## 2 Materials and Methods  
Several batches of highly bismuth-substituted iron garnet films were sputtered on 0.5 mm thick quartz substrates from an oxide-mix-based target of nominal composition Bi\({}_{2.1}\)Dy\({}_{0.9}\)Fe\({}_{3.9}\)Ga\({}_{1.1}\)O\({}_{12}\) with some variations in their deposition process parameters (using different substrate temperatures and substrate stage rotation rates). This target was prepared by the manufacturer (AJA Inc., Scituate, MA, USA) by sintering a stoichiometrically adjusted mix of oxides such as Bi\({}_{2}\)O\({}_{3}\), Dy\({}_{2}\)O\({}_{3}\), Fe\({}_{2}\)O\({}_{3}\), and Ga\({}_{2}\)O\({}_{3}\). As the sputter gas pressure during the layer growth typically does affect the film's microstructure and properties (according to our previous garnet microstructure observations, measurements of the film's refractive index, and the measurements of specific Faraday rotation), the sputtering process gas chemistry (Ar) and pressure were kept constant (at 2 mTorr) for all batches of samples. During the sputtering processes, RF powers of up to 175 W (3.8 W/cm\({}^{2}\)) were applied to ablate targets 7.62 cm. (3 in.) in diameter. The sputtering deposition system (KVS-T4065, from Korea Vacuum Technology Ltd., Gyeonggi-do, Korea) was of the down-sputtering type. Its geometric features allowed high-uniformity deposition over a substrate holder area of about 5 cm in diameter, owing to the relatively large substrate-to-target distance of 18 cm. In the vertical plane cross section, the directions normal to the sputtering target surfaces form 30\({}^{\circ}\) angles with the normal to the (horizontal) substrate stage surface. In the horizontal plane cross section passing through the target centers, the target centers are positioned at the vertices of an equilateral triangle having side dimension of about 150 mm. The optimizations of high-temperature annealing process parameters were performed by running several trials of both the deposition and annealing processes, followed by the selection of parameters, which led to maximizing specific Faraday rotation in films of good optical quality. The effects of variation in the substrate temperature and substrate stage rotation rate used during the deposition process on the final properties of material were first assessed by analyzing the obtained specific Faraday rotations at 532 nm and also the MO figures of merit. The presence of high specific Faraday rotations observed in these highly Bi-substituted garnet layers confirmed the formation of crystalline garnet phase, which was also reconfirmed by performing the X-ray diffractometry (XRD) measurements. The physical thicknesses of all garnet layers were measured directly during the deposition processes using a quartz microbalance sensor, and were also reconfirmed by spectrally fitting the transmission spectra of all films to their predicted transmission spectra using specialized software tools [5]. The software-assisted indirect film thickness measurements also allowed detection of any differences in the layer thickness values for the different samples from within the same deposition batch, which could arise due to the slight nonuniformities in the deposited thickness. The optical transmission spectra of both the as-deposited and post-annealed garnet films were measured using a UV-Visible spectrophotometer (Beckman Coulter Inc., Atlanta, GA, USA) and the specific Faraday rotation of annealed garnet layers was measured using a Thorlabs PAX polarimeter system (Thorlabs Inc, Newton, NJ, USA) in conjunction with a custom-made calibrated electromagnet. XRD measurements were performed by using Cu K\(\alpha_{1}\) radiation line in theta-theta diffractometer configuration, at near-grazing incidence of X-ray radiation. The measurements were performed using a diffracted beam collimator with 2\(\theta\) in the range of 20\({}^{\circ}\) to 70\({}^{\circ}\). The angular positions of the X-ray diffraction peaks were determined by using the peak-listing options of the Jade ver.