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.

The element bismuth has been chosen as a substituent, or major element, in a diverse range of functional materials, including multiferroics, superconductors, and catalysts (1–3). On account of the often significantly improved performance and various unique phenomena when bismuth is introduced in functional materials, investigations on the local order parameters underpinning such effects have attracted considerable attention. In the past few years, it has been verified that bismuth doping is also an effective method to enhance the performance of magneto-optical devices (4, 5). Among the iron oxides, ferrimagnetic insulators with the complex iron garnet structure R₃Fe₅O₁₂ (where R is an element with large radius) are already widely utilized in magneto-optic devices owing to their combination of small spin-wave damping, good optical transparency, and a pronounced Faraday effect (6–12). The strength of the Faraday effect, which describes a rotation of the plane of polarization of electromagnetic radiation in a magnetic field, is linearly proportional to the Verdet constant (13, 14) for a given material, which for magneto-optical materials such as substituted garnets depends strongly on the coupling effect of multiple quantum-order parameters (15, 16), including those of lattice, spin, and electronic orbitals (12, 17, 18). In particular, diverse polyhedral sites in the garnet structure are bridged via oxygen atoms with a strong exchange interaction effect, resulting in complex electronic and crystal structures (19–22). Although pure yttrium iron garnet (YIG) has several advantages in terms of magneto-optical response, it has not been widely applied in integrated devices due to its low Verdet constant, resulting in a limited Faraday rotation (23, 24). Due, however, to its chemical flexibility, selective substitution has been established as an effective method to tune various physical properties of iron garnets (7, 12, 25, 26), and it is noteworthy that Bi-substituted lutetium iron garnet films prepared via liquid phase epitaxy (LPE) demonstrate an appreciable enhancement in magneto-optical performance (8). Several models based on diamagnetic transitions have been proposed to explain the effect of Bi substitution on magneto-optical response (4, 12, 17, 19, 21, 27–30), in each case with a strong dependence on the crystal energy levels of the Fe³⁺ ions in differently coordinated lattice sites. There is still, however, a lack of experimental evidence to test these models, as this requires the distribution of substituent atoms to be characterized and related to their effect on the crystal lattice and electronic structure at different lattice sites. In this work, we address this limitation by the use of several advanced electron microscopy techniques (31–40) applied synergistically to a Bi-substituted lutetium iron garnet.