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We report on theoretical studies on ferromagnetic superconductors, URhGe, andUCoGe and identifies the pairing state as a non-unitary spin-triplet one,analogous to superfluid $^3$He-A phase. A recently found superconductor UTe$_2$with almost ferromagnet is analyzed by the same manner. Through investigatingtheir peculiar upper critical field $H_{\rm c2}$ shapes, it is shown that thepairing symmetry realized in all three compounds can be tuned by theirmagnetization curves under applied fields. This leads to the reentrant $H_{\rmc2}$ in URhGe, an S-shaped in UCoGe and an L-shaped $H_{\rm c2}$ in UTe$_2$observed under the field direction parallel to the magnetic hard axis inorthorhombic crystals in common. The identification with double chiral form:${\bf d}(k)=(\hat{b}+i\hat{c})(k_b+ik_c)$ in UTe$_2$ naturally enables us tounderstand (1) multiple phases with A$_1$, A$_2$, and A$_0$ phases observedunder pressure, (2) the enhanced reentrant $H_{\rm c2}$ for the off-axisdirection fields associated with first order meta-magnetic transition, and (3)Weyl point nodes oriented along the $a$-axis. All three compounds are found tobe topologically rich solid-state materials worth further investigation.

Non-unitary triplet superconductivity tuned by field-controlled magnetization --URhGe, UCoGe and UTe$_2$--