Nuclear Quadrupole Resonance in Superconducting Gallium

Abstract

The nuclear quadrupole resonance (NQR) of ${\mathrm{Ga}}^{69}$ is investigated between 0.8 and 4.2°K. (The super-conducting critical temperature is 1.084°K.) Progressive saturation of the resonance is produced at increasing rf power levels of a frequency-modulated marginal oscillator. The nuclear spin-lattice relaxation rate $\frac{1}{T_1}$ (${\sec }^{-1\mathrm{}}$) is approximately $\frac{1}{2}T$ (°K) in the normal state. The contact part of the hyperfine interaction appears to be predominant in producing relaxation. Although the saturation method does not permit a precise determination of the constant of proportionality, the comparison of normal and superconducting relaxation rates is considerably more reliable. The rf fields are assumed to obey the London law of penetration, and an average rf field is determined in the superconductor. The relaxation rate shows a maximum enhancement by a factor 1.8 at approximately 0.95 $T_c$, a result which agrees with that obtained by Slichter and Hebel, and Redfield for the nuclear magnetic resonance of aluminum, and which serves as an additional experimental justification for certain features of the Bardeen-Cooper-Schrieffer theory of superconductivity. Unsaturated signal intensities in normal and superconducting states furnish a basis for estimating the penetration depth in superconducting metal spheres: $\lambda \mathrm{}\left(0\right)=1200\mathrm{}$ A for an average particle diameter of 2.7 μ. The NQR frequency of Ga in the superconductor shifts by (+)5×${10}^{-5\mathrm{}}$ of the normal frequency [the corresponding result for indium is found to be approximately (-)${10}^{-2\mathrm{}}$. This means that the contribution of the conduction electrons to the average nuclear quadrupole coupling is modified by the rearrangement of the conduction band in the superconductor. It is demonstrated that, if the quadrupole term in the hyperfine interaction were to predominate, the spin relaxation rate in the superconductor would have a temperature dependence like that of the ultrasonic attenuation.