the coherent potential approximation for partially ordered and noncollinear magnetic states and is able to account for competing interactions and multiple magnetic phases. Application to the ${\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x\mathrm{Pt}$ “magnetic chameleon” system yields the sequence of magnetic phases at $T=0$ and the $c-T$ magnetic phase diagram in good agreement with experiment, and a new low-temperature phase is predicted at the Mn-rich end. The importance of non-Heisenberg interactions for the description of the magnetic phase diagram is demonstrated.

Figure 1

Magnetic exchange parameters $J_{\mu \nu }$ in the paramagnetic state corresponding to ($F$) ferromagnetic ordering, ${\mathbf{Q}}_F=0$; ($G$) $G$-type ordering, ${\mathbf{Q}}_G=(1,0,1/2)$; ($C$) $C$-type ordering, ${\mathbf{Q}}_C=(1,0,0)$. Red circles, $J_{\mathrm{Fe}\mathrm{Fe}}(\mathbf{Q})$; blue diamonds, $J_{\mathrm{Mn}\mathrm{Mn}}(\mathbf{Q})$; black squares, $J_{\mathrm{FeMn}}(\mathbf{Q})$.

Figure 2

Same as in Fig. 1 but normalized by the concentrations ${\tilde{J}}_{\mu \nu }(\mathbf{Q})=J_{\mu \nu }(\mathbf{Q})/(c_{\mu }{c}_{\nu })$.

Figure 3

(a) Accuracy of the fit at $x=0.26$. (b) The magnetic energy $E_{\text{mag}}$ (meV per $\mathrm{Fe}/\mathrm{Mn}$ atom) in the $F/G$ phase at $x=0.26$. The global minimum at ($\pi /2,\pi /2$) corresponds to the collinear $G$-type phase.

Figure 4

Magnetic energies of different phases at zero temperature (per $\mathrm{Fe}/\mathrm{Mn}$ atom). Arrows show the boundaries between the $F$, $F/G$, $G$, $G/C$, $F/C$, and $C$ phases (in the order of increasing $x$).

Figure 5

Angles ${\theta }_{\nu }$ made by the spin moments of Fe and Mn with the $z$ axis at zero temperature. By convention, the $G$ order parameter, as well as the $F$ order parameter in the $F/C$ phase, are assumed to be orthogonal to the $z$ axis; all others are parallel to $z$.

Figure 6

Magnetic phase diagram of ${\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x\mathrm{Pt}$. Temperatures are rescaled by the ratio $T_{\text{expt}}(x)/T_{\text{theor}}(x)$, where $T(x)=(1-x)T_C+x{T}_N$; $T_C$ and $T_N$ are the ordering temperatures of FePt and MnPt from Ref. [23] (expt) or theory (theor). (MFA gives $T_C=924\mathrm{K}$ and $T_N=1670\mathrm{K}$.) Thick (blue) lines, full fit for $E_{\text{mag}}$. Thin (red) lines, same fit but with non-Heisenberg terms set to zero. Solid (dashed) lines, second-(first-)order phase transitions. Symbols, experimental data [23].