Measurement of the ${}^{101}\mathrm{R}\mathrm{u}$-Knight Shift of Superconducting ${\mathrm{S}\mathrm{r}}_2{\mathrm{R}\mathrm{u}\mathrm{O}}_4$ in a Parallel Magnetic Field

${}^{101}\mathrm{R}\mathrm{u}$-Knight shift (${}^{101}K$) in the spin-triplet superconductor ${\mathrm{S}\mathrm{r}}_2{\mathrm{R}\mathrm{u}\mathrm{O}}_4$ was measured under magnetic fields parallel to the $c$ axis (perpendicular to the ${\mathrm{R}\mathrm{u}\mathrm{O}}_2$ plane), which is the promising superconducting (SC) $\mathit{d}$-vector direction in a zero field. We succeeded in measuring $K_c$ in the field range from 200 to 1200 Oe and at temperatures down to 80 mK, using nuclear-quadrupole-resonance spectra. We found that ${}^{101}K_c$ is invariant with respect to the field and temperature on passing through $H_{c2}$ and $T_c$ above 200 Oe. This indicates that the spin susceptibility along the $c$ axis does not change in the SC state, at least, in the field greater than 200 Oe. The results imply that the SC $\mathit{d}$ vector is in the ${\mathrm{R}\mathrm{u}\mathrm{O}}_2$ plane when the magnetic field is applied to the $c$ axis.

Figure 1

(a) ${}^{101}\mathrm{R}\mathrm{u}$-NQR spectrum arising from the $I_z=\pm 1/2\leftrightarrow \pm 3/2$ transition and ${}^{87}\mathrm{S}\mathrm{r}$-NQR spectrum arising from the $I_z=\pm 7/2\leftrightarrow \pm 9/2$ transition under zero field (upper) and magnetic field along the $c$ axis (bottom) at 80 mK. (b) NQR-transition levels under zero field, and a small magnetic field which is treated as a perturbative interaction. For the level scheme on the right, the relevant level splitting is magnified by a factor of 10.

Figure 2

(a) Temperature dependence of ${\chi }_{\mathrm{a}\mathrm{c}}$ at 3.3 MHz in various fields along with the $c$ axis. (b) Temperature dependence of $H_{c2}$ obtained by the present measurements along with previous results by the specific-heat measurement [20]. The arrows show the Knight-shift scans in the present measurements.

Figure 3

(a) Field dependence of ${}^{101}K_c$ at 90 mK. (b) Temperature dependence of ${}^{101}K_c$ at 440 Oe. The solid curve in (a) is the conceivable field dependence of ${}^{101}K_c$ deduced from that of $C/T$ at 90 mK, and the curve in (b) is the Yosida function, both of which are expected when the SC $\mathit{d}$ vector is locked in the $c$ axis.

Figure 4

Sketches of Cooper pair $\mathit{S}$ and $\mathit{L}$ vectors for two variant $A$ states, as well as $A_1$ and $A_2$ states, in the magnetic field. The small arrows denote the spins $\mathit{S}$ and the large arrows denote the orbital moment $\mathit{L}$ (see text).