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A-site ordered perovskites, CaCu$_3$B$_4$O$_{12}$, which are derivatives ofconventional ABO$_3$ perovskites, exhibit varying electronic and magneticproperties. With the objective of examining the role of Cu in this work, wehave studied CaCu$_3$Ti$_4$O$_{12}$ and CaCu$_3$Zr$_4$O$_{12}$ and presentedthe cause of the crystallization of A-site ordered perovskite from conventionalABO$_3$ perovskite and the underlying mechanism leading to the stabilization ofnon-trivial and experimentally estabilished G-type antiferromagnetic (G-AFM)ordering in these systems. The first-principles electronic structurecalculations supplemented with phonon studies show that the formation of A-siteordered perovskite is driven by Jahn-Teller distortion of the CuO$_{12}$icosahedron. The crystal orbital Hamiltonian population analysis and magneticexchange interactions estimated using spin dimer analysis infers that thenearest and next-nearest-neighbor interactions (J$_1$ and J$_2$) are direct andweakly ferromagnetic whereas the third-neighbor interaction (J$_3$) isunusually strong and antiferromagnetic driven by indirect superexchangemechanism. The structural geometry reveals that stabilization of G-AFM requiresJ$_1$ $<$ 2J$_2$, J$_1$ $<$ 2J$_3$. The experimental and theoretical values ofNeel Temperature agrees well for $U$ $\approx$ 7 eV, highlighting the role ofstrong correlation. The magnetic ordering is found to be robust againstpressure and strain.

Stabilization of A-site ordered perovskites and formation of spin-half antiferromagnetic lattice: CaCu$_3$Ti$_4$O$_{12}$ and CaCu$_3$Zr$_4$O$_{12}$