Anomalous magnetic fluctuations in superconducting ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ revealed by ${}^{101}\mathrm{Ru}$ nuclear spin-spin relaxation

We carried out ${}^{101}\mathrm{Ru}$ nuclear quadrupole resonance (NQR) measurement on superconducting (SC) ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ under zero magnetic field $(H=0)$ and found that the nuclear spin-spin relaxation rate $1/T_2$ is enhanced in the SC state. The $1/T_2$ measurement in the SC state under $H=0$ is effective for detecting slow magnetic fluctuations parallel to the quantized axis of the nuclear spin. Our results indicate that low-energy magnetic fluctuations perpendicular to the ${\mathrm{RuO}}_2$ plane emerge when the superconductivity sets in, which is consistent with the previous ${}^{17}\mathrm{O}\text{-NQR}$ result that the nuclear spin-lattice relaxation rate $1/T_1$ of the in-plane O site exhibits anomalous behavior in the SC state. The enhancement of the magnetic fluctuations in the SC state is unusual and suggests that the fluctuations are related to the unconventional SC pairing. We suggest that this phenomenon is a consequence of the spin degrees of freedom of the spin-triplet pairing.

Figure 1

(a) The ac susceptibility under zero magnetic field obtained by an NMR coil. The upper (lower) curve indicates the sample 1 (2) result. The arrows indicate the SC transition temperatures $T_c$. The frequency is typically $f\sim 7$–10 MHz. (b) Enlarged view around $T_c$.

Figure 2

Nuclear spin-lattice relation rate $1/T_1$ divided by temperature of samples 1 (circles) and 2 (triangles) near $T_c$. The data for sample 1 are from Ref. [4].

Figure 3

${}^{101}\mathrm{Ru}\text{-NQR}$ spectra of ${\text{Sr}}_{\text{2}}{\text{RuO}}_{\text{4}}$. (a) The $\pm 1/2\leftrightarrow \pm 3/2$ lines (sample 2) and (b) the $\pm 3/2\leftrightarrow \pm 5/2$ lines (samples 1 and 2) are shown for both above and below $T_c$. In (a), a sharper $\pm 7/2\leftrightarrow \pm 9/2$ line of ${}^{87}\mathrm{Sr}$ arises at $f=3.288$ MHz, which happens to be close to the ${}^{101}\mathrm{Ru}\pm 1/2\leftrightarrow \pm 3/2$ line at $f=3.28$ MHz. Each component of the signal is indicated with a dotted line, obtained from two-component Lorentzian fitting.

Figure 4

Nuclear spin-spin relaxation rate $1/T_2$ of ${}^{101}\mathrm{Ru}$ in ${\text{Sr}}_{\text{2}}{\text{RuO}}_{\text{4}}$ at the $\pm 3/2\leftrightarrow \pm 5/2$ line under $H=0$. The circle and triangle symbols represent sample 1 and 2, respectively. The above square symbol represents the $1/T_2$ result of the field-induced normal state at ${\mu }_{0}H=3$ T parallel to the $c$ axis, obtained at the ${}^{99}\mathrm{Ru}1/2\leftrightarrow -1/2$ line (sample 1). The result of ${}^{101}\mathrm{Ru}\text{-NQR} 1/T_2$ in Ru metal is also shown. The dotted line for Ru metal indicates the extrapolation of the high-temperature data (see Fig. 6).

Figure 5

Spin-echo decay curves of ${}^{101}\mathrm{Ru}\pm 3/2\leftrightarrow \pm 5/2$ signals (a) at 1.00 K (open circle) and 1.63 K (closed circle) for sample 1, and (b) at 0.40 K (open) and 1.68 K (closed) for sample 2. All the data were measured using a dilution refrigerator. The exponential functions shown as solid lines are the fitting results, in the whole range in sample 1 and in $2\tau \le 1.5$ ms for sample 2.

Figure 6

Temperature dependence of $1/T_1$ (open circle, right axis) and $1/T_2$ (closed square, left axis) of hcp Ru metal. The dotted lines represent the linear fitting. Both the data were obtained with ${}^{101}\mathrm{Ru}\text{-NQR} \pm 3/2\leftrightarrow \pm 5/2$ transition line at $f=3.48$ MHz. The value of $1/T_1$ is in good agreement with previous reports by NMR [23, 24].