Bismuth and rare earth elements have been identified as effective substituent elements in the iron garnet structure, allowing an enhancement in magneto-optical response by several orders of magnitude in the visible and near-infrared region. Various mechanisms have been proposed to account for such enhancement, but testing of these ideas is hampered by a lack of suitable experimental data, where information is required not only regarding the lattice sites where substituent atoms are located but also how these atoms affect various order parameters. Here, we show for a Bi-substituted lutetium iron garnet how a suite of advanced electron microscopy techniques, combined with theoretical calculations, can be used to determine the interactions between a range of quantum-order parameters, including lattice, charge, spin, orbital, and crystal field splitting energy. In particular, we determine how the Bi distribution results in lattice distortions that are coupled with changes in electronic structure at certain lattice sites. These results reveal that these lattice distortions result in a decrease in the crystal-field splitting energies at Fe sites and in a lifted orbital degeneracy at octahedral sites, while the antiferromagnetic spin order remains preserved, thereby contributing to enhanced magneto-optical response in bismuth-substituted iron garnet. The combination of subangstrom imaging techniques and atomic-scale spectroscopy opens up possibilities for revealing insights into hidden coupling effects between multiple quantum-order parameters, thereby further guiding research and development for a wide range of complex functional materials.

铋和稀土元素已被确定为铁石榴石结构中的有效取代元素，可以在可见光和近红外区域将磁光响应增强几个数量级。已经提出了各种机制来解释这种增强，但是由于缺乏合适的实验数据，这些想法的测试受到阻碍，其中不仅需要关于取代原子所在的晶格位点的信息，还需要关于这些原子如何影响各种有序参数的信息. 在这里，我们展示了双取代镥铁石榴石如何使用一套先进的电子显微镜技术结合理论计算来确定一系列量子阶参数之间的相互作用，包括晶格、电荷、自旋、轨道, 和晶体场分裂能量。特别是，我们确定了 Bi 分布如何导致晶格畸变，这些畸变与某些晶格位点的电子结构变化相结合。这些结果表明，这些晶格畸变导致 Fe 位点的晶体场分裂能降低和八面体位点的轨道简并性升高，而反铁磁自旋顺序保持不变，从而有助于增强铋的磁光响应。替代铁石榴石。亚埃成像技术和原子尺度光谱的结合为揭示多个量子阶参数之间隐藏的耦合效应提供了可能性，从而进一步指导了广泛的复杂功能材料的研究和开发。我们确定 Bi 分布如何导致晶格畸变，而这些畸变与某些晶格位点的电子结构变化有关。这些结果表明，这些晶格畸变导致 Fe 位点的晶体场分裂能降低和八面体位点的轨道简并性升高，而反铁磁自旋顺序保持不变，从而有助于增强铋的磁光响应。替代铁石榴石。亚埃成像技术和原子尺度光谱的结合为揭示多个量子阶参数之间隐藏的耦合效应提供了可能性，从而进一步指导了广泛的复杂功能材料的研究和开发。我们确定 Bi 分布如何导致晶格畸变，而这些畸变与某些晶格位点的电子结构变化有关。这些结果表明，这些晶格畸变导致 Fe 位点的晶体场分裂能降低和八面体位点的轨道简并性升高，而反铁磁自旋顺序保持不变，从而有助于增强铋的磁光响应。替代铁石榴石。亚埃成像技术和原子尺度光谱的结合为揭示多个量子阶参数之间隐藏的耦合效应提供了可能性，从而进一步指导了广泛的复杂功能材料的研究和开发。