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

TL;DR

The study uses $^{125}$Te Knight-shift and ac-susceptibility measurements on high-quality UTe$_2$ to probe spin susceptibility in the superconducting state under strong fields along $H \parallel c$ and $H \parallel b$. It finds that the spin component of the Knight shift along $c$ rapidly recovers to near normal-state values by ~5 T, implying spin alignment of triplet pairs and supporting spin-triplet pairing with a multicomponent $\bm{d}$-vector; along $b$, the spin response remains reduced up to high fields and a field-induced crossover coincides with a multi-phase SC region (LFSC/IFSC/HFSC), indicating anisotropic spin pinning and a strong link between spin configuration and $H_{c2}$. The results argue against spin-singlet scenarios and for spin-triplet superconductivity with axis-dependent $\bm{d}$-vector components, drawing parallels to superfluid $^3$He and highlighting the role of magnetic fluctuations in stabilizing high-field SC states. Together, these findings provide robust evidence for spin-triplet superconductivity in UTe$_2$ and reveal a nuanced relationship between triplet-spin orientation and upper critical fields, with potential implications for unconventional pairing mechanisms in correlated electron systems.

Abstract

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.

Figures (8)

• Figure 1: (Color online) a Te(II) and Te(I) NMR spectra measured under various $H$ at 70 mK and the normal state are shown against $K$. To determine the Te(II) and Te(I) peak positions, the double-peak spectrum was fitted with the two Lorentian functions and $K_{c,{\rm II}}$ (purple peak) and $K_{c,{\rm I}}$ (green peak) were evaluated. Full Width at Half Maximum (FWHM) of the Te(II) peak estimated with the fitting is shown. b Temperature dependence of the Knight shift measured at the Te(II)-NMR peak $K_{c,{\rm II}}$ under various magnetic fields in $H \parallel c$. The arrows shows the SC transition temperature under $H$, $T_c$($H$). c$H$ dependence of $K_{c,{\rm II}}$ measured at 70 mK and 2 K. The open circles indicates $K_{c}^{\rm dia}$ corrected $K_{c,{\rm II}}$ at 70 mK. The dotted curve shows the eye-guide of the $H$ dependence of $K_{c,{\rm II}}$ at 2 K. The SC upper-critical field $H_{\rm c2}$ is shown by arrow. The characteristic field $H^*$ determined in Fig. \ref{['f3']} is shown. d$H$ dependence of the difference between $K_{c,{\rm II}}$ and $K_{c,{\rm I}}$ measured at $T \sim 70$ mK and normal state in $H \parallel c$. The dotted line shows the average of $K_{c,{\rm II}} - K_{c,{\rm I}}$ measured at 2 K.
• Figure 2: (Color online) a Temperature dependence of the SC upper critical field in $H \parallel c$, $H_{c2}^{H \parallel c}$ is plotted to the left axis. In the figure, $\Delta \chi_{\rm ac}$ corresponding to the Meissner signals measured at various fields are also shown. The magnetic field, where the $T$ dependence of $H_{c2}$ is changed, is denoted as $H^*$. The kink becomes clearer when two lines are drawn. The slope change around 13 T is a conventional suppression of superconductivity near $H_{\rm c2}$ seen in the WHH modelWHH, thus the high-field region is not included in the linear fitting. b the relationship between the Knight shift and $H_{c2}$ along the $c$ axis. The temperature dependence of $\mu_0H_{c2}(T)$ is overlaid on a color contour map of the $K_c(H,T)$ in the $\mu_0H$–$T$ plane.
• Figure 3: (Color online) Te(II) NMR spectra measured under various $H$ in the SC state (0.07 K or 0.5 K) and the normal state (2.0 or 1.5 K). The NMR spectra above 15 T were measured at the High-Field Laboratory for Superconducting Materials at the Institute for Materials Research at Tohoku University.
• Figure 4: (Color online) a Temperature dependence of the Knight shift measured at the Te(II)-NMR peak under various fields in $H \parallel b$, $K_{b,{\rm II}}$. The arrows indicates $T_c(H)$ determined from the $\Delta \chi_{\rm ac}$ measurements. The dotted curve shows the fitting of the temperature dependence of $K_{b,{\rm II}}$ in the normal-state data at 15.3 T with the quartic function, which is extrapolate to $T = 0$ so as to estimate the $K_{b,{\rm II}}$ decrease in the SC state. b Field dependence of $K_{b,{\rm II}}$ measured at 0.5 K and 2 K. The horizontal dotted line shows the value of the normal-state $K_{b,{\rm II}}$ in low-$H$ region, where $K_{b,{\rm II}}$ is almost constant with $H$. The magnetic field of $\mu_0H_{\chi}$ determined in Fig. \ref{['f5']}b is shown by an arrow. The inset shows the decrease in $K_{b,{\rm II}}$ ascribed to the SC transition $\Delta K_{b,{\rm II}}$. The open circles indicates $K_{b}^{\rm dia}$ corrected $K_{b,{\rm II}}$, which corresponds to the decrease in the spin-part Knight shift in the SC state at 0.5 K.
• Figure 5: (Color online) a Temperature dependence of $\Delta \chi_{\rm ac}$ corresponding to the Meissner signals measured at various $H$ is shown. Arrows show $T_c(H)$ determined with $T$ dependence of $\Delta \chi_{\rm ac}$. The low-$T$ arrow in 17.4 T shows the kink in $\Delta \chi_{\rm ac}$ corresponding to the boundary between HFSC and LFSC. The results above 16 T was obtained at the High-Field Laboratory for Superconducting Materials at the Institute for Materials Research at Tohoku University. b$H$ dependence of $\Delta \chi_{\rm ac}$ measured at 0.6, 0.3, and 0.055 K. The arrows show the change in the $H$ dependence of $\Delta \chi_{\rm ac}$. c$H$-$T$ phase diagram of UTe$_2$ determined by $\Delta \chi_{\rm ac}$ measurements. The previous results obtained on the same-quality UTe$_2$ with the resistivity and $\Delta \chi_{\rm ac}$ measurements are also plottedSakaiPRL2023. LFSC, IFSC, and HFSC indicate the low-field, intermediate-field and high-field superconducting state, respectively.