Features of the Faraday and Kerr magneto-optical effects in nanoscale Y$_3$Fe$_5$O$_{12}$ films and Gd$_3$Ga$_5$O$_{12}$, Nd$_3$Ga$_5$O$_{12}$ substrates

The Faraday and Kerr magneto-optical effects for ultra-thin films of yttrium iron garnet Y$_3$Fe$_5$O$_{12}$ and monocrystalline substrates Gd$_3$Ga$_5$O$_{12}$ and Nd$_3$Ga$_5$O$_{12}$ were studied in the visible spectrum range 1.3 eV $< E <$ 4.5 eV in fields up to 1 T. Verdet constants for the substrates Gd$_3$Ga$_5$O$_{12}$ (V $\approx$ +1048 min/(T $\cdot$ cm)) and Nd$_3$Ga$_5$O$_{12}$ ($\approx$ 4000 min/(T $\cdot$ cm)) were determined, and features of the Faraday and Kerr effects spectra related to the magneto-optical properties of the substrates for Y$_3$Fe$_5$O$_{12}$/ Gd$_3$Ga$_5$O$_{12}$ and Y$_3$Fe$_5$O$_{12}$/Nd$_3$Ga$_5$O$_{12}$ structures were identified. It was shown that, by excluding the contribution from the substrates, the spectral and field dependencies of the magneto-optical effects in nanoscale films correspond to the data for bulk Y$_3$Fe$_5$O$_{12}$. An estimation of the relaxation layer was carried out, and it was shown that nanoscale films, being comparable in thickness to the critical layer, can possess a specific Faraday rotation (15–20 deg/$\mu$m) close to that of bulk materials, demonstrating the high quality of the obtained samples.