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

Abstract

We report on a theoretical study on ferromagnetic superconductors, URhGe, and UCoGe and identify the pairing state as a non-unitary spin-triplet one with time reversal symmetry broken, analogous to superfluid 3 He-A phase. A recently found superconductor UTe2 with almost ferromagnet is analyzed by the same manner. Through investigating their peculiar upper critical field Hc2 shapes, it is shown that the pairing symmetry realized in all three compounds can be tuned by their magnetization curves under applied fields. This leads to the reentrant Hc2 in URhGe, an S-shaped in UCoGe and an L-shaped Hc2 in UTe2 observed under the field direction parallel to the magnetic hard b-axis in orthorhombic crystals in common. The identification with double chiral form: d(k) = ( b + iĉ)(k b + ikc) in UTe2 naturally enables us to understand (1) multiple phases with A1, A2, and A0 phases observed under pressure, (2) the enhanced reentrant Hc2 for the off-axis direction is associated with first order meta-magnetic transition, and (3) Weyl point nodes oriented along the magnetic easy a-axis. All three compounds are found to be topologically rich solid-state materials worth further investigation.