Interplay between magnetism and short-range order in medium- and high-entropy alloys: CrCoNi, CrFeCoNi, and CrMnFeCoNi

The impact of magnetism on predicted atomic short-range order in three medium- and high-entropy alloys is studied using a first-principles all-electron Landau-type linear-response theory, coupled with lattice-based atomistic modeling. We perform two sets of linear-response calculations: One in which the paramagnetic state is modeled within the disordered local moment picture, and one in which systems are modeled in a magnetically ordered state, which is ferrimagnetic for the alloys considered in this paper. We show that the treatment of magnetism can have a significant impact both on the predicted temperature of atomic ordering and the nature of atomic order itself. In CrCoNi, we find that the nature of atomic order changes from being $\mathrm{L}{1}_2$-like when modeled in the paramagnetic state to ${\mathrm{MoPt}}_2$-like when modeled assuming the system has magnetically ordered. In CrFeCoNi, atomic correlations between Fe and other elements present are dramatically strengthened when we switch from treating the system as magnetically disordered to magnetically ordered. Our results show it is necessary to consider the magnetic state when modeling multicomponent alloys containing mid- to late-$3d$ elements. Furthermore, we suggest that there may be high-entropy alloy compositions containing $3d$ transition metals that will exhibit specific atomic short-range order when thermally treated in an applied magnetic field. This has the potential to provide a route for tuning physical and mechanical properties in this class of materials.

Figure 1

Plots of the total and species-resolved density of states for the three systems in both magnetically disordered (“PM”) and magnetically ordered (“FM”) states. The total DoS is given by the weighted average of the species-resolved curves. It can be seen that there are significant shifts to the DoS for elements acquiring a large magnetic moment in the magnetically ordered calculations. In the majority spin channel of CrCoNi, for instance, Co starts to look, such as Ni, whereas in CrMnFeCoNi, Mn makes a similar contribution to Cr to the total DoS.

Figure 2

Plots of the eigenvalues of the chemical stability matrix around the irreducible Brillouin zone for the three systems, generated from both the magnetically disordered (PM) and magnetically ordered (FM) potentials. It can be seen that the nature of modes in all three materials are altered when the magnetic symmetry is broken; there is more mixing between modes, and previously flat modes acquire more distinct shape, indicative of strengthening correlations. Most notably, in CrCoNi, there is clear competition between minima, i.e., the dominant SRO. From magnetically disordered to ordered states, the location of the minimum shifts from $\mathbf{k}=(0,0,1)$, i.e., the $X$ point, to $\mathbf{k}=(0,\frac{2}{3},\frac{2}{3})$, a point along the line from $\mathrm{\Gamma }$ to $K$. This is indicative of competition between $\mathrm{L}{1}_2$-like and ${\mathrm{MoPt}}_2$-like order.

Figure 3

Comparison of the partially ordered structures predicted with our linear-response theory for CrCoNi in both its magnetically ordered (FM) and magnetically disordered (PM) states. Both orderings are driven by Cr, but in the magnetically ordered state, ${\mathrm{MoPt}}_2$-like order is predicted, whereas in the paramagnetic state it is $\mathrm{L}{1}_2$-like order that is favored.

Figure 4

Plots of the Warren-Cowley short-range order parameters on first and second coordination shells for the three considered systems along with a measure of the system's specific-heat capacity, $C$. Each subplot is labeled to indicate the alloy and magnetic state for which it shows results. The magnetically ordered results show a significant weakening of ordering between Cr and Co and a strengthening of interactions between Fe and the other elements.