Superconductivity with broken time-reversal symmetry inside a superconducting s-wave state

In general, magnetism and superconductivity are antagonistic to each other. However, there are several families of superconductors, in which superconductivity may coexist with magnetism, and only a few examples are known, when superconductivity itself induces spontaneous magnetism. The most known compounds are Sr$_2$RuO$_4$ and some noncentrosymmetric superconductors. Here, we report the finding of a narrow dome of a novel $s+is'$ superconducting (SC) phase with broken time-reversal symmetry (BTRS) inside the broad $s$-wave SC region of the centrosymmetric multiband superconductor Ba$_{\rm 1-x}$K$_{\rm x}$Fe$_2$As$_2$ ($0.7 \lesssim x \lesssim 0.85$). We observe spontaneous magnetic fields …