Study of Superconducting Hg by Nuclear Magnetic Resonance Techniques

Abstract

Since nuclear magnetic resonance techniques can provide rather microscopic information about conduction electrons in metals, their application to the study of superconducting metals is of considerable interest. The difficulties associated with the failure of magnetic fields to penetrate inside superconductors can be overcome by the use of dense colloids consisting of particles mostly less than 500 A in diameter. The preparation and characteristics of such Hg colloids are described and some comments are made about the experimental equipment. Experiments show that the superconducting particles give rise to a resonance line with a Knight shift less than that of the line in the normal metal. Considerations affecting the analysis of the data are discussed at some length. Calculations are given for the resonance line shape due to a single spherical superconducting particle and also for that expected from a distribution of such particles of different sizes. A criterion is developed for determining the Knight shift from the observed superconducting line. Corrections for the microscopic broadening of the resonance line and for the bulk diamagnetism of the sample are derived. It is pointed out that the bulk magnetization curve of the superconducting colloid can also readily be measured by means of the nuclear resonance equipment. In measurements ranging from 750 to 2300 gauss the Knight shift $K_s$ in the superconductor at 1.20°K is found to be 1.6%, or about $\frac{2}{3}$ of its value in the normal metal. Experiments designed to elucidate the temperature dependence of the Knight shift $K_s$ are also discussed. Some general quasi-thermodynamic comments are made to relate the Knight shift to some properties of the electron interaction energy responsible for superconductivity. Remarks based on the two-fluid model lead to some speculative predictions concerning the temperature dependence of $K_s$ which seem to be in at least qualitative agreement with the temperature dependence suggested by experiment. The need and interest of some further experiments is pointed out.