Although experimental evidence shows that structural variation or defects induced by the fluctuation of growth conditions lead to increased or decreased performance in fabricated garnet structure 13, 15, 16, investigations on the atomic structure for these defective structures, combined with the revelation of their hidden coupling effect between multiple order parameters, have been rarely discussed. For example, as candidates for MO devices with high laser-induced-damage threshold (LIDT), element substituted garnet films prepared with different synthetic methods or heat treatment exhibit significantly different properties 8, 11, 14. Meanwhile, impurities in large sizes can always induce cracks in the surface of films, which degrades the stability and tolerance of the incident laser, thus impairing functionalities 12, 13. These impurities, such as Bi 2O 3 or CeO 2, can decrease the single crystallinity and exhibit almost no MO response. However, because components for preparation exhibit different chemical and physical stabilities, the adjustment of growth conditions, for example, such as temperature, growth rate, and atmosphere, can always induce some unexpected defects or impurities. To achieve the adjustable composition of garnet that can be tailored for specific applications, garnet films epitaxially grown on different substrates with high qualities have been prepared by different synthetic methods, such as liquid phase epitaxial (LPE) 11. Due to the strong coupling effects among multiple order parameters, including lattice, charge, spin, and orbital, the introduced substituent in the garnet structure would change the local lattice and electronic structure, which further influences the exchange interaction between different cation sites. Among these specific compositions, bismuth and rare earth elements such as cerium were chosen as effective substituents to increase the Faraday rotation angle by several magnitudes compared with YIG, to attain the material suitable for integrated MO devices 9, 11. Much effort has been given towards enhancing MO properties by designing specific element compositions in different cation sites for the garnet structure 8, 9, 10. Iron garnets also attract a large amount of attention because of the high figure of merit of MO properties. Furthermore, based on the availability of low-damping iron garnet waveguides, many spin-wave-based analogue signal processing devices have been developed. In addition, the production of spin-wave waveguides composed of thin-film YIG having high quality makes it possible for spin waves and spin-wave dynamics to be studied. Therefore, because of their unique linear and nonlinear spin-wave dynamics, these materials have been widely used as microwave devices such as high- Q microwave oscillators, filters, generators, and power limiters) 6, 7. Moreover, this ferrimagnetic insulator has the narrowest known line of ferromagnetic resonance (FMR), resulting in a magnon lifetime of a few nanoseconds 4. In particular, yttrium iron garnet Y 3Fe 5O 12 (YIG) exhibits low spin-wave damping, leading to spin-wave propagation with over centimeter distances 3, 4, 5. Iron garnet materials have been extensively utilized in magneto-optical (MO) devices because of their high thermal strength, high Verdet constants, and low optical absorption coefficient 1, 2. These analyses at the atomic scale provide important guidance for optimizing MO functional materials.

Furthermore, the formation of APBs can be eliminated by optimizing the growth rate, thus contributing to the enhanced MO performance. In particular, the segregation of oxygen deficiencies across the APBs directly leads to reduced magnetic elements, further decreases the magnetic moment of Fe and results in a higher absorption coefficient close to the APBs. We reveal that magnetic signals decrease in the regions close to APBs, which implies degraded MO performance. Here, by analyzing the structure and magnetic properties, two different antiphase boundaries (APBs) with individual interfacial structure are investigated in substituted iron garnet film. The adjustment on synthesis always induces structural variation, which is underestimated due to the limited knowledge of the local structures. The ferrimagnetic insulator iron garnets, tailored artificially with specific compositions, have been widely utilized in magneto-optical (MO) devices.

K atomic radius