Quantum size effect in copper: NMR in small particles

Abstract

Nuclear-magnetic-resonance line shifts are measured for copper particles of diameters between 25 and 450 \AA{} at temperatures between 0.4 and 77 K in magnetic fields between 2 and 9 kG. At temperatures such that $kT$ is small compared to the average electronic level spacing, effects attributable to the predicted spin pairing in even particles and Curie-type paramagnetism in odd particles are observed for diameters of 100 \AA{} or less. Residual shifts, indicating imperfect spin pairing at $T=0$ in even particles, are attributable to spin-reversing scattering by spin-orbit coupling in analogy to superconducting small particles with comparable energy gaps. It is estimated that the conduction-electron spins in copper particles flip once per approximately 150 boundary scatterings. The spin-orbit coupling is thus relatively weak, which is consistent with the experimental dependence of spin pairing with temperature, indicating that the smallest copper particles are describable by Dyson's orthogonal case.