Fig. 1: Crystal structure, growth pattern, and spin-projected density of states.

a Crystal structure of the (3, 1) film showing how a LuFe₂O₄ slab (which has an iron oxide double layer with both Fe²⁺ and Fe³⁺ between two Lu layers) is sandwiched between three layers of LuFeO₃²⁰. d represents the Lu-layer displacement. b HAADF-STEM images of the m = 3, 7, and 9 superlattices viewed along the [1\(\overline{1}\)0] zone axis. Atomic number contrast shows the bright, heavy lutetium atomic rows layered with the less bright iron atomic rows. The scale bar is the same for all images. Trends in the ferrimagnetic T_C and Lu-layer distortion (which increases with the number of LuFeO₃ layers) are also shown. c Spin-projected density of states of the Fe double layer in LuFe₂O₄, an adjacent monolayer of LuFeO₃ and the central LuFeO₃ monolayer. These calculations were performed using the self-doped charge-ordering model as discussed in the text (Fig. 4b). The Fe double layer is nonpolar, and the Lu-layer displacement is asymmetric with both down/up/up and down/up/down distortion patterns around the Fe bilayer. The Fe³⁺ and Fe²⁺ states are indicated with dark and light blue, respectively. The arrows denote different types of excitations.