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The thermodynamic, magnetic, dielectric, and magnetoelectric properties ofHoFe$_3$(BO$_3$)$_4$ and Ho$_{0.5}$Nd$_{0.5}$Fe$_3$(BO$_3$)$_4$ areinvestigated. Both compounds show a second order Ne\'{e}l transition above 30 Kand a first order spin reorientation transition below 10 K.HoFe$_3$(BO$_3$)$_4$ develops a spontaneous electrical polarization below theNe\'{e}l temperature (T$_N$) which is diminished in external magnetic fields.No magnetoelectric effect could be observed in HoFe$_3$(BO$_3$)$_4$. Incontrast, the solid solution Ho$_{0.5}$Nd$_{0.5}$Fe$_3$(BO$_3$)$_4$ exhibitsboth, a spontaneous polarization below T$_N$ and a magnetoelectric effect athigher fields that extends to high temperatures. The superposition ofspontaneous polarization, induced by the internal magnetic field in the orderedstate, and the magnetoelectric polarizations due to the external field resultsin a complex behavior of the total polarization measured as a function oftemperature and field.

Magnetoelectric Effect and Spontaneous Polarization in HoFe$_3$(BO$_3$)$_4$ and Ho$_{0.5}$Nd$_{0.5}$Fe$_3$(BO$_3$)$_4$