Intimate relationship between spin configuration in the triplet pair and superconductivity in UTe$_2$

Spin-triplet superconductivity is an intriguing quantum coherent state with both spin and orbital degrees of freedom, which holds significant potential for future applications in quantum technology. However, how the spin of the triplet pairs responds to an external magnetic field remains poorly understood. This is mainly due to the absence of suitable spin-triplet superconductors. Here, we report results of Knight-shift and ac-susceptibility measurements on UTe$_2$. We demonstrate that the spin susceptibility, which slightly decreases compared to the normal-state value below the superconducting (SC) transition temperature $T_{\rm c}$, is rapidly restored and nearly recovers to the normal-state values around 5 T, well below the SC upper critical field $H_{c2}$ when the magnetic field is applied along the $c$ axis ($H \parallel c$). In addition, we found that $H_{\rm c2}$ of superconductivity becomes larger when the SC spin aligns with the magnetic field. By considering the results on $H \parallel b$, our results suggest the presence of a close relationship between the spin configuration of the triplet pair and $H_{\rm c2}$, as well as the anisotropic pinning interaction acting on the triplet pairs. These phenomena, which have never been observed in spin-singlet superconductors, represent characteristic features unique to spin-triplet superconductors. We discuss the similarities between superconductivity in UTe$_2$ and superfluid $^3$He, focusing on their spin-triplet pairing states.