# Universal Hall coefficient correction in strongly coupled Cr-SiO$_2$ nanogranular metals

## TL;DR

This study investigates the electrical transport and microstructure of Cr-SiO$_2$ nanogranular films, revealing a universal correction to the Hall coefficient explained by recent granular metal theory, with specific temperature-dependent behaviors.

## Contribution

It demonstrates a universal Hall coefficient correction in strongly coupled nanogranular metals, aligning experimental results with recent theoretical models and clarifying the temperature dependence of transport properties.

## Key findings

- Hall coefficient varies linearly with ln(T) above 60 K
- Hall coefficient saturates below 60 K
- Conductivity follows a √T law from 2 K to 50 K

## Abstract

The microstructure and electrical transport of Cr$_x$(SiO$_2$)$_{1-x}$ nanogranular films with Cr volume faction $x$$\simeq$0.67 and 0.72 are systematically investigated. The transmission electron microscopy images and elemental mappings indicate that the films are quite inhomogeneous: some Cr granules directly connect to others while some Cr granules with size $\sim$1 to $\sim$3\,nm disperse in the SiO$_2$ dielectric matrix. For each film, the Hall coefficient $R_H$ varies linearly with the natural logarithm of temperature, i.e., $\Delta R_H$$\propto$$\ln T$, above $\sim$60\,K, saturates at $\sim$60\,K, and retains the saturating value below $\sim$60\,K. The temperature dependence of Hall coefficient can be explained by the recent theory in granular metals and originates from \emph{virtual diffusion} of electrons through the metallic granules. For the conductivity $\sigma$, a robust $\Delta \sigma$$\propto$$\sqrt{T}$ law is observed from $\sim$50 down to 2\,K. The behavior of the conductivity stems from the ``Altshuler-Aronov" correction, whose influence on the Hall coefficient is not present in the films.