Low-field cross spin relaxation of ${}^8\text{L}\text{i}$ in superconducting ${\text{NbSe}}_2$

A low energy beam of spin polarized ${}^8\text{L}\text{i}$ has been used to investigate nuclear spin relaxation in the multiband superconductor ${\text{NbSe}}_2$. In low magnetic fields there is significant cross relaxation between the ${}^8\text{L}\text{i}$ and the host ${}^{93}\text{N}\text{b}$ spins, which is driven by low frequency fluctuations in the nuclear magnetic dipolar interaction. The rate of cross relaxation is strongly field dependent and thus the $1/T_1$ spin relaxation rate of the ${}^8\text{L}\text{i}$ is a sensitive monitor of the static local magnetic field $B$ just below the surface. This in turn is used to determine the absolute value of the magnetic penetration depth $\lambda$ in the Meissner state. The temperature variations in $1/T_1$ and $\lambda$ are consistent with a wide distribution of superconducting gaps expected for a multiband superconductor.

Figure 1

Experimental setup used to measure the spin relaxation rate of ${}^8\text{L}\text{i}$ in low magnetic fields. The initial polarization and small external magnetic field are in the $\widehat{y}$ direction. The cryostat is held from above on a high voltage platform which will be used in the future to control the mean depth of implantation.

Figure 2

(Color online) The nuclear resonance spectrum of ${}^8\text{L}\text{i}$ in the normal state of ${\text{NbSe}}_2$ in a high magnetic field of 30 kG. The linewidth is attributed to magnetic dipolar broadening from host ${}^{93}\text{N}\text{b}$ nuclear moments. Note that there is no evidence for any quadrupolar splitting (see Ref. 19 for more details).

Figure 3

(Color online) The time dependence of the nuclear polarization of ${}^8\text{L}\text{i}$ in the normal state of ${\text{NbSe}}_2$ at 8K at various magnetic fields. The fitted curves are generated by assuming a single exponential spin relaxation rate as explained in the text.

Figure 4

The $1/T_1$ spin relaxation rate of ${}^8\text{L}\text{i}$ as a function of magnetic field at 8 K. The curve is a fit to a simple Lorentzian corresponding to an exponential time correlation function for the nuclear dipolar fields from the host Nb nuclear spins.

Figure 5

(Color online) Low-field nuclear spin relaxation of ${}^8\text{L}\text{i}$ in ${\text{NbSe}}_2$ above and below $T_c=7.0\text{K}$. A magnetic field of 30 G, which is much less than $H_{c1}$ (Ref. 22), is applied parallel to the surface after zero-field cooling. Note the sharp increase in the relaxation rate below the transition temperature. This is attributed to the Meissner screening of the external field. The size of the increase is a direct measure of the London penetration depth near the surface.

Figure 6

(Color online) The temperature dependence of the $1/T_1$ of ${}^8\text{L}\text{i}$ in ${\text{NbSe}}_2$ with a small external magnetic field of 30 G applied parallel to the surface (open circles) and with a 100 G applied perpendicular to the surface (filled diamonds). The fitted curve through the vortex state data (filled diamonds) is based on the Hebel-Slichter theory assuming a multigap model as described in the text. The curve through the Meissner state data (open circles) is also derived from this model, taking into account the reduction in magnetic field from Meissner screening, using the temperature dependent London penetration depth given in Fig. 8.

Figure 7

The depth dependence of the magnetic field $B\left(x\right)$, the stopping density $\rho \left(x\right)$, and the spin relaxation rate $1/T_1\left(x\right)$.

Figure 8

(Color online) (a) The magnetic penetration depth ${\lambda }_{ab}$ in the Meissner state of ${\text{NbSe}}_2$ as a function of temperature. The solid lines are a fit to the multigap model, whereas the dashed line is a fit to the single gap model given by Eq. (4). (b) The inverse square of the penetration depth versus temperature normalized the value at $T=0$.