Optical spectra, crystal-field parameters, and magnetic susceptibility of multiferroicNdFe3(BO3)4

We report high-resolution optical absorption spectra for $\mathrm{Nd}{\mathrm{Fe}}_{3}{(\mathrm{B}{\mathrm{O}}_{3})}_{4}$ trigonal single crystal, which is known to exhibit a giant magnetoelectric effect below the temperature of magnetic ordering ${T}_{N}=33\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The analysis of the temperature-dependent polarized spectra reveals the energies and, in some cases, symmetries and exchange splittings of ${\mathrm{Nd}}^{3+}$ 84 Kramers doublets. We perform crystal-field calculations starting from the exchange-charge model, obtain a set of six real crystal-field parameters, and calculate wave functions and magnetic $g$ factors. In particular, the values ${g}_{\ensuremath{\perp}}=2.385$ and ${g}_{\ensuremath{\Vert}}=1.376$ were found for the ${\mathrm{Nd}}^{3+}$ ground-state doublet. We obtain ${B}_{\mathit{loc}}=7.88\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ and $\ensuremath{\mid}{J}_{\mathit{FN}}\ensuremath{\mid}=0.48\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ for the values of the local effective magnetic field at liquid-helium temperatures at the ${\mathrm{Nd}}^{3+}$ site and the Nd-Fe exchange integral, respectively, using the experimentally measured ${\mathrm{Nd}}^{3+}$ ground-state splitting of $8.8\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. To check the reliability of our set of crystal-field parameters, we model the magnetic susceptibility data from literature. A dimer containing two nearest-neighbor iron ions in the spiral chain is considered to partly account for quasi-one-dimensional properties of iron borates, and then the mean-field approximation is used. The results of calculations with the exchange parameters for ${\mathrm{Fe}}^{3+}$ ions ${J}_{\mathit{nn}}=\ensuremath{-}6.25\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ (intrachain interactions) and ${J}_{\mathit{nnn}}=\ensuremath{-}1.92\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ (interchain interactions) obtained from fitting agree well with the experimental data.