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 similar to 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.