Fig. 5: Effects of magnetic elements with a lower valence state on MO properties.

a The schematic diagram shows that regions with APBs exhibit a decreased net magnetism and enhanced light absorption, this is because the Fe³⁺ in different sites can be reduced to Fe²⁺ due to the oxygen deficiencies. O_V is referred to the oxygen vacancies, and green dots represent the oxygen vacancies. Green rectangle and parallelogram indicate the APBs. b STEM-bright field (BF) image of the film with a larger growth rate ~1.00 µm/min, yellow arrows mark the APBs. c. STEM-BF image of the film in low magnification with a growth rate of 0.84 µm/min, while films prepared with a growth rate of 0.84 µm/min show perfect crystal structure without any obvious boundaries. An enlarged view extracted from the region marked by cubic lines in (b) shows perfect atomic arrangement as an atomic model along the [001] zone axis. Insets in (b) and (c) are Fast Fourier transform (FFT) images, where diffraction planes are highlighted by red circles. d Plots of the absorption coefficient as the function of wavelength are compared between samples prepared with different growth rates. e The histogram shows the comparison of the LIDT between the sample prepared with different growth rates and GGG substrates. f Plots of Faraday rotation angles as the function of wavelength are compared between samples prepared with different growth rates. The error bar is defined by the standard deviation of measured Faraday rotation angles.