Magnetic and magnetodielectric properties of Ho$_{0.5}$Nd$_{0.5}$Fe$_{3}$(BO$_{3}$)$_{4}$

The magnetic and magnetodielectric properties of Ho$_{0.5}$Nd$_{0.5}$Fe$_{3}$(BO$_{3}$)$_{4}$ ferroborate with the competing Ho–Fe and Nd–Fe exchange couplings have been experimentally and theoretically investigated. Step anomalies in the magnetization curves at the spin-reorientation transition induced by the magnetic field $\mathbf{B}\parallel\mathbf{c}$ have been found. The spontaneous spin-reorientation transition temperature $T_{\operatorname{SR}}\approx$ 8 K has been refined. The measured magnetic properties and observed features are interpreted using a single theoretical approach based on the molecular field approximation and calculations within the crystal field model of the rare-earth ion. Interpretation of the experimental data includes determination of the crystal field parameters for Ho$^{3+}$ and Nd$^{3+}$ ions in Ho$_{0.5}$Nd$_{0.5}$Fe$_{3}$(BO$_{3}$)$_{4}$ and parameters of the Ho–Fe and Nd–Fe exchange couplings.