Ab initiostudy of magnetic coupling in CaCu3B4O12(B=Ti, Ge, Zr, and Sn)

Abstract

Magnetism of $A$-site-ordered perovskites, CaCu${}_{3}$Ti${}_{4}$O${}_{12}$, CaCu${}_{3}$Ge${}_{4}$O${}_{12}$, CaCu${}_{3}$Sn${}_{4}$O${}_{12}$, and CaCu${}_{3}$Zr${}_{4}$O${}_{12}$, is comprehensively studied by means of ab initio electronic structure calculations. The magnetic exchange coupling constants between Cu-site spins, ${J}_{1}$, ${J}_{2}$, and ${J}_{3}$, are estimated within an effective Heisenberg model, revealing relative importance of ${J}_{3}$ despite its long interaction length. The ground-state magnetic order is reasonably explained by the combination of (i) relatively weak ferromagnetic superexchange interaction (${J}_{1}$) that works for all the oxides and (ii) antiferromagnetic long-range superexchange interaction (${J}_{3}$) that works selectively for CaCu${}_{3}$Ti${}_{4}$O${}_{12}$ and CaCu${}_{3}$Zr${}_{4}$O${}_{12}$.