Signature of the coexistence of ferromagnetism and superconductivity at KTaO$_3$ heterointerfaces

The coexistence of superconductivity and ferromagnetism is a long-standing issue in the realm of unconventional superconductivity due to the antagonistic nature of these two ordered states. Experimentally identifying and characterizing novel heterointerface superconductors that coexist with magnetism is challenging. Here, we report the experimental observation of long-range ferromagnetic order at the verge of two-dimensional superconductivity at KTaO$_3$ heterointerfaces. Remarkably, we observe in-plane magnetization hysteresis loop persisting to above room temperature with direct current superconducting quantum interference device measurements. Furthermore, both the first-principles calculations and the x-ray magnetic circular dichroism measurements reveal that the observed robust ferromagnetism is attributed to the presence of oxygen vacancies that localize electrons in nearby Ta 5$d$ states. Our findings not only indicate KTaO$_3$ heterointerfaces as unconventional superconductors with time-reversal symmetry breaking, but also inject a new momentum to the study of the delicate interplay between superconductivity and magnetism boosted by strong spin-orbit coupling inherent to the heavy Ta in 5$d$ orbitals of KTaO$_3$ heterointerfaces.