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

We investigate the dependence 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 a 2 unit cells. For the thinnest LSMO layers, an approximately constant magnetic moment as a function of strain is observed. As the LSMO thickness is increased, the average magnetic moment per Mn decreases for compressive strain on LaAlO$_3$ while it increases for the tensile strain. The differences in the magnetic responses are related to ordering of the Mn d-orbitals which are found to be $x^2-y^2$ (in-plane) for tensile strain and $3z^2-r^2$ (out-of-plane) 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 oxides.