NMR lineshape in Metallic Nanoparticles: a Matrix Continued Fraction evaluation

TL;DR

This paper models the NMR lineshape in metallic nanoparticles by analyzing local density of states fluctuations using a matrix continued fraction approach, revealing size and temperature effects on line broadening and shifts.

Contribution

It introduces a novel application of matrix continued fractions to evaluate NMR lineshapes in metallic nanoparticles considering surface states and universal scaling behaviors.

Findings

Line broadening becomes asymmetric with decreasing particle size.

Line shift decreases as particle size or temperature diminishes.

Surface states influence lineshape in very small particles.

Abstract

In metallic nanoparticles, the different electronic environment seen by each magnetic nucleus produces a distribution of Knight shifts of the NMR frequencies which is observed as an inhomogeneously broadened lineshape. We study the fluctuations in the local density of states for s electrons at the Fermi energy in a simple LCAO model. We resort to a Matrix Continued Fractions calculation of the Green's functions. Results show that line broadens asymmetrically and its shift decreases as the particle size or the temperature diminish satisfying a universal scaling function. However, for very small particles, surface states become relevant to determine a lineshape that departs from the universal scaling behavior. These trends are consistent with the observed tendencies in Cu and Pt particles.