Nuclear magnetic resonance in small superconducting particles. I

Abstract

A theoretical treatment of the effects of superconducting fluctuations on nuclear spin-lattice relaxation in small particles given by šimánek, Imbro, and MacLaughlin is refined, taking into account the Zeeman energy and the pairbreaking effect introduced by a magnetic field dependence of impurity vertex corrections. The dimensions of the particle are supposed to be less than the coherence length and the penetration depth, but still large enough for electronic levels to have a continuous spectrum. In this paper, spin-orbit interactions are not considered, though they have a large effect on the role of the Zeeman energy. Calculations are valid in the dirty limit and at temperatures not necessarily close to the transition temperature of the bulk superconductor. The spin susceptibility and the nuclear spin-lattice relaxation time are calculated as functions of the particle size and the field. The former turns out to be in good agreement with the theoretical results by Mühlschlegel, Scalapino, and Denton, in which energy levels are considered to be discrete. It is shown that the Zeeman energy and the pair-breaking mechanism give opposite effects on the behavior of the relaxation time at low temperatures. Recent experiments have found a characteristic field dependence of the relaxation time, which is reproduced fairly well by the present calculations.