Fig. 1: The complexion diagram of the Fe/Fe₃O₄ interface.

a Experimental (Exp.) differential phase contrast (DPC) - four-dimensional scanning transmission electron microscopy (4DSTEM) reconstruction for Fe₃O₄[110]: i Reconstructed virtual dark-field image ii Electric field vector map iii Projected electrostatic potential map iv Charge-density map. The white arrows in i, iii, and iv indicate the positions of the O atomic columns. b Experimental/theoretical study of the Fe[001]/Fe₃O₄[001] interface includes: experimental DPC-4DSTEM i virtual dark-field image and iv charge-density map, along with results from DFT calculations comprising charge-density maps (ii, vi) and relaxed structures (iii, v) of the interface between Fe[001] and Fe₃O₄[001]. The first DFT set (ii, iii) illustrates the pristine interface configuration, while the second set (v, vi) depicts the interface with a reconstructed two-layer thick FeO slab. In iii, v, Fe atoms in the body-centered cubic (BCC) structure are represented in yellow. In the Fe₃O₄ structure, Fe atoms are color-coded based on their spin orientation: spin-up atoms are shown in orange and spin-down atoms in purple. O atoms are depicted in red. In iii, yellow and white arrows highlight atomic columns that deviate from the positions observed experimentally in the Fe₃O₄ structure when the two-layer thick FeO slab is not inserted. c DFT predicted complexion diagram versus the O chemical potential shift, with Δμ_O taking molecular O₂ as the reference upper limit, and dissociation of Fe₃O₄ into metallic Fe and molecular O₂ as the lower limit (vertical black dashed line). The explored interface configurations include: Fe/Fe₃O₄ (solid orange), Fe/FeO (solid grey), and Fe/{FeO}_n/Fe₃O₄, with n being the number of FeO layers (dark blue). A horizontal dashed line is included in the graph as a visual reference. The inset on the right shows a magnification in the range of chemical potentials where the transition occurs from four to two intermediate FeO layers, separated by the vertical thin blue line. The O chemical potential is also converted to O₂ pressure at the 300 °C temperature of the experiments, with the black shaded region showing typically accessible experimental conditions under ultra-high vacuum (UHV).