Superconductivity in ${\mathrm{UTe}}_2$ has attracted significant attention, as it is widely recognized as a promising candidate for a spin-triplet superconductor. However, the symmetry of superconductivity and the microscopic origin of spin-triplet pairing remain subjects of debate. Nevertheless, various experiments imply an intimate coupling between magnetism and superconductivity. In this paper, we analyze a multisublattice periodic Anderson model that incorporates spin-orbit coupling allowed in locally noncentrosymmetric crystals to discuss magnetic fluctuations and superconductivity in ${\mathrm{UTe}}_2$. Due to the sublattice-dependent spin-orbit coupling, magnetic fluctuations become anisotropic, and the spin degeneracy of superconducting states is lifted. Our calculations reveal anisotropic antiferromagnetic fluctuations along the $b$ and $c$ axes, anisotropic ferromagnetic fluctuations along the $a$ axis, and their coexistence. These fluctuations can be tuned by the $f$ electron's level. Superconductivity in the $A_u$ representation is predominant for a wide range of parameters, whereas the $B_{2u}$ representation is almost degenerate and can be stabilized. The direction of the $d$ vector changes as we increase the spin-orbit coupling. We discuss the consistency between our results and several experiments.

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• Magnetism
• Spin-triplet pairing
• Superconducting gap
• Superconductivity
• Noncentrosymmetric materials
• Unconventional superconductors
• Eliashberg theory
• Random phase approximation
• Tight-binding model