Two-carrier Magnetoresistance: Applications to Ca$_3$Ru$_2$O$_7$

TL;DR

This paper develops an analytical two-band conductivity model for magnetoresistance in Ca$_3$Ru$_2$O$_7$, revealing limitations of the model at intermediate temperatures and suggesting complex underlying electronic and magnetic interactions.

Contribution

It introduces a phase space formulation of the two-band model and applies it to Ca$_3$Ru$_2$O$_7$, extending previous low-temperature studies across a broad temperature range.

Findings

Negative magnetoresistance observed below 48 K.

Model fits low-temperature data but fails at intermediate temperatures.

Complex electronic and magnetic interactions are indicated at intermediate temperatures.

Abstract

Ambipolar transport is a commonly occurring theme in semimetals and semiconductors. Here we present an analytical formulation of the conductivity for a two-band system. Electron and hole carrier densities and their respective conductivities are mapped into a two-dimensional unit-less phase space. Provided that one of the carrier densities is known, the dimensionless phase space can be probed through magnetoresistance measurements. This formulation of the two-band model for conductivity is applied to magnetoresistance experiments on Ca$_3$Ru$_2$O$_7$. While previous such measurements focused on the low-temperature limit, we cover a broad temperature range and find negative magnetoresistance in an intermediate interval below the electronic transition at 48 K. The low-temperature magnetoresistance in Ca$_3$Ru$_2$O$_7$ is consistent with a two-band structure. However, the model fails to describe the full temperature and magnetic field dependence. Negative magnetoresistance found in an intermediate temperature range is, for example, not captured by this model. We thus conclude that the electronic and magnetic structure in this intermediate temperature range render the system beyond the most simple two-band model.