  The intimate connection between magnetism and superconducting pairing
routinely plays a central role in determining the occurrence of unconventional
superconducting states. In high-transition-temperature (high-Tc) stripe-ordered
cuprate superconductors and a magnetically ordered iron-based superconductor,
the coupling between magnetism and superconductivity gives birth to novel
phases of matter with modulation of the superconducting pairing in the real
space. Further exploration of these phases can shed light on the mechanism of
unconventional superconductivity. Here we report on the discovery of a peculiar
spatially-varying superconducting state residing at the interface between
(110)-oriented KTaO3 and ferromagnetic EuO. Electrical transport measurements
reveal different Tc and upper critical fields (Hc2) with current applied along
the two orthogonal in-plane directions. Such anisotropy persistently occurs in
the low-carrier-density samples that are characterized by strong coupling
between Ta 5d and Eu 4f electrons, whereas in the high-carrier-density samples
the coupling is weakened and Tc and Hc2 becomes isotropic. Complemented by
local imaging of diamagnetism and theoretical analysis, our observations imply
an unprecedented emergence of superconducting stripes wherein the phase
coherence is established ahead of the rest of the interface, arising from a
band-filling-dependent ferromagnetic proximity. The realization of such exotic
superconducting states provides impetus for the study of novel physics in
heterostructures possessing both magnetism and superconductivity.
