The local epitaxial growth of pulsed laser deposited Ca$_2$MnO$_4$ films on polycrystalline spark plasma sintered Sr$_2$TiO$_4$ substrates was investigated to determine phase formation and preferred epitaxial orientation relationships ($ORs$) for isostructural Ruddlesden-Popper (RP) heteroepitaxy, further developing the high-throughput synthetic approach called Combinatorial Substrate Epitaxy (CSE). Both grazing incidence X-ray diffraction and electron backscatter diffraction (EBSD) patterns of the film and substrate were indexable as single-phase RP-structured compounds. The optimal growth temperature (between 650 $^{circ}$C and 800 $^{circ}$C) was found to be 750 $^{circ}$C using the maximum value of the average image quality (IQ) of the backscattered diffraction patterns. Films grew in a grain-over-grain pattern such that each Ca$_2$MnO$_4$ grain had a single $OR$ with the Sr$_2$TiO$_4$ grain on which it grew. Three primary $ORs$ described 47 out of 49 grain pairs that covered nearly all of RP orientation space. The first $OR$, found for 20 of the 49, was the expected RP unit-cell over RP unit-cell $OR$, expressed as [100][001]$_{film}$||[100][001]$_{sub}$. The other two $ORs$ were essentially rotated from the first by 90$^{circ}$, with one (observed for 17 of 49 pairs) being rotated about the [100] and the other (observed for 10 of 49 pairs) being rotated about the [110] (and not exactly by 90$^{circ}$). These results indicate that only a small number of $ORs$ are needed to describe isostructural RP heteroepitaxy and further demonstrate the potential of CSE in the design and growth of a wide range of complex functional oxides.
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