Topological insulators in the quaternary chalcogenide compounds and ternary famatinite compounds Abstract. We present first-principles calculations to predict several threedimensional (3D) topological insulators in quaternary chalcogenide compounds of compositions I 2 -II-IV-VI 4 and ternary famatinite compounds of compositions I 3 -V-VI 4 . Among the large number of members of these two families, we give examples of naturally occurring compounds that are mainly Cu-based chalcogenides. We show that these materials are candidates for 3D topological insulators or can be tuned to obtain topologically interesting phases by manipulating the atomic number of the various cations and anions. A band inversion can occur at a single point with large inversion strength, in addition to the opening of a bulk bandgap throughout the Brillouin zone. We discuss how the two investigated families of compounds are related to each other by cross-substitution of cations in the underlying tetragonal structure.

We discuss the ground state electronic structure and magnetization properties of a series of NiFe2-x Al x O4 solid solutions (x  =  0.0, 0.4, 0.8, 1.2, 1.6, and 2.0) using magnetic Compton scattering measurements, together with parallel first-principles computations. In this way, we systematically extract the complicated cation distributions in this ferrite system as a function of x. The relationship between the electronic ground state, magnetism, and cation distributions is explained in terms of a model, validated by our first-principles computations, wherein the magnetic properties of the three cation distributions are assumed to be different. A good accord is found between the computed and measured magnetic Compton profiles.