Anisotropic response of spin susceptibility in the superconducting state of ${\mathrm{UTe}}_2$ probed with ${}^{125}\mathrm{Te}\text{−}\mathrm{NMR}$ measurement

To investigate spin susceptibility in a superconducting (SC) state, we measured the ${}^{125}\mathrm{Te}$-NMR Knight shifts at magnetic fields ($H$) up to 6.5 T along the $b$ and $c$ axes of single-crystal ${\mathrm{UTe}}_2$, a promising candidate for a spin-triplet superconductor. In the SC state, the Knight shifts along the $b$ and $c$ axes ($K_b$ and $K_c$, respectively) decreased slightly, and the decrease in $K_b$ was almost constant up to 6.5 T. The reduction in $K_c$ decreased with increasing $H$, and $K_c$ was unchanged through the SC transition temperature at 5.5 T, excluding the possibility of spin-singlet pairing. Our results indicate that spin susceptibilities along the $b$ and $c$ axes slightly decrease in the SC state in low $H$, and the $H$ response of SC spin susceptibility is anisotropic on the $bc$ plane. We discuss the possible $\mathit{d}$-vector state within the spin-triplet scenario and suggest that the dominant $\mathit{d}$-vector component for the case of $H\parallel b$ changes above 13 T, where $T_{\mathrm{c}}$ increases with increasing $H$.

Figure 1

(a) Image of the crystal structure of ${\mathrm{UTe}}_2$ prepared with the program vesta [21]. (b) Upper critical field $H_{\mathrm{c}2}$ for a magnetic field applied along the $b$ (diamonds) and $c$ (circles) axes. The solid circles denote $T_{\mathrm{c}}$ of the ${}^{125}\mathrm{Te}$-enriched sample, which is consistent with previous results [2, 3]. The dotted line indicates the $\mathit{d}$-vector pinning field $H_{\mathrm{pin}}$ for $H\parallel b$ estimated from the decrease in $K_b$ and $A_{\mathrm{hf},b}$. (c) and (d) ${}^{125}\mathrm{Te}\mathrm{NMR}$ spectra measured when (c) $H\parallel b$ and (d) $H\parallel c$, respectively. The dotted peaks show signals from the Te(1) and Te(2) sites, which are simulated with the resonance frequencies estimated from the angle dependence of the spectrum shown in the Supplemental Material [22].

Figure 2

NMR spectra at several temperatures at 3 T along the (a) $b$ and (b) $c$ axes. NMR spectra at 5.5 T along the (c) $c$ axis. The dotted lines in each figure represent the normal-state peak position.

Figure 3

Temperature dependence of (a) $\mathrm{\Delta }{K}_b$ and (b) $\mathrm{\Delta }{K}_c$ measured at 1, 3, and 5.5 T (see the text). Dashed lines are added as a guide to the eye. Temperature dependence of the AC susceptibility $\chi$ at the same magnetic fields along the (c) $b$ and (d) $c$ axes. The errors of the NMR Knight shift are determined from the resolution of FT signals.

Figure 4

The magnetic-field dependence of the decrease in $\mathrm{\Delta }{K}_b$ (diamonds) and $\mathrm{\Delta }{K}_c$ (circles). The solid and dashed lines represent the calculated SC diamagnetic shielding effects $\mathrm{\Delta }{K}_{\mathrm{dia},b}$ and $\mathrm{\Delta }{K}_{\mathrm{dia},c}$, respectively. The inset shows the $H$ dependence of the decrease in $K_{\mathrm{spin},i}$ ($\mathrm{\Delta }{K}_{\mathrm{spin},i}$) estimated by subtracting $\mathrm{\Delta }{K}_{\mathrm{dia},i}$ from $\mathrm{\Delta }{K}_i$.