Ab initio study of magnetic coupling in CaCu 3 B 4 O 12 ( B = Ti , Ge , Zr , and Sn )

Magnetism of A-site-ordered perovskites, CaCu3Ti4O12, CaCu3Ge4O12, CaCu3Sn4O12, and CaCu3Zr4O12, is comprehensively studied by means of ab initio electronic structure calculations. The magnetic exchange coupling constants between Cu-site spins, J1, J2, and J3, are estimated within an effective Heisenberg model, revealing relative importance of J3 despite its long interaction length. The ground-state magnetic order is reasonably explained by the combination of (i) relatively weak ferromagnetic superexchange interaction (J1) that works for all the oxides and (ii) antiferromagnetic long-range superexchange interaction (J3) that works selectively for CaCu3Ti4O12 and CaCu3Zr4O12.