Unifying principle for Hall coefficient in systems near magnetic instability

Typically, Hall coefficient of materials near magnetic instabilities exhibits pronounced temperature dependence. To explore the reasons involved, the temperature dependence of Hall coefficient in \({Cr}_{1-x}{V}_x\), \({V}_{2-y}{O}_3\) and some high-\(T_c\) superconducting cuprates is studied. We argue that it can be rationalized using the following unifying principle: 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. Our findings 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.