$A$-site Magnetism in Perovskites CaCu$_{3}B_{4}$O$_{12}$ ($B$ = Ge, Ti, Sn).

$A$-site-ordered perovskites CaCu$_{3}$Ge$_{4}$O$_{12}$ and CaCu$_{3}$Sn$_{4}$O$_{12}$, both isostructural to antiferromagnetic CaCu$_{3}$Ti$_{4}$O$_{12}$, were found to be ferromagnets, which are very rare in cuprates. All of these materials may be called ``$A$-site magnets'', since they contain magnetic species only at the $A$-site of the perovskite \textit{AB}O$_{3}$ structure. The ferromagnetism of CaCu$_{3}B_{4}$O$_{12}$ ($B$ = Ge, Sn) is attributed to the ferromagnetic direct exchange interaction, whereas antiferromagnetic superexchange interaction, due to the Cu(3$d)$-O(2$p)$-Ti-(3$d)$ orbital hybridization, is dominant in antiferromagnetic CaCu$_{3}$Ti$_{4}$O$_{12}$. The $A$-site magnetism is controlled by the electronic structure of the non-magnetic $B$ site. Solid solutions CaCu$_{3}$(Ge,Ti)$_{4}$O$_{12}$ and CaCu$_{3}$(Ti,Sn)$_{4}$O$_{12}$ display phase boundary between ferromagnetic and antiferromagnetic phases. [1] H. Shiraki, T. Saito, Y. Shimakawa et al., \textit{Phys. Rev. B}, \textbf{76}, (2007) 140403. [2] Y. Shimakawa, H. Shiraki and T. Saito, \textit{J. Phys. Soc. Jpn.}, \textbf{77}, (2008) 113702.