Fig. 4: Candidate charge-ordering patterns for (LuFeO3)3/(LuFe2O4)1 and comparison of calculated vs. measured dichroic spectra.

a Ferroelectric single-domain type (CO-FE) charge-ordered state with a polar Fe bilayer. The Lu-layer displacement is symmetric, and red arrows indicate the polarization direction. b Self-doped-type (CO-DOPED) multi-domain charge-ordered state with a nonpolar Fe bilayer, unveiling spontaneous electron transfer from the Fe bilayers to the LuFeO3 layers. The polarization changes direction across the domain boundaries (dashed lines) as shown by the red and blue net dipole arrows, and the Lu-layer displacement is asymmetric with both down/up/up and down/up/down Lu distortion patterns surrounding the Fe double layer. c Experimental dichroic spectra Δα(E)MCD along with calculated Δα(E)MCD of the CO-FE (polar Fe bilayer) and CO-DOPED (nonpolar Fe bilayer) charge-ordering states in the (3, 1) superlattice.