Figure 4. Transparency, optical band gap, and spontaneous electric polarization of ε-Fe₂O₃ by UV-vis absorption spectra measurement and first-principles calculation.

(a) Photograph of the colloidal solution of S-1020 nanocrystal with an average particle size of 8.2 nm, whose concentration is 1 × 10⁻² mol dm⁻³. The solution has a light orange color. (b) Observed UV-vis absorption spectrum of S-1020 colloidal solution shown by the molar absorption coefficient (ε). The inset shows the calculated optical spectrum obtained from the first-principles calculation. The left axis is the absorption coefficient (α). (c) The band structure of ε-Fe₂O₃ near the Fermi energy. Solid and dotted black lines indicate α and β spins, respectively. (d) The difference charge density map, which shows the difference between the charge density of ε-Fe₂O₃ and those of the neutral Fe and O atoms, obtained by the first-principles calculation (left). Green and magenta surfaces in the difference charge density map show the isosurface levels of +0.385e Å⁻³ and –0.252e Å⁻³, respectively. The green arrow shows that the spontaneous electric polarization (P) of ε-Fe₂O₃ is along the crystallographic c-axis. The crystal structure of ε-Fe₂O₃ (right). The grey and white balls in the crystal structure show the Fe and O atoms, respectively. (e) Sublattice magnetizations of Fe_A–Fe_D shown by the arrow on the crystal structure of ε-Fe₂O₃. Red and blue arrows on the Fe sites indicate the sublattice magnetizations. The yellow curved arrows express the zJ values, where z is the number of exchange pathways and J is the superexchange interaction constant, with antiferromagnetic superexchange interaction between the Fe sites (z_AB J_AB < 0, z_AC J_AC < 0, z_CD J_CD < 0), and the thickness of the arrows indicate that the magnitude of zJ is . The red arrow below the crystal structure shows that the magnetic polarization (M) of ε-Fe₂O₃ is along the crystallographic a-axis.