Evidence for a collinear easy-plane magnetic structure of multiferroic EuF e 3 ( B O 3 ) 4 : Spectroscopic and theoretical studies

We performed high-resolution polarized optical transmission spectroscopy and theoretical studies of multiferroic $\mathrm{EuF}{\mathrm{e}}_{3}{(\mathrm{B}{\mathrm{O}}_{3})}_{4}$ single crystals in the three phases: paramagnetic $R32\phantom{\rule{0.28em}{0ex}}(Tg{T}_{\mathrm{s}}=84\phantom{\rule{0.28em}{0ex}}\mathrm{K})$ and $P{3}_{1}21\phantom{\rule{0.28em}{0ex}}({T}_{\mathrm{s}}gTg{T}_{\mathrm{N}}=34\phantom{\rule{0.28em}{0ex}}\mathrm{K})$, and antiferromagnetic $(Tl{T}_{\mathrm{N}})$ ones. The analysis of the spectra reveals interesting details of the magnetic structure, namely, a collinear arrangement of the iron magnetic moments along the ${C}_{2}$ symmetry axis in the $ab$ crystallographic plane of $\mathrm{EuF}{\mathrm{e}}_{3}{(\mathrm{B}{\mathrm{O}}_{3})}_{4}$ below ${T}_{\mathrm{N}}$. Spectral signatures of the phase transitions and the spin-phonon interaction are observed and discussed. Reliable crystal-field and exchange-interaction parameters are obtained and used to model the magnetic susceptibility of the compound. The results of detailed calculations of the electric polarization of $\mathrm{EuF}{\mathrm{e}}_{3}{(\mathrm{B}{\mathrm{O}}_{3})}_{4}$ in the $R32$ phase are presented, and mechanisms of the magnetoelectric response are discussed. We detect a strong effect of impurities (that enter the crystal from a flux in the course of the crystal growth) on the structural phase-transition temperature and demonstrate a coexistence of both $R32$ and $P{3}_{1}21$ phases down to the lowest temperatures in a $\mathrm{EuF}{\mathrm{e}}_{3}{(\mathrm{B}{\mathrm{O}}_{3})}_{4}$ crystal grown with the $\mathrm{B}{\mathrm{i}}_{2}\mathrm{M}{\mathrm{o}}_{3}{\mathrm{O}}_{12}$ based flux, due to inhomogeneous distribution of impurity $\mathrm{B}{\mathrm{i}}^{3+}$ ions. Our study can be considered as a demonstration of the abilities of optical spectroscopy in delivering new information on a magnetic compound, even in the case when other methods fail.