${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ is a fascinating material that displays physical properties governed by spin-orbit interactions and structural distortions, showing a wide range of remarkable electronic phenomena. Here, we present a density-functional-based analysis of the interplay among degrees of freedom, such as magnetism, Coulomb repulsion (Hubbard $U$), and structural degrees of freedom, considering two exchange-correlation methods: local density approximation (LDA) and Perdew-Burke-Ernzerhof revised for solids (PBEsol). Our goal is twofold: first, to present a brief overview of the current state of the art on this compound underpinning to the last proposed theoretical models and experimental research, and second, to provide an alternative interpretation of the electronic properties compared with the previous theoretical models. Our findings show that ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ displays several electronic states (metal, semimetal, and narrow insulator) as a function of Hubbard $U$ while it exhibits structural transition depending on the functional. We disentangle the effect of the different degrees of freedom involved, clarifying the role of exchange correlation in the observed electronic and structural transitions.

中文翻译：

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Ca3Ru2O7：自由度之间的相互作用和交换相关性的作用

${钙}_3{茹}_2{\mathrm{氧}}_7$是一种令人着迷的材料，它显示出受自旋轨道相互作用和结构扭曲控制的物理特性，显示出各种显着的电子现象。在这里，我们提出了基于密度泛函的自由度之间相互作用的分析，例如磁性、库仑斥力（Hubbard$U$）和结构自由度，考虑两种交换相关方法：局域密度近似 (LDA) 和针对固体修正的 Perdew-Burke-Ernzerhof (PBEsol)。我们的目标有两个：首先，简要概述该化合物的最新技术水平，为最后提出的理论模型和实验研究奠定基础；其次，与之前的理论相比，提供电子特性的替代解释楷模。我们的研究结果表明${钙}_3{茹}_2{\mathrm{氧}}_7$显示几种电子态（金属、半金属和窄绝缘体）作为哈伯德函数$U$同时它根据功能表现出结构转变。我们理清了所涉及的不同自由度的影响，阐明了交换相关性在观察到的电子和结构转变中的作用。