Stabilization of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>A</mml:mi></mml:math> -site ordered perovskites and formation of spin-half antiferromagnetic lattice: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>CaCu</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>Ti</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>12</mml:mn></mml:msub></mml:mrow></mml:math> and <mml:math xmlns:mml="…

A-site ordered perovskites, CaCu$_3$B$_4$O$_{12}$, which are derivatives of conventional ABO$_3$ exhibit varying electronic and magnetic properties. With the objective examining role Cu in this work, we have studied CaCu$_3$Ti$_4$O$_{12}$ CaCu$_3$Zr$_4$O$_{12}$ presented cause crystallization perovskite from underlying mechanism leading to stabilization non-trivial experimentally estabilished G-type antiferromagnetic (G-AFM) ordering these systems. The first-principles structure calculations supplemented with phonon studies show that formation is driven by Jahn-Teller distortion CuO$_{12}$ icosahedron. crystal orbital Hamiltonian population analysis exchange interactions estimated using spin dimer infers nearest next-nearest-neighbor (J$_1$ J$_2$) direct weakly ferromagnetic whereas third-neighbor interaction (J$_3$) unusually strong indirect superexchange mechanism. structural geometry reveals G-AFM requires J$_1$ $<$ 2J$_2$, 2J$_3$. experimental theoretical values Neel Temperature agrees well for $U$ $\approx$ 7 eV, highlighting correlation. found be robust against pressure strain.