Spontaneous magnetization in unitary superconductors with time reversal symmetry breaking

We report the study of spontaneous magnetization (i.e., spin-polarization) for time-reversal symmetry (TRS)-breaking superconductors with unitary pairing potentials, in the absence of external magnetic fields or Zeeman fields. Spin-singlet (${\mathrm{\Delta }}_s$) and spin-triplet (${\mathrm{\Delta }}_t$) pairings can coexist in superconductors whose crystal structure lacks inversion symmetry. The TRS can be spontaneously broken once a relative phase of $\pm \pi \mathrm{/}2$ is developed, forming a TRS-breaking unitary pairing state (${\mathrm{\Delta }}_s\pm i{\mathrm{\Delta }}_t$). We demonstrate that such unitary pairing could give rise to spontaneous spin-polarization with the help of spin-orbit coupling. Our result provides an alternative explanation to the TRS breaking, beyond the current understanding of such phenomena in the noncentrosymmetric superconductors. The experimental results of Zr${}_3$Ir and CaPtAs are also discussed in the view of our theory.