Knight Shifts and Linewidths of thePb207Nuclear Magnetic Resonance in Lead-Indium Alloys

Abstract

The nuclear magnetic resonance of ${\mathrm{Pb}}^{207}$ was observed and accurately measured at room temperature and 77°K, in pure lead metal powder and in a series of lead-indium alloy powders containing up to 75% indium. Upon the addition of indium, the central frequency of the ${\mathrm{Pb}}^{207}$ absorption line increases by a small fraction of the linewidth. At 5 Mc/sec, this frequency shift between pure lead and 20 at.% In is 800 cps, compared to a linewidth of 14 kc/sec in the 20 at.% In sample. The increase in frequency is also a small fraction of the Knight shift, $\frac{\Delta k}{k}=1.1\%$ up to 20 at.% In. In the cubic lead phase, the frequency shift is linear with composition. Volume effects which may be of sufficient magnitude to cause appreciable frequency shifts preclude the possibility of a definite conclusion regarding charge oscillations of the type discussed by Friedel and others. From the temperature dependence of the linewidth, the spin-lattice relaxation time is found to be $T_1=3.6\mathrm{}\times {10}^{-4\mathrm{}}$ sec at 77°K. The linear field dependence of the linewidth in the alloys is primarily attributed to anisotropic Knight-shift broadening, although isotropic Knight-shift broadening is not excluded. Upon alloying, the low-field absorption linewidth increases rapidly due to a combination of indirect spin exchange and pseudodipolar coupling, and the line shape changes from Lorentzian toward Gaussian. A second moment analysis yields a value for the near-neighbor exchange constant $h^{-1\mathrm{}}\left|A_{\mathrm{P}\mathrm{b}-\mathrm{I}\mathrm{n}}\right|=0.9\mathrm{}$ kc/sec. The pseudodipolar exchange constant is found to be $h^{-1\mathrm{}}\left|B_{\mathrm{P}\mathrm{b}-\mathrm{I}\mathrm{n}}\right|=1.0\mathrm{}$ kc/sec. Large values for the ratio $\frac{B_{\mathrm{P}\mathrm{b}-\mathrm{I}\mathrm{n}}}{A_{\mathrm{P}\mathrm{b}-\mathrm{I}\mathrm{n}}}$ and the ratio of pseudodipolar to classical dipolar indicate that the amount of $p$ character probably greatly exceeds the amount of $s$ character in the electron wave functions at the Fermi surface in this alloy and is consistent with the observation of anisotropic Knight-shift broadening.