Optical 4$f$–4$f$ transitions in multiferroic HoMnO$_3$

In the absorption spectra of the hexagonal single-crystal manganite HoMnO$_3$ in the paramagnetic ferroelectric state, lines near 1.1 and 2.0 $\mu$m were observed associated with the transitions $^5I_8$ $\to$ $^5I_6$ and $^5I_8$ $\to$ $^5I_7$, respectively, within the 4$f^{10}$ configuration of the Ho$^{3+}$ ion. At $T$ = 80 K, to the $^5I_8$ $\to$ $^5I_7$ transition corresponds one band at 1.9 $\mu$m for both polarizations $\mathbf{E}\parallel c$ and $\mathbf{E}\perp c$. As the temperature increases from 80 to 293 K, a low-energy band with a peak at 2.04 $\mu$m for $\mathbf{E}\perp c$ and a peak at 2.07 $\mu$m for $\mathbf{E}\parallel c$ arises associated with transitions from an excited Stark level of the ground $^5I_8$ multiplet to the Stark levels of the $^5I_7$ multiplet and with an increase in the population of the initial Stark level, the energy of which is $\sim$100 K.