High-resolution optical spectroscopy, magnetic properties, and single-crystal neutron diffraction of multiferroic HoFe3(BO3)4 : Magnetic …

The magnetic structure is usually determined by the neutron diffraction measurements. However, in the case of complex multisublattice magnetics, this method fails to give an unambiguous result. Here, on the example of multiferroic ${\mathrm{HoFe}}_{3}{({\mathrm{BO}}_{3})}_{4}$, we show that in the case of rare-earth (RE) compounds the right magnetic structure can be determined by additionally using optical spectroscopy and a theoretical analysis based on spectroscopic data. ${\mathrm{HoFe}}_{3}{({\mathrm{BO}}_{3})}_{4}$ demonstrates a series of phase transitions and interesting magnetic and magnetoelectric properties. The available information on the magnetic structure of the compound, necessary for understanding and utilizing these properties, is contradictory. To resolve the existing ambiguities, we apply a combined approach. The high-resolution spectroscopy data deliver a set of the ${\mathrm{Ho}}^{3+}$ crystal-field (CF) levels in the paramagnetic and both easy-plane and easy-axis magnetic phases. These data are used to determine CF and ${\mathrm{Ho}}^{3+}\text{\ensuremath{-}}{\mathrm{Fe}}^{3+}$ exchange parameters and, then, to calculate the temperature dependencies of the magnetic susceptibility tensor of ${\mathrm{HoFe}}_{3}{({\mathrm{BO}}_{3})}_{4}$. Based on these calculations, we suggest an easy-plane antiferromagnetic structure with a collinear arrangement of the Fe spins along the $a$ axis and induced noncolinear moments of magnetically nonequivalent Ho ions. The suggested structure is further confirmed by single-crystal elastic neutron scattering experiments. We argue that specific features of the magnetic properties of RE iron borates isostructural to ${\mathrm{HoFe}}_{3}{({\mathrm{BO}}_{3})}_{4}$ are governed by the energy patterns and the symmetry properties of the wave functions of the lower CF levels of the RE ground multiplet in the crystal field of the ${C}_{2}$ symmetry.