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.