Tensile-strained $\mathrm{LaCo}{\mathrm{O}}_{3\ensuremath{-}\ensuremath{\delta}}$ thin films are ferromagnetic, in sharp contrast to the zero-spin bulk, although no clear consensus has emerged as to the origin of this phenomenon. While magnetism has been heavily studied, relatively little attention has been paid to electronic transport, due to the insulating nature of the strain-stabilized ferromagnetic state. Here, structure, magnetism, and transport are studied in epitaxial $\mathrm{LaCo}{\mathrm{O}}_{3\ensuremath{-}\ensuremath{\delta}}$ films (10--22-nm thick) on various substrates (from 1.4% compressive to 2.5% tensile strain), using synchrotron x-ray diffraction, scanning probe and transmission electron microscopy, magnetometry, polarized neutron reflectometry, resistivity, and Hall effect. High quality, smooth films are obtained, exhibiting superstructures associated with both oxygen vacancy ordering and periodic in-plane ferroelastic domains. Consistent with prior work, ferromagnetism with an approximately 80--85 K Curie temperature is observed under tension; polarized neutron reflectometry confirms a relatively uniform magnetization depth profile, albeit with interfacial dead layer formation. Electrical transport is found to have similar semiconducting nature to bulk, but with reduced resistivity and activation energy. Hall effect measurements, however, reveal a striking inversion of the majority carrier type, from $p$-type in the bulk and under compression to n-type under tension. While thus far overlooked, ferromagnetism in epitaxial $\mathrm{LaCo}{\mathrm{O}}_{3\ensuremath{-}\ensuremath{\delta}}$ films is thus directly correlated with $n$-type behavior, providing important insight into the ferromagnetic state in this system. Aided by density functional theory calculations, these results are interpreted in terms of tensile-strain-induced orbital occupation and band structure changes, including a rapid decrease in effective mass at the ${e}_{g}$-derived conduction band minimum, and corresponding increase at the valence band maximum.
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