Pairing symmetries of multiple superconducting phases in ${\mathrm{UTe}}_2$: Competition between ferromagnetic and antiferromagnetic fluctuations

The putative spin-triplet superconductor ${\mathrm{UTe}}_2$ exhibits multiple superconducting phases under applied pressure [Braithwaite et al., Commun. Phys. 2, 147 (2019)]. The clarification of pairing mechanisms and symmetries of gap functions are essentially important for understanding the multiple-phase diagram. Since the coexistence of ferromagnetic and antiferromagnetic spin fluctuations with Ising-like anisotropy is suggested from measurements of magnetic susceptibilities and neutron scattering measurements, it is expected that the interplay between these spin fluctuations plays a crucial role in the emergence of the multiple superconducting phases. Motivated by these observations, we examine the spin-fluctuation-mediated pairing mechanism, analyzing the linearized Eliashberg equations for an effective model of $f$-electron bands. It is found that the Ising-like ferromagnetic fluctuations stabilize spin-triplet pairings in either the $A_u$ or $B_{3u}$ states, whereas Ising-like antiferromagnetic fluctuations stabilize spin-triplet pairings in the $B_{1u}$ state. These results provide a plausible scenario elucidating the multiple superconducting phases under pressure.