Atomic-scale insights into quantum-order parameters in bismuth-doped iron garnet

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.