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The combination of ferromagnets with topological superconductors orinsulators allows for new phases of matter that support excitations such aschiral edge modes and Majorana fermions. EuS, a wide-band-gap ferromagneticinsulator with a Curie temperature around 16 K, and SrTiO$_3$ (STO), animportant substrate for engineering heterostructures, may support these phases.We present scanning superconducting quantum interference device (SQUID)measurements of EuS grown epitaxially on STO that reveal micron-scalevariations in ferromagnetism and paramagnetism. These variations are orientedalong the STO crystal axes and only change their configuration upon thermalcycling above the STO cubic-to-tetragonal structural transition temperature at105 K, indicating that the observed magnetic features are due to couplingbetween EuS and the STO tetragonal structure. We speculate that the STOtetragonal distortions may strain the EuS, altering the magnetic anisotropy ona micron-scale. This result demonstrates that local variation in the inducedmagnetic order from EuS grown on STO needs to be considered when engineeringnew phases of matter that require spatially homogeneous exchange.

Spatially modulated magnetic structure of EuS due to the tetragonal domain structure of SrTiO$_3$