  The interplay of lattice, electronic, and spin degrees of freedom at
epitaxial complex oxide interfaces provides a route to tune their magnetic
ground states. Unraveling the competing contributions is critical for tuning
their functional properties. We investigate the relationship between magnetic
ordering and magnetic anisotropy and the lattice symmetry, oxygen content, and
film thickness in compressively strained LaMnO$_3$/LaCrO$_3$ superlattices.
Mn-O-Cr antiferromagnetic superexchange interactions across the heterointerface
resulting in a net ferrimagnetic magnetic structure. Bulk magnetometry
measurements reveal isotropic in-plane magnetism for as-grown oxygen-deficient
thinner thin samples due to equal fractions of orthorhombic a+a-c-, and a-a+c-
twin domains. As the superlattice thickness is increased, in-plane magnetic
anisotropy emerges as the fraction of the a+a-c- domain increases. On annealing
in oxygen, the suppression of oxygen vacancies results in a contraction of the
lattice volume, and an orthorhombic to rhombohedral transition leads to
isotropic magnetism independent of the film thickness. The complex interactions
are investigated using high-resolution synchrotron diffraction and X-ray
absorption spectroscopy. These results highlight the role of the evolution of
structural domains with film thickness, interfacial spin interactions, and
oxygen-vacancy-induced structural phase transitions in tuning the magnetic
properties of complex oxide heterostructures.
