  We have studied the correlation between the structural distortion and the
electronic/magnetic properties in single-crystalline (Lu,Sc)Fe$_2$O$_4$
(Sc=0.05 and 0.3) by using X-ray diffraction (XRD), magnetic susceptibility,
and X-ray absorption spectroscopy (XAS)/x-ray magnetic circular dichroism
(XMCD)measurements. The Rietveld structure analysis of the XRD patterns
revealed that the Sc substitution induced an elongation of the FeO$_5$
bipyramidal cages in LuFe$_2$O$_4$ and increased the Fe$_2$O$_4$ bilayer
thickness. A non-negligible decrease in the ferrimagnetic transition
temperature T$_C$ is observed in the magnetic susceptibility curve of the
Sc=0.3 sample, but the XAS/XMCD spectra do not show any difference except for a
small reduction of dichroism signals at the Fe$^{3+}$ absorption edge. We
interpret this suppression of T$_C$ to be the result of a decreased spin-orbit
coupling effect in the Fe$^{2+}$ $e_{1g}$ doublet under $D_{3h}$ symmetry,
which is induced by the weakened structural asymmetry of the FeO$_5$
bipyramids.
