Spectroscopic properties and structure of the ErFe$_3$(BO$_3$)$_4$ single crystal

Single crystals of the ErFe$_3$(BO$_3$)$_4$ borate were synthesized and their structure was studied. Absorption spectra of the Er3+ ion in $\sigma$- and $\pi$-polarizations of $f$–$f$ transitions $^4I_{15/2}\to^4I_{13/2}$, $^4I_{11/2}$, $^4I_{9/2}$, $^4F_{9/2}$, $^4S_{3/2}$, $^2H_{11/2}$, and $^4F_{7/2}$ were measured. The refractive index and birefringence were measured as a function of the wavelength. The transition intensities were analyzed within the Judd-Ofelt theory, and the following parameters of the theory were obtained: $\Omega_2$ = 7.056 $\times$ 10$^{-20}$ cm$^2$, $\Omega_4$ = 1.886 $\times$ 10$^{-20}$ cm$^2$, and $\Omega_6$ = 2.238$\times$10$^{-20}$ cm$^2$. Using these parameters, the radiative transition probabilities, luminescence branching ratios, and radiative lifetimes of multiplets were calculated.