Magnetism and unusual Cu valency in quadruple perovskites

We study a selection of Cu-containing magnetic quadruple perovskites (CaCu$_{3}$Ti$_{4}$O$_{12}$, LaCu$_{3}$Fe$_{4}$O$_{12}$, and YCu$_{3}$Co$_{4}$O$_{12}$) by ab initio calculations, and show that Cu is in an effective divalent Cu(II)-like state or a trivalent Cu(III) state depending on the choice of octahedral cation. Based on the electronic structure, we also discuss the role of Mott and Zhang-Rice physics in this materials class.