Fig. 1: Film characterization and electronic structure.

Schematic depicting the exchange coupling in a square lattice with a one kind of atom exhibiting uniform nearest neighbor interactions b random distribution of five different kinds of atoms with different nearest neighbor couplings. c Crystal structure of an Ni-Mn ordered RE⁵NMO where the A-site is shown for a random distribution of 5 RE cations [Legend for colors representing each RE cation has been shown at the bottom]. d Experimental XRR data and corresponding footprint-corrected, GenX-based model fitting for a 6 nm RE⁵NMO film on STO substrate, showing well-defined Kiessig fringes. e The reflectance data were used to derive the Kubelka-Munk function, which is an absorption equivalent commonly used for the diffused reflectance mode given by, F(R) = (1-R²) / 2R, where R is the reflectance⁹⁰. The Tauc relation using the reflectance mode is given by [\({\left[F(R)\cdot h\nu \right]}^{n}=A(h\nu -{E}_{g})\)] where, F(R) is the Kubelka-Munk function described above, A is a characteristic constant independent of the photon energy, hν is the photon energy and E_g is the band gap⁵⁵. We use n = 2 here as RE₂NiMnO₆ exhibit direct optical band gaps^91,92. The black line is the linear extrapolation for the Tauc plot to find the band gap. f XRD for 6 nm (upper panel) and 100 nm (lower panel) RE⁵NMO film on STO, * denotes the film peak. While the overlap of the substrate and film prohibits the estimation of the out-of-plane pseudocubic lattice parameter (c_pc) for the 6 nm film, it is found to be ~ 3.83 Å for the 100 nm film.