Magnetoelectric and magnetic properties of aluminum borates Ho$_{1-x}$Nd$_x$Al$_3$(BO$_3)_4$

The magnetoelectric and magnetic properties of substituted aluminum borates Ho$_{1-x}$Nd$_x$Al$_3$(BO$_3)_4$ have been studied experimentally and theoretically. A large magnetoelectric effect exceeding all known values in isostructural compounds except for HoAl$_3$(BO$_3)_4$ has been found. The magnetoelectric polarization of Ho$_{0.8}$Nd$_{0.2}$Al$_3$(BO$_3)_4$ and Ho$_{0.5}$Nd$_{0.5}$Al$_3$(BO$_3)_4$ at $T=5$ K in a field of $9 T$ is $\Delta P_{ab}(B_b)\approx-2630$ and $1380$ $\mu C/m^2$, respectively. A theoretical consideration based on the crystal field model for the rare-earth ion made it possible to interpret all measured properties within the unified approach. The crystal field parameters have been determined. The temperature ($3$–$300$ K) and field (up to $9 T$) dependences of the magnetization and the temperature ($5$–$100$ K) and field (up to $9 T$) dependences of the polarization have been described. The studied properties of Ho$_{1-x}$Nd$_x$Al$_3$(BO$_3)_4$ have been compared with those of HoAl$_3$(BO$_3$)$_4$ demonstrating record-high polarization values.