First-Principles Combinatorial Design of Transition Temperatures in Multicomponent Systems: The Case of Mn in GaAs

The transition temperature $T_C$ of multicomponent systems—ferromagnetic, superconducting, or ferroelectric—depends strongly on the atomic arrangement, but an exhaustive search of all configurations for those that optimize $T_C$ is difficult, due to the astronomically large number of possibilities. Here we address this problem by parametrizing the $T_C$ of a set of $\sim 50$ input configurations, calculated from first principles, in terms of configuration variables (“cluster expansion”). Once established, this expansion allows us to search almost effortlessly the transition temperature of arbitrary configurations. We apply this approach to search for the configuration of Mn dopants in GaAs having the highest ferromagnetic Curie temperature. Our general approach of cluster expanding physical properties opens the way to design based on exploring a large space of configurations.

Figure 1

The exchange interaction between pairs of Mn atoms, calculated in the linear-response approximation, is shown as a function of the Mn-Mn distance for (a) a ${\mathrm{Ga}}_{92}{\mathrm{Mn}}_8{\mathrm{As}}_{100}$ supercell containing 6 Mn spectator atoms in addition to the Mn pair, and (b) a set of isolated Mn-Mn pairs in a ${\mathrm{Ga}}_{30}{\mathrm{Mn}}_2{\mathrm{As}}_{32}$ supercell. Red circles indicate pairs of Mn atoms that are separated by the same distance, but have different $J_{ij}$’s because of the presence of spectator Mn atoms.

Figure 2

Final iteration cluster expansion. Part (a) shows the many-body figures obtained from the genetic-algorithm search. Part (b) shows the predicted $T_C$ of $\sim 2^{20}$ ordered structures. The black circles indicate structures that fall inside the composition range used for the cluster expansion ($0.12<x<0.46$), while green or light gray circles denote structures outside that range. Red or medium gray circles denote the input structures that were used in the fit of the cluster-expansion coefficients. The solid blue line shows the predicted $T_C$ of a random alloy as a function of Mn concentration.

Figure 3

(a) Predicted $T_C$ of several $(\mathrm{GaAs}{)}_m/(\mathrm{MnAs}{)}_n$ pure superlattices in different crystallographic orientations. Also shown is the $T_C$ of the random alloy (black dashed line). (b) Predicted $T_C$ of $({\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}{)}_m/({\mathrm{Ga}}_{1-y}{\mathrm{Mn}}_y\mathrm{As}{)}_n$ alloy superlattices in the (001) orientation. For each set of layer compositions $(x,y)$, the layer thicknesses $(m,n)$ are allowed to vary between 1 and 4. The dashed line denotes the $T_C$ of the random alloy.