# Verdet Constant of Magneto-Active Materials Developed for High-Power Faraday Devices
## 2 Characterization of the Verdet Constant as a Function of Wavelength and Temperature
### UV Region (\(\lambda<400\) nm)  
The historical development of magneto-active materials for the UV region has already been very well summarized in Refs. [59; 61]. The very first investigations were performed on the commonly used solids and liquids (e.g., quartz, water, etc. ), which, however, exhibit only very small values of the Verdet constant because of their diamagnetic character. The following research was therefore focused more on various materials containing rare-earth (RE) paramagnetic ions, which were reported to have high magneto-optical characteristics [62; 63; 64; 65]. In this manner, several RE-containing glasses were investigated as possible magneto-active materials for the UV FDs, with the cut-off wavelengths equal to \(\sim\)200-300 nm [66; 67; 68]. It was observed that the Verdet constant in these glasses is directly proportional to the concentration of the RE ions. Unfortunately, the increase in the concentration (and the Verdet constant) was found to be constricted by the composition of the glass and, furthermore, it is counterbalanced by increased absorption losses [67; 69]. Phosphates (KDP, DKDP, ADP, etc.) and arsenates (ADA, KDA or DKDA) were studied as possible material candidates for deeper UV (\(\lambda<200\) nm) [70; 71]. Nevertheless, these compounds exhibit serious drawbacks for their further utilization in the FDs because they are relatively soft and hygroscopic. The focus of attention was then switched to fluoride crystals, which were already studied in Refs. [72; 73; 74], but more comprehensively, with a focus on the UV region, in Refs. [59; 61]. In the latter, magneto-optical characteristics of CeF\({}_{3}\), PrF\({}_{3}\)[61] and of LiREF\({}_{4}\) (RE = Tb, Dy, Ho, Er and Yb) [59] crystals were reported and studied in detail. The conclusion is that these fluorides exhibit high Verdet constant values and low absorption in the UV (inside their local transmission windows), with the cut-off wavelengths \(>\)158 nm. To the best of our knowledge, only the CeF\({}_{3}\) crystal has been more extensively studied in the following years. These investigations were focused mainly on the magneto-optical characteristics of the CeF\({}_{3}\) in the VIS-NIR region, which we discuss in the following subsection. The reason is the higher FOM parameter of CeF\({}_{3}\) as compared to the most commonly used magneto-active material in the VIS-NIR--the terbium gallium garnet crystal. A successful design and construction of CeF\({}_{3}\)-based UV Faraday isolators was reported in Ref. [75]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Material** & **F [rad/(Tm)]** & \(\lambda_{0}\) [nm]** & \(|V|\) at 248 nm & \(|V|\) at 308 nm & **Reference** & **Additional References** \\ \hline CeF\({}_{3}\) & 743.6 & 239 & - & 1146 & [61] & [73; 74; 75] \\ PrF\({}_{3}\) & 1357.7 & 184 & 1658 & 752 & [61] & [73; 74] \\ LiTbF\({}_{4}\) & 1190.6 & 198 & 2101 & 840 & [59] & [72; 76] \\ LiDyF\({}_{4}\) & 1530.9 & 156 & 1002 & 528 & [59] & - \\ LiHoF\({}_{4}\) & 3815.0 & 87 & 536 & 331 & [59] & - \\ LiErF\({}_{4}\) & 1700.0 & 93 & 279 & 171 & [59] & - \\ LiYbF\({}_{4}\) & 58.0 & 163 & 44 & 23 & [59] & - \\ Pr\({}_{2}\)O\({}_{3}\)-doped oxide glass & - & - & 1538 & - & [66] & - \\ Dy\({}_{2}\)O\({}_{3}\)-doped oxide glass & - & - & 782 & - & [66] & - \\ Pr-doped phosphate glass & - & - & - & 311 & [69] & - \\ Dy-doped alumino-borate glass & - & - & 489 & [69] & - \\ KDP & - & - & 31 & 18 & [71] & [70] \\ DKDP & - & - & 36 & 21 & [71] & [70] \\ ADP & - & - & 32 & 19 & [71] & [70] \\ KDA & - & - & 61 & 35 & [71] & [70] \\ DKDA & - & - & 71 & 39 & [71] & [70] \\ ADA & - & - & 71 & 38 & [71] & [70] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: A brief overview of magneto-active materials for the UV FDs (\(\lambda<400\) nm). The Verdet constant dispersion \(V(\lambda)\) is given by the single-transition model in Equation (13) with the specified (\(F,\lambda_{0}\))-parameters; the \(G\)-parameter is equal to 0 for all materials.