Optical spectroscopy of Kramers doublets of an Er$^{3+}$ ion in a two-dimensional frustrated magnetic Cu$_{3}$Er(SeO$_{3}$)$_{2}$O$_{2}$Cl

Francisites, Cu$_{3}$M(YO$_{3}$)$_{2}$O$_{2}$X (M = Bi or rare earth, Y = Se, Te, X = Br, Cl, or I), attract close attention from researchers because of their interesting magnetic properties, such as metamagnetic transitions in relatively weak magnetic fields and magnetic phase transitions with spin reorientation; they also can serve as model systems for the study of two-dimensional and frustrated magnetism. In this work, we have performed a low-temperature optical spectroscopic study of erbium francisite, Cu$_{3}$Er(SeO$_{3}$)$_{2}$O$_{2}$Cl. The observed splitting of spectral lines corresponding to $f$–$f$ transitions in the Er$^{3+}$ Kramers ion unambiguously indicates the magnetic ordering of the crystal at a temperature of $T_{\mathrm{N}}$ = 37.5 K. The temperature dependence of the splitting of the ground doublet of the erbium ion is determined. The contributions of erbium to the heat capacity and to the magnetic susceptibility of Cu$_{3}$Er(SeO$_{3}$)$_{2}$O$_{2}$Cl are calculated.