Spin-triplet superconductivity in the paramagnetic UCoGe under pressure studied by ${}^{59}\mathrm{Co}$ NMR

A ${}^{59}\mathrm{Co}$ nuclear magnetic resonance (NMR) measurement was performed on the single-crystalline ferromagnetic (FM) superconductor UCoGe under a pressure of 1.09 GPa, where the FM state is suppressed and superconductivity occurs in the paramagnetic (PM) state, to study the superconducting (SC) state in the PM state. ${}^{59}\mathrm{Co}$-NMR spectra became broader but hardly shifted across the SC transition temperature. The Knight-shift change determined from fitting the spectral peak with a Gaussian was much smaller than the spin part of the Knight shift; this is in good agreement with the spin-triplet pairing suggested from the large upper critical field. The spectrum broadening in the SC state cannot be attributed to the SC diamagnetic effect but is related to the properties of spin-triplet superconductivity. The origins of the broadening are discussed herein.

Figure 1

Temperature dependence of ac susceptibilities $\delta {\chi }_{\text{ac}}$ of UCoGe at some magnetic fields perpendicular to the $c$ axis as measured using an NMR coil on cooling. Superconducting transition is detected in all fields. The frequencies are 8–9 MHz. Inset: field-angle dependence of $\delta {\chi }_{\text{ac}}$ at 3 T and 0.11 K.

Figure 2

(a) The schematic image of the static field $H$, NMR rf field $H_1$, and the sample directions. (b) The field-angle direction. The magnetic field is not perpendicular to the $c$ axis in most directions and is perpendicular to the $c$ axis only at a point. (c) The field slightly tilted toward the $c$ axis.

Figure 3

Field-swept ${}^{59}\mathrm{Co}$ NMR spectra with the field perpendicular to the $c$ axis at 0.8 K (normal state). The vertical red line is the best fit of the spectra with ${\varphi }_{ba}={40}^{\circ }$ by numerical diagonalization of the nuclear Hamiltonian. The vertical black arrow indicates the “central” $\left(1/2\leftrightarrow -1/2\right)$ peak, at which the Knight shift was measured. This peak is not located at the center of the seven splitting lines owing to the low-symmetric field direction.

Figure 4

${}^{59}\mathrm{Co}$ NMR spectra with field perpendicular to the $c$ axis. The solid black lines indicate the fitted result obtained using a Gaussian and represent the fitting range. The range was shifted lower to avoid the effect of the first satellite peak at higher frequency near the central peak. The red (blue) lines represent the result of the normal (SC) state. The spectra were also fitted with two-component Gaussians at 2.06 T in the SC state, and each part is shown for 0.15 K with green lines (see the Appendix for details).

Figure 5

Temperature dependence of the ${}^{59}\mathrm{Co}$ NMR Knight shift of UCoGe with the field 40° away from the $b$ axis to the $a$ axis at the central $\left(1/2\leftrightarrow -1/2\right)$ line. The errors are estimated from the 90% (80% for the SC state at 2.06 T) width of the spectra. The open black squares indicate the result of the two-component fitting in the SC state (see text for details). Inset: ${}^{59}\mathrm{Co}$-NMR spectra at the central line at 2.84 T. Another peak at around 29 MHz originates from the first satellite owing to quadrupole splitting.

Figure 6

Temperature dependence of the full width at half maximum (FWHM) of ${}^{59}\mathrm{Co}$ NMR spectra at the central line represented in terms of the Knight-shift distribution. The ac susceptibilities are shown for comparison.

Figure 7

${}^{59}\mathrm{Co}$ NMR spectra with 2.00-T field tilted to the $c$ axis by $\delta {\theta }_c\sim 5^{\circ }$ at 20.5 MHz. (a) The spectra in the normal state (0.80 and 0.40 K). No large shifts are observed in the normal state at these temperatures. (b) The spectra in the normal and SC states (0.80 and 0.15 K). The NMR spectrum slightly shifts to higher frequency in the SC state. The solid curves indicate results fitted with a Gaussian.

Figure 8

Field-swept ${}^{59}\mathrm{Co}$ NMR spectra with the field perpendicular to the $a$ axis at 0.8 K (normal state). The vertical solid red lines indicate the best fit of the spectra with $\delta {\theta }_c={11}^{\circ }$. The dashed blue lines indicate the calculated result with $H\parallel b$.

Figure 9

${}^{59}\mathrm{Co}$ NMR spectra with the field perpendicular to the $c$ axis, analyzed by two Gaussians in the SC state. The experimental data are the same as the ones shown in Fig. 4. The solid black lines indicate the best fit with the Gaussian(s). The solid gray lines indicate the partial components of two-component fitting.

Figure 10

Field-swept ${}^{59}\mathrm{Co}$ NMR spectra at 0 GPa at 20 K at the PM state before (gray) and after (red) applying pressure. The vertical blue line is the best fit of the spectra with ${\varphi }_{ba}={51}^{\circ }$.

Figure 11

${}^{59}\mathrm{Co}$ NQR spectra without field at 0 GPa at 4.2 K (the PM state) before (gray circles) and after (red line) applying pressure.