# Diamagnetism of metallic nanoparticles as the result of strong spin-orbit interaction

## TL;DR

This paper explains how strong spin-orbit interaction causes metallic nanoparticles to transition from paramagnetic to diamagnetic behavior, supported by symmetry analysis and random matrix theory, aligning with experimental observations.

## Contribution

It introduces a theoretical framework using symmetry analysis and random matrix theory to quantify the diamagnetism in metallic nanoparticles due to spin-orbit interaction.

## Key findings

- Magnetic susceptibility shifts from paramagnetic to diamagnetic with increasing spin-orbit interaction.
- Analytical and numerical results match experimental data on gold nanorods.
- The study maps susceptibility changes as a function of symmetry-breaking parameters.

## Abstract

The magnetic susceptibility of an ensemble of clean metallic nanoparticles is shown to change from paramagnetic to diamagnetic one with the onset of spin-orbit interaction. The effect is quantified on the basis of symmetry analysis with the help of the random matrix theory. In particular, the magnetic susceptibility is investigated as the function of symmetry breaking parameter representing magnetic flux in the crossover from symplectic to unitary and from orthogonal to unitary ensembles. Corresponding analytical and numerical results provide a qualitative explanation to the experimental data on diamagnetism of an ensemble of gold nanorods.