Superconductivity Induced by Longitudinal Ferromagnetic Fluctuations in UCoGe

From detailed angle-resolved NMR and Meissner measurements on a ferromagnetic (FM) superconductor UCoGe ($T_{\mathrm{Curie}}\sim 2.5\mathrm{K}$ and $T_{\mathrm{SC}}\sim 0.6\mathrm{K}$), we show that superconductivity in UCoGe is tightly coupled with longitudinal FM spin fluctuations along the $c$ axis. We found that magnetic fields along the $c$ axis ($H\parallel c$) strongly suppress the FM fluctuations and that the superconductivity is observed in the limited magnetic-field region where the longitudinal FM spin fluctuations are active. These results, combined with model calculations, strongly suggest that the longitudinal FM spin fluctuations tuned by $H\parallel c$ induce the unique spin-triplet superconductivity in UCoGe. This is the first clear example that FM fluctuations are intimately related with superconductivity.

Figure 1

Temperature dependence of resistivity along each axis in the single-crystal UCoGe. The inset shows the plot of the resistivity against $T^2$ below 2 K.

Figure 2

(a) Temperature dependence of $1/T_1$ measured in fields along the three crystal axes under $\sim 2\mathrm{T}$ and tilted by 3 degrees from the $b$ axis. The broad peak in $1/T_1$, ascribed to the FM anomaly, is strongly suppressed when the magnetic field is tilted by 3 degrees. (b) Angle dependence of $1/T_1$ in the $bc$ plane at 20, 4.2, and 1.7 K under $\sim 2\mathrm{T}$. The angle dependence at 20 K can be consistently explained by Eq. (2), while these at 4.2 and 1.7 K cannot, indicative of the strong suppression of $1/T_1$ by $H^c$.

Figure 3

Angle dependence of $1/T_1$ in the $bc$ plane measured in three different magnetic fields at 1.7 K. (b) Plot of the $1/T_1$ against $H^c$. The $1/T_1$ data collapse onto a single curve when plotted against $H^c$. (c) $H^c$ dependence of magnetic fluctuations along the $c$ axis $⟨(\delta H^c{)}^2⟩$ at 1.7 K, extracted using Eq. (3). $H_{c2}$ data are plotted against $H^c=H_{c2}\sin \theta$. Inset: plot of $⟨(\delta H^c{)}^2⟩$ against $|H^c|$. The relation of $⟨(\delta H^c{)}^2⟩\propto 1/\sqrt{H^c}$ is shown by dashed lines in (c).

Figure 4

Angular dependence of $H_{c2}$ in the $ac$ plane, which is determined by the onset of the Meissner signal. $H_{c2}$ data reported by Aoki et al [9] are also plotted, which are determined by resistive measurements, and $H_{c2}$ above 16 T was estimated from the linear extrapolation. The red curve in the main panel is the calculation of the angle dependence of $H_{c2}$ based on the spin-triplet $A$ state by taking into account the field dependence of the Ising FM fluctuations shown in the inset of Fig. 3c. Inset: angular dependences of the Meissner signals measured in various magnetic fields. The arrows denote the onset angles, below which the Meissner signals come out.

Figure 5

Temperature dependence of $H_{c2}$ along the $a$ and $c$ axes calculated with the $A$ state with the parameters of $c=1$, 3, and 5.