Orbital magnetism in ensembles of gold nanoparticles

TL;DR

This paper investigates the orbital magnetic response of gold nanoparticles, showing that ensembles exhibit paramagnetism with size distribution influencing the magnetic behavior, aligning with experimental observations.

Contribution

It provides a theoretical analysis of orbital magnetism in gold nanoparticle ensembles, explaining the observed paramagnetic responses and the influence of size distribution.

Findings

Individual nanoparticles can have large diamagnetic or paramagnetic orbital responses.

Ensembles with smooth size distributions are always paramagnetic at low fields.

The susceptibility follows a Curie-like law for small sizes or low temperatures.

Abstract

The last two decades have witnessed various experiments reporting very unusual magnetic properties of ensembles of gold nanoparticles surrounded by organic ligands, including ferromagnetic, paramagnetic, or (large) diamagnetic responses. These behaviors are at odds with the small diamagnetic response of macroscopic gold samples. Here we theoretically investigate the possibility that the observed unusual magnetism in capped gold nanoparticles is of orbital origin. Employing semiclassical techniques, we calculate the orbital component to the zero-field susceptibility of individual as well as ensembles of metallic nanoparticles. While the result for the orbital response of individual nanoparticles can exceed by orders of magnitude the bulk Landau susceptibility in absolute value, and can be either diamagnetic or paramagnetic depending on nanoparticle size, we show that the magnetic susceptibility of a noninteracting ensemble of nanoparticles with a smooth size distribution is always paramagnetic at low magnetic fields. In particular, we predict that the zero-field susceptibility follows a Curie-type law for small nanoparticle sizes and/or low temperatures. The calculated field-dependent magnetization of an ensemble of diluted nanoparticles is shown to be in good agreement with existing experiments that yielded a large paramagnetic response. The width of the size distribution of the nanoparticles is identified as a key element for the quantitative determination of the orbital response.