Energetics of the coupled electronic–structural transition in the rare-earth nickelates

Rare-earth nickelates exhibit a metal–insulator transition accompanied by a structural distortion that breaks the symmetry between formerly equivalent Ni sites. The quantitative theoretical description of this coupled electronic–structural instability is extremely challenging. Here, we address this issue by simultaneously taking into account both structural and electronic degrees of freedom using a charge self-consistent combination of density functional theory and dynamical mean-field theory, together with screened interaction parameters obtained from the constrained random phase approximation. Our total energy calculations show that the coupling to an electronic instability toward a charge disproportionated insulating state is crucial to stabilize the structural distortion, leading to a clear first order character of the coupled transition. The decreasing octahedral rotations across the series suppress this electronic instability and simultaneously increase the screening of the effective Coulomb interaction, thus weakening the correlation effects responsible for the metal–insulator transition. Our approach allows to obtain accurate values for the structural distortion and thus facilitates a comprehensive understanding, both qualitatively and quantitatively, of the complex interplay between structural properties and electronic correlation effects across the nickelate series.

稀土镍酸盐（Rare-earth nickelates）表现出金属-绝缘体转变（metal–insulator transition），伴随有打破原本等价镍位点对称性的结构畸变（structural distortion）。针对这一耦合电子-结构不稳定性的定量理论描述极具挑战性。本文中，我们采用密度泛函理论（density functional theory）与动态平均场理论（dynamical mean-field theory）的电荷自洽耦合方案，并结合由约束随机相位近似（constrained random phase approximation）得到的屏蔽相互作用参数，同时兼顾结构与电子自由度，以此解决该难题。我们的总能量计算结果显示，与朝向电荷歧化绝缘态的电子不稳定性之间的耦合作用，对稳定该结构畸变至关重要，这使得耦合转变呈现出清晰的一级相变特征。随着该系列体系的八面体旋转程度逐渐降低，该电子不稳定性受到抑制，同时有效库仑相互作用的屏蔽效应得以增强，进而削弱了引发金属-绝缘体转变的关联效应。本方法可精准获取结构畸变的数值，从而有助于从定性与定量两个维度，全面理解稀土镍酸盐系列中结构性质与电子关联效应之间的复杂相互作用。