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Effect of strain on magnetic and orbital ordering of LaSrCrO$_3$/LaSrMnO$_3$ heterostructures

We investigate the effect of strain and film thickness on the orbital and magnetic properties of LaSrCrO$_3$ (LSCO)/LaSrMnO$_3$ (LSMO) heterostructures using bulk magnetometry, soft X-ray magnetic spectroscopy, first-principles density functional theory, high-resolution electron microscopy and X-ray diffraction. We observe an anti-parallel ordering of the magnetic moments between the ferromagnetic LSMO layers and the LSCO spacers leading to a strain-independent ferromagnetic ground state of the LSCO/LSMO heterostructures for LSMO layers as thin as 2 unit cells. As the LSMO thickness is increased, a net ferromagnetic state is maintained, however, the average magnetic moment per Mn is found to be dependent on the magnitude of the substrate-induced strain. The differences in the magnetic responses are related to preferential occupation of the Mn $x^2-y^2$ (in-plane) d-orbitals for tensile strain and $3z^2-r^2$ (out-of-plane) orbitals under compressive strain leading to competing ferromagnetic and anti-ferromagnetic exchange interactions within the LSMO layers. These results underscore the relative contributions of orbital, structural and spin degree of freedom and their tunability in atomically-thin crystalline complex oxide layers.