$A$-site ordered perovskites, ${\mathrm{CaCu}}_3{\mathrm{B}}_4{\mathrm{O}}_{12}$, which are derivatives of conventional ${AB\text{O}}_3$ perovskites, exhibit varying electronic and magnetic properties. With the objective of examining the role of Cu in this work, we have studied ${\mathrm{CaCu}}_3{\mathrm{Ti}}_4{\mathrm{O}}_{12}$ and ${\mathrm{CaCu}}_3{\mathrm{Zr}}_4{\mathrm{O}}_{12}$ and presented the cause of the crystallization of $A$-site ordered perovskite from conventional ${AB\text{O}}_3$ perovskite and the underlying mechanism leading to the stabilization of nontrivial and experimentally established $G$-type antiferromagnetic ($G$-AFM) ordering in these systems. The first-principles electronic structure calculations supplemented with phonon studies show that the formation of $A$-site ordered perovskite is driven by Jahn-Teller distortion of the ${\mathrm{CuO}}_{12}$ icosahedron. The crystal orbital Hamiltonian population analysis and magnetic exchange interactions estimated using spin dimer analysis infer that the nearest and next-nearest-neighbor interactions ($J_1$ and $J_2$) are direct and weakly ferromagnetic, whereas the third-neighbor interaction ($J_3$) is unusually strong and antiferromagnetic driven by an indirect superexchange mechanism. The structural geometry reveals that stabilization of $G$-AFM requires $J_1<2J_2, J_1<2J_3$. The experimental and theoretical values of Néel temperature agree well for $U\approx$ 7 eV, highlighting the role of strong correlation. The magnetic ordering is found to be robust against pressure and strain.

中文翻译：

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A位有序钙钛矿的稳定和自旋半反铁磁晶格的形成：CaCu3Ti4O12和CaCu3Zr4O12

$\mathrm{一个}$-现场订购钙钛矿，${\mathrm{钙铜}}_3{\mathrm{乙}}_4{\mathrm{○}}_{12}$，它们是常规的衍生物${\mathrm{一个}乙\text{○}}_3$钙钛矿，表现出不同的电子和磁性。为了检查 Cu 在这项工作中的作用，我们研究了${\mathrm{钙铜}}_3{钛}_4{\mathrm{○}}_{12}$和${\mathrm{钙铜}}_3{锆}_4{\mathrm{○}}_{12}$并提出了结晶的原因$\mathrm{一个}$-现场从常规订购钙钛矿${\mathrm{一个}乙\text{○}}_3$钙钛矿和导致非平凡和实验建立的稳定的潜在机制$G$型反铁磁（$G$-AFM）在这些系统中排序。辅以声子研究的第一性原理电子结构计算表明，$\mathrm{一个}$- 位点有序钙钛矿是由 Jahn-Teller 畸变驱动的${\mathrm{氧化铜}}_{12}$二十面体。使用自旋二聚体分析估计的晶体轨道哈密顿群体分析和磁交换相互作用推断最近和次近邻相互作用（${Ĵ}_1$和${Ĵ}_2$) 是直接且弱铁磁性的，而第三邻域相互作用 (${Ĵ}_3$) 是由间接超交换机制驱动的异常强和反铁磁。结构几何表明，稳定$G$-AFM 需要${Ĵ}_1<2{Ĵ}_2, {Ĵ}_1<2{Ĵ}_3$. Néel 温度的实验值和理论值非常吻合$ü\approx$7 eV，突出强相关作用。发现磁性排序对压力和应变具有鲁棒性。