Unifying principle for Hall coefficient in systems near magnetic instability

TL;DR

This paper proposes a unifying principle explaining the temperature dependence of the Hall coefficient near magnetic instabilities, attributing it to a progressive loss of carriers due to growing magnetic correlations, supported by quantitative analysis.

Contribution

It introduces a unifying principle for the Hall coefficient behavior near magnetic instabilities and demonstrates its validity across various materials using the GTTA model.

Findings

Hall coefficient increases as temperature decreases near magnetic instability.

The unifying principle explains the reduction of carrier density with temperature.

A single relaxation time can describe Hall angle data when considering temperature-dependent carrier density.

Abstract

Typically, Hall coefficient of materials near magnetic instabilities exhibits pronounced temperature dependence. To explore the reasons involved, we studied the temperature dependence of Hall coefficient in $Cr_{1-x}V_x$, $V_{2-y}O_3$ and some high-$T_c$ superconducting cuprates. We argue that it can be rationalized using the following unifying principle:\textit{ When a system is near a magnetic instability and temperature is reduced towards the instability, there is a progressive "loss" of carriers (progressive "tying down" of electrons) as they participate in long-lived and long-ranged magnetic correlations.} In other words, magnetic correlations grow in space and are longer-lived as temperature is reduced towards the magnetic instability. This is the mechanism behind reduced carrier density with reducing temperature and leads to an enhancement of the Hall coefficient. This unifying principle is implemented and quantitative analysis is done using the Gor'kov Teitel'baum Thermal Activation (GTTA) model. We also show that the Hall angle data can be understood using one relaxation time (in contrast to the "two-relaxation" times idea of Anderson) by taking into consideration of temperature dependence of carrier density. This unifying principle is shown to be working in above studied systems, but authors believe that it is of much more general validity.