Analysis of Far-Infrared Spectra of Antiferromagnetic FeC<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

The transmission spectrum of antiferromagnetic FeC${\mathrm{O}}_{3}$ has been investigated in the far-infrared region from 20 to 300 ${\mathrm{cm}}^{\ensuremath{-}1}$, for temperatures from 4.2 to 70 K and in applied fields up to 90 kOe. Spectra were obtained from natural single crystals and high-purity synthetic powders. At 4.2 K, a sharp electronic transition (magnetic dipole) was observed at 112.5 ${\mathrm{cm}}^{\ensuremath{-}1}$, exhibiting parallel and perpendicular splitting factors of 6.6 and O, respectively. Its oscillator strength is $f=2.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$. An additional weak electronic line is observed at 160 ${\mathrm{cm}}^{\ensuremath{-}1}$. The details of these transitions and electronic Raman transitions observed by others are successfully described by the ${\mathrm{Fe}}^{2+}$ single-ion Hamilitonian $\mathcal{H}=R\ensuremath{\lambda}\stackrel{\ensuremath{\rightarrow}}{\mathrm{L}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}+{R}^{2}\ensuremath{\zeta}({L}_{z}^{2}\ensuremath{-}\frac{2}{3})+\mathcal{J}{S}_{z}$, where $\ensuremath{\lambda}$, $\ensuremath{\zeta}$, and $\mathcal{J}$ are the spin-orbit, trigonal-field, and Ising-molecular-field parameters, respectively, and $R$ is an "orbital-reduction" factor. The analysis yields values for these parameters of $R\ensuremath{\lambda}=105$ ${\mathrm{cm}}^{\ensuremath{-}1}$, $\ensuremath{-}{R}^{2}\ensuremath{\zeta}=1506$ ${\mathrm{cm}}^{\ensuremath{-}1}$, $R\ensuremath{\approx}1$, and $\mathcal{J}=19$ ${\mathrm{cm}}^{\ensuremath{-}1}$. The observed far-infrared transitions are identified as being within the low $^{5}E$ spin-orbit manifold from the ground state (${M}_{J}=\ensuremath{-}1$) to the two components of the ${M}_{J}=0$ doublet. The temperature dependence of the 112.5-${\mathrm{cm}}^{\ensuremath{-}1}$ transition is studied from 4.2 to 70 K, and its intensity is observed to drop sharply as the temperature is raised to the vicinity of ${T}_{N}=38.4$ K. This behavior is compared to that of an Ising spin system. In addition, three phonons are observed at 186, 201, and 224 ${\mathrm{cm}}^{\ensuremath{-}1}$ and are identified as external ${E}_{u}$, ${A}_{2u}$, and ${E}_{u}$ modes, respectively.

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