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 ${\mathrm{LaSrCrO}}_{3}\phantom{\rule{0.16em}{0ex}}(\mathrm{LSCO})/{\mathrm{LaSrMnO}}_{3}$ (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 antiparallel 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 two 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 ${x}^{2}\ensuremath{-}{y}^{2}$ (in-plane) $d$ orbitals for tensile strain and $3{z}^{2}\ensuremath{-}{r}^{2}$ (out-of-plane) orbitals under compressive strain, leading to competing ferromagnetic and antiferromagnetic exchange interactions within the LSMO layers. These results underscore the relative contributions of orbital, structural, and spin degrees of freedom and their tunability in atomically thin crystalline complex oxide layers.