Structural and magnetic interplay in multiferroic Ho0.5Nd0.5Fe3(BO3)4

https://doi.org/10.1103/PhysRevB.107.214106

Rare-earth iron borates, $R{\mathrm{Fe}}_3{\left({\mathrm{BO}}_3\right)}_4$ ($R$ = rare earth), are of considerable interest because of their structural and magnetic complexities due to the involvement of both $3d$ and $4f$ magnetic interactions in a helical lattice. Among them ${\mathrm{Ho}}_{0.5}{\mathrm{Nd}}_{0.5}{\mathrm{Fe}}_3{\left({\mathrm{BO}}_3\right)}_4$ has attracted the most attention, as it exhibits a multiferroic property with a large, spontaneous, and magnetic-field-induced electric polarization ($P$) below the antiferromagnetic transition temperature ($T_N\sim 32$ K). This compound has been reported to be noncentrosymmetric (nonpolar) down to the lowest temperature, and the origin of spontaneous electric polarization below $T_N$ is not known. By utilizing temperature-dependent synchrotron x-ray powder diffraction, we report here the observation of structural phase transition, i.e., the lowering of crystal symmetry from $R32$ to $P{3}_{1}21$ below $T_N$ in ${\mathrm{Ho}}_{0.5}{\mathrm{Nd}}_{0.5}{\mathrm{Fe}}_3{\left({\mathrm{BO}}_3\right)}_4$, which is further confirmed by single-crystal x-ray diffraction measurements as well as substantiated by dielectric and Raman spectroscopic results. With the help of x-ray resonant magnetic scattering, we have studied the element-specific magnetic ordering behavior, and by combining all the results, we show that the spontaneous electric polarization below the antiferromagnetic ordering transition emerges through the p-d hybridization mechanism associated with the ${\mathrm{FeO}}_6$ octahedra. The observations of subtle structural changes at low temperature and element-specific magnetic ordering behavior provide a comprehensive understanding of the multiferroicity in this family of compounds.